International Association for Cryptologic Research

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for Cryptologic Research

CryptoDB

Papers from EPRINT 2001

Year
Venue
Title
2001
EPRINT
Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack
A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first public-key encryption schemes in the literature that are simultaneously practical and provably secure.
2001
EPRINT
New Notions of Soundness and Simultaneous Resettability in the Public-Key Model
I n this paper, some new notions of soundness in public-key model are presented. We clarify the relationships among our new notions of soundness and the original 4 soundness notions presented by Micali and Reyzin. Our new soundness notions also characterize a new model for ZK protocols in public key model: weak soundness model. By ``weak? we mean for each common input x selected by a malicious prover on the fly, x is used by the malicious prover at most a-priori bounded polynomial times. The weak soundness model just lies in between BPK model and UPK model. Namely, it is weaker than BPK model but stronger than UPK model. In the weak soundness model (also in the UPK model, since weak soundness model implies UPK model), we get a 3-round black-box rZK arguments with weak resettable soundness for NP. Note that simultaneous resettability is an important open problem in the field of ZK protocols. And Reyzin has proven that there are no ZK protocols with resettable soundness in the BPK model. It means that to achieve simultaneous resettability one needs to augment the BPK model in a reasonable fashion. Although Barak et al. [BGGL01] have proven that any language which has a black-box ZK arguments with resettable soundness is in BPP. It is the weak soundness that makes us to get simultaneous resettability. More interestingly, our protocols work in a somewhat ``parallel repetition? manner to reduce the error probability and the verifier indeed has secret information with respect to historical transcripts. Note that in general the error probability of such protocols can not be reduced by parallel repetition. [BIN97] At last, we give a 3-round non-black-box rZK arguments system with resettable soundness for NP in the preprocessing model in which a trusted third party is assumed. Our construction for such protocol is quite simple. Note that although the preprocessing model is quite imposing but it is still quite reasonable as indicated in [CGGM00]. For example, in many e-commerce setting a trusted third party is often assumed. The critical tools used in this paper are: verifiable pseudorandom functions, zap and complexity leveraging. To our knowledge, our protocols are also the second application of verifiable pseudorandom functions. The first application is the 3-round rZK arguments with one-time soundness for NP in the public-key model as indicated by Micali and Reyzin [MR01a].
2001
EPRINT
RSA hybrid encryption schemes
This document compares the two published RSA-based hybrid encryption schemes having linear reduction in their security proof: RSA-KEM with DEM1 and RSA-REACT. While the performance of RSA-REACT is worse than the performance of RSA-KEM+DEM1, a complete proof of its security has already been published. This is indeed an advantage, because we show that the security result for RSA-KEM+DEM1 has a small hole. We provide here a complete proof of the security of RSA-KEM+DEM1. We also propose some changes to RSA-REACT to improve its efficiency without changing its security, and conclude that this new RSA-REACT is a generalisation of RSA-KEM+DEM1, with at most the same security, and with possibly worse performance. Therefore we show that RSA-KEM+DEM1 should be preferred to RSA-REACT.
2001
EPRINT
An Identity Based Authenticated Key Agreement Protocol Based on the Weil Pairing
We describe an ID based authenticated two pass key agreement protocol which makes use of the Weil pairing. The protocol is described and its properties are discussed including the ability to add key confirmation.
2001
EPRINT
A Proposal for an ISO Standard for Public Key Encryption
This document is an initial proposal for a draft for a forthcoming ISO standard on public-key encryption. It is hoped that this proposal will serve as a basis for discussion, from which a consensus for a standard may be formed.
2001
EPRINT
Efficient Revocation of Anonymous Group Membership
An accumulator scheme, introduced be Benaloh and de Mare and further studied by Bari{\'c} and Pfitzmann, is an algorithm that allows to hash a large set of inputs into one short value, called the \textit{accumulator}, such that there is a short witness that a given input was incorporated into the accumulator. We put forward the notion of \textit{dynamic accumulators}, i.e., a method that allows to dynamically add and delete inputs from the accumulator, such that the cost of an add or delete is independent on the number of accumulated values. We achieve this under the strong RSA assumption. For this construction, we also show an efficient zero-knowledge protocol for proving that a committed value is in the accumulator. In turn, our construction of dynamic accumulator enables efficient membership revocation in the anonymous setting. This method applies to membership revocation in group signature schemes, such as the one due to Ateniese et al., and efficient revocation of credentials in anonymous credential systems, such as the one due to Camenisch and Lysyanskaya. Using our method, allowing revocation does not alter the complexity of any operations of the underlying schemes. In particular, the cost of a group signature verification or credential showing increases by only a small constant factor, less than 2. All previously known methods (such as the ones due to Bresson and Stern and Ateniese and Tsudik incurred an increase in these costs that was linear in the number of members.
2001
EPRINT
Efficient Algorithms for Computing Differential Properties of Addition
In this paper we systematically study the differential properties of addition modulo $2^n$. We derive $\Theta(\log n)$-time algorithms for most of the properties, including differential probability of addition. We also present log-time algorithms for finding good differentials. Despite the apparent simplicity of modular addition, the best known algorithms require naive exhaustive computation. Our results represent a significant improvement over them. In the most extreme case, we present a complexity reduction from $\Omega(2^{4n})$ to $\Theta(\log n)$.
2001
EPRINT
Separating Decision Diffie-Hellman from Diffie-Hellman in cryptographic groups
In many cases, the security of a cryptographic scheme based on Diffie--Hellman does in fact rely on the hardness of the Diffie--Hellman Decision problem. In this paper, we show that the hardness of Decision Diffie--Hellman is a much stronger hypothesis than the hardness of the regular Diffie--Hellman problem. Indeed, we describe a reasonably looking cryptographic group where Decision Diffie--Hellman is easy while Diffie--Hellman is equivalent to a -- presumably hard -- Discrete Logarithm Problem. This shows that care should be taken when dealing with Decision Diffie--Hellman, since its security cannot be taken for granted.
2001
EPRINT
MinRank problem and Zero-knowledge authentication
A zero-knowledge protocol provides provably secure authentication based on a computational problem. Several such schemes have been proposed since 1984, and the most practical ones rely on problems such as factoring that are unfortunately subexponential. Still there are several other (practical) schemes based on NP-complete problems. Among them, the problems of coding theory are in spite of some 20 years of significant research effort, still exponential to solve. The problem MinRank recently arouse in cryptanalysis of HFE (Crypto'99) and TTM (Asiacrypt'2000) public key cryptosystems. It happens to ba a strict generalization of those hard problems of (decoding) error correcting codes. We propose a new Zero-knowledge scheme based on MinRank. We prove it to be Zero-knowledge by black-box simulation. We compare it to other practical schemes based on NP-complete problems. The MinRank scheme allows also an easy setup for a public key shared by a few users, and thus allows anonymous group signatures.
2001
EPRINT
A Note on Cryptanalysis of the Preliminary Version of the NTRU Signature Scheme
In this paper a preliminary version of the NTRU signature scheme is cryptanalyzed. The attack exploits a correlation between some bits of a signature and coefficients of a secret random polynomial. The attack does not apply to the next version of the signature scheme.
2001
EPRINT
Secure and Efficient Asynchronous Broadcast Protocols
Reliable broadcast protocols are a fundamental building block for implementing replication in fault-tolerant distributed systems. This paper addresses secure service replication in an asynchronous environment with a static set of servers, where a malicious adversary may corrupt up to a threshold of servers and controls the network. We develop a formal model using concepts from modern cryptography, present modular definitions for several broadcast problems, including reliable, atomic, and secure causal broadcast, and present protocols implementing them. Reliable broadcast is a basic primitive, also known as the Byzantine generals problem, providing agreement on a delivered message. Atomic broadcast imposes additionally a total order on all delivered messages. We present a randomized atomic broadcast protocol based on a new, efficient multi-valued asynchronous Byzantine agreement primitive with an external validity condition. Apparently, no such efficient asynchronous atomic broadcast protocol maintaining liveness and safety in the Byzantine model has appeared previously in the literature. Secure causal broadcast extends atomic broadcast by encryption to guarantee a causal order among the delivered messages. Threshold-cryptographic protocols for signatures, encryption, and coin-tossing also play an important role.
2001
EPRINT
Are 'Strong' Primes Needed for RSA
We review the arguments in favor of using so-called ``strong primes'' in the RSA public-key cryptosystem. There are two types of such arguments: those that say that strong primes are needed to protect against factoring attacks, and those that say that strong primes are needed to protect against ``cycling'' attacks (based on repeated encryption). We argue that, contrary to common belief, it is unnecessary to use strong primes in the RSA cryptosystem. That is, by using strong primes one gains a negligible increase in security over what is obtained merely by using ``random'' primes of the same size. There are two parts to this argument. First, the use of strong primes provides no additional protection against factoring attacks, because Lenstra's method of factoring based on elliptic curves (ECM) circumvents any protection that might have been offered by using strong primes. The methods that 'strong' primes are intended to guard against, as well as ECM, are probabalistic in nature, but ECM succeeds with higher probability. For RSA key sizes being proposed now, the probability of success of these methods is very low. Additionally, the newer Number Field Sieve algorithm can factor RSA keys with certainty in less time than these methods. Second, a simple group-theoretic argument shows that cycling attacks are extremely unlikely to be effective, as long as the primes used are large. Indeed, even probabalistic factoring attacks will succeed much more quickly and with higher probability than cycling attacks.
2001
EPRINT
Fully Distributed Threshold RSA under Standard Assumptions
The aim of the present article is to propose a fully distributed environment for the RSA scheme. What we have in mind is highly sensitive applications and even if we are ready to pay a price in terms of efficiency, we do not want any compromise of the security assumptions that we make. Recently Shoup proposed a practical RSA threshold signature scheme that allows to share the ability to sign between a set of players. This scheme can be used for decryption as well. However, Shoup's protocol assumes a trusted dealer to generate and distribute the keys. This comes from the fact that the scheme needs a special assumption on the RSA modulus and this kind of RSA moduli cannot be easily generated in an efficient way with many players. Of course, it is still possible to call theoretical results on multiparty computation, but we cannot hope to design efficient protocols. The only practical result to generate RSA moduli in a distributive manner is Boneh and Franklin protocol but this protocol cannot be easily modified to generate the kind of RSA moduli that Shoup's protocol requires. The present work takes a different path by proposing a method to enhance the key generation with some additional properties and revisits the proof of Shoup to work with the resulting RSA moduli. Both of these enhancements decrease the performance of the basic protocols. However, we think that in the applications that we target, these enhancements provide practical solutions. Indeed, the key generation protocol is usually run only once and the number of players have time to perform their task so that the communication or time complexity are not overly important.
2001
EPRINT
Robust key-evolving public key encryption schemes
We propose a key-evolving paradigm to deal with the key exposure problem of public key encryption schemes. The key evolving paradigm is like the one used for forward-secure digital signature schemes. Let time be divided into time periods such that at time period $j$, the decryptor holds the secret key $SK_j$, while the public key PK is fixed during its lifetime. At time period $j$, a sender encrypts a message $m$ as $\langle j, c\rangle$, which can be decrypted only with the private key $SK_j$. When the time makes a transit from period $j$ to $j+1$, the decryptor updates its private key from $SK_j$ to $SK_{j+1}$ and deletes $SK_j$ immediately. The key-evolving paradigm assures that compromise of the private key $SK_j$ does not jeopardize the message encrypted at the other time periods. \par We propose two key-evolving public key encryption schemes with $z$-resilience such that compromise of $z$ private keys does not affect confidentiality of messages encrypted in other time periods. Assuming that the DDH problem is hard, we show one scheme semantically secure against passive adversaries and the other scheme semantically secure against the adaptive chosen ciphertext attack under the random oracle.
2001
EPRINT
How to achieve a McEliece-based Digital Signature Scheme
McEliece is one of the oldest known public key cryptosystems. Though it was less widely studied that RSA, it is remarkable that all known attacks are still exponential. It is widely believed that code-based cryptosystems like McEliece does not allow practical digital signatures. In the present paper we disprove this belief and show a way to build a practical signature scheme based on coding theory. It's security can be reduced in the random oracle model to the well-known {\em syndrome decoding problem} and the distinguishability of permuted binary Goppa codes from a random code. For example we propose a scheme with signatures of $81$-bits and a binary security workfactor of $2^{83}$.
2001
EPRINT
New Zero-knowledge Undeniable Signatures - Forgery of Signature Equivalent to Factorisation
We propose a new zero-knowledge undeniable signature scheme which is based on the intractability of computing high-order even powers modulo a composite. The new scheme has a number of desirable properties: (i) forgery of a signature (including existential forgery) is proven to be equivalent to factorisation, (ii) perfect zero-knowledge, (iii) efficient protocols for signature verification and non-signature denial: both measured by $O(\log k)$ (multiplications) where $1/k$ bounds the probability of error. For a denial protocol, this performance is unprecedented.
2001
EPRINT
Ciphers with Arbitrary Finite Domains
We introduce the problem of enciphering members of a finite set $M$ where $k=|M|$ is arbitrary (in particular, it need not be a power of two). We want to achieve this goal starting from a block cipher (which requires a message space of size $N=2^n$, for some $n$). We look at a few solutions to this problem, focusing on the case when $M=[0, k-1]$.
2001
EPRINT
Digitally Watermarking RSA Moduli
The moduli used in RSA (see \cite{rsa}) can be generated by many different sources. The generator of that modulus knows its factorization. They have the ability to forge signatures or break any system based on this moduli. If a moduli and the RSA parameters associated with it were generated by a reputable source, the system would have higher value than if the parameters were generated by an unknown entity. An RSA modulus is digitally marked, or digitally trade marked, if the generator and other identifying features of the modulus can be identified and possibly verified by the modulus itself. The basic concept of digitally marking an RSA modulus would be to fix the upper bits of the modulus to this tag. Thus anyone who sees the public modulus can tell who generated the modulus and who the generator believes the intended user/owner of the modulus is. Two types of trade marking will be described here. The first is simpler but does not give verifiable trade marking. The second is more complex, but allows for verifiable trade marking of RSA moduli. The second part of this paper describes how to generate an RSA modulus with fixed upper bits.
2001
EPRINT
Timed-Release Cryptography
Let $n$ be a large composite number. Without factoring $n$, the validation of $a^{2^t} (\bmod \, n)$ given $a$, $t$ with $gcd(a, n) = 1$ and $t < n$ can be done in $t$ squarings modulo $n$. For $t \ll n$ (e.g., $n > 2^{1024}$ and $t < 2^{100}$), no lower complexity than $t$ squarings is known to fulfill this task (even considering massive parallelisation). Rivest et al suggested to use such constructions as good candidates for realising timed-release crypto problems. We argue the necessity for zero-knowledge proof of the correctness of such constructions and propose the first practically efficient protocol for a realisation. Our protocol proves, in $\log_2 t$ standard crypto operations, the correctness of $(a^e)^{2^t} (\bmod\,n)$ with respect to $a^e$ where $e$ is an RSA encryption exponent. With such a proof, a {\em Timed-release RSA Encryption} of a message $M$ can be given as $a^{2^t} M (\bmod \,n)$ with the assertion that the correct decryption of the RSA ciphertext $M^e (\bmod \, n)$ can be obtained by performing $t$ squarings modulo $n$ starting from $a$. {\em Timed-release RSA signatures} can be constructed analogously.
2001
EPRINT
An observation regarding Jutla's modes of operation
Recently, Jutla suggested two new modes of operation for block ciphers. These modes build on traditional CBC and ECB modes, respectively, but add to them masking of the outputs and inputs. Jutla proved that these masking operations considerably strengthen CBC and ECB modes. In particular, together with a simple checksum, the modified modes ensure not only confidentiality, but also authenticity. Similar modes were also suggested by Gligor and Donsecu and by Rogaway. In Jutla's proposal (as well as in some of the other proposals), the masks themselves are derived from an IV via the same block cipher as used for the encryption (perhaps with a different key). In this work we note, however, that the function for deriving these masks need not be cryptographic at all. In particular, we prove that a universal hash function (a-la-Carter-Wegman) is sufficient for this purpose.
2001
EPRINT
Efficient Traitor Tracing Algorithms using List Decoding
We apply powerful, recently discovered techniques for the list decoding of error-correcting codes to the problem of efficiently tracing traitors. Traitor tracing schemes have been extensively studied for use as a piracy deterrent. In a widely studied model for protecting digital content, each user in the system is associated with a unique set of symbols. For example, the sets may be used to install a software CD or decrypt pay-TV content. The assignment of sets is done in such a way that if a bounded collection of sets is used to form a new set to enable piracy, at least one of the traitor sets can be identified by applying a traitor tracing algorithm to the newly formed set. Much work has focused on methods for constructing such traceability schemes, but the complexity of the traitor tracing algorithms has received little attention. A widely used traitor tracing algorithm, the TA algorithm, has a running time of $O(\n)$ in general, where $\n$ is number of sets in the system (e.g., the number of copies of the CD), and therefore is inefficient for large populations. In this paper we use a coding theoretic approach to produce traceability schemes for which the TA algorithm is very fast. We show that when suitable error-correcting codes are used to construct traceability schemes, and fast list decoding algorithms are used to trace, the run time of the TA algorithm is polynomial in the codeword length. We also use the strength of the error-correcting code approach to construct traceability schemes with more efficient algorithms for finding all possible traitor coalitions. Finally, we provide evidence that amongst traceability schemes in general, TA traceability schemes are the most likely to be amenable to efficient tracing methods.
2001
EPRINT
On adaptive vs. non-adaptive security of multiparty protocols
Security analysis of multiparty cryptographic protocols distinguishes between two types of adversarial settings: In the non-adaptive setting, the set of corrupted parties is chosen in advance, before the interaction begins. In the adaptive setting, the adversary chooses who to corrupt during the course of the computation. We study the relations between adaptive security (i.e., security in the adaptive setting) and non-adaptive security, according to two definitions and in several models of computation. While affirming some prevailing beliefs, we also obtain some unexpected results. Some highlights of our results are: o According to the definition of Dodis-Micali-Rogaway (which is set in the information-theoretic model), adaptive and non-adaptive security are equivalent. This holds for both honest-but-curious and Byzantine adversaries, and for any number of parties. o According to the definition of Canetti, for honest-but-curious adversaries, adaptive security is equivalent to non-adaptive security when the number of parties is logarithmic, and is strictly stronger than non-adaptive security when the number of parties is super-logarithmic. For Byzantine adversaries, adaptive security is strictly stronger than non-adaptive security, for any number of parties.
2001
EPRINT
Analysis of a Subset Sum Randomizer
In [5] an efficient pseudo-random number generator (PRNG) with provable security is described. Its security is based on the hardness of the subset sum or knapsack problem. In this paper we refine these ideas to design a PRNG with independent seed and output generation. This independence allows for greater parallelism, design flexibility, and possibly greater security.
2001
EPRINT
An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation
A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance because it is the best means of providing privacy for users. In this paper we propose a practical anonymous credential system that is based on the strong RSA assumption and the decisional Diffie-Hellman assumption modulo a safe prime product and is considerably superior to existing ones: (1) We give the first practical solution that allows a user to unlinkably demonstrate possession of a credential as many times as necessary without involving the issuing organization. (2) To prevent misuse of anonymity, our scheme is the first to offer optional anonymity revocation for particular transactions. (3) Our scheme offers separability: all organizations can choose their cryptographic keys independently of each other. Moreover, we suggest more effective means of preventing users from sharing their credentials, by introducing {\em all-or-nothing} sharing: a user who allows a friend to use one of her credentials once, gives him the ability to use all of her credentials, i.e., taking over her identity. This is implemented by a new primitive, called {\em circular encryption}, which is of independent interest, and can be realized from any semantically secure cryptosystem in the random oracle model.
2001
EPRINT
Some observations on the theory of cryptographic hash functions
In this paper, we study several issues related to the notion of ``secure'' hash functions. Several necessary conditions are considered, as well as a popular sufficient condition (the so-called random oracle model). We study the security of various problems that are motivated by the notion of a secure hash function. These problems are analyzed in the random oracle model, and we prove that the obvious trivial algorithms are optimal. As well, we look closely at reductions between various problems. In particular, we consider the important question ``does preimage resistance imply collision resistance?''. Finally, we study the relationship of the security of hash functions built using the Merkle-Damgard construction to the security of the underlying compression function.
2001
EPRINT
The Rectangle Attack - Rectangling the Serpent
Serpent is one of the 5 AES finalists. The best attack published so far analyzes up to 9 rounds. In this paper we present attacks on 7-round, 8-round, and 10-round variants of Serpent. We attack 7-round variant of Serpent with all key lengths, and 8- and 10-round variants wih 256-bit keys. The 10-roun attack on the 256-bit keys variants is the best published attack on the cipher. The attack enhances the amplified boomerang attack and uses better differentials. We also present the best 3-round, 4-round, 5-round and 6-round differential characteristics of Serpent.
2001
EPRINT
Optimistic Asynchronous Atomic Broadcast
This paper presents a new protocol for atomic broadcast in an asynchronous network with a maximal number of Byzantine failures. It guarantees both safety and liveness without making any timing assumptions or using any type of failure detector. Under normal circumstances, the protocol runs in an optimistic mode, with extremely low message and computational complexity -- essentially, just performing a Bracha broadcast for each request. In particular, no potentially expensive public-key cryptographic operations are used. In rare circumstances, the protocol may briefly switch to a pessimistic mode, where both the message and computational complexity are significantly higher than in the optimistic mode, but are still reasonable.
2001
EPRINT
Robustness for Free in Unconditional Multi-Party Computation
We present a very efficient multi-party computation protocol unconditionally secure against an active adversary. The security is maximal, i.e., active corruption of up to $t<n/3$ of the $n$ players is tolerated. The communication complexity for securely evaluating a circuit with $m$ multiplication gates over a finite field is $\O(mn^2)$ field elements, including the communication required for simulating broadcast. This corresponds to the complexity of the best known protocols for the passive model, where the corrupted players are guaranteed not to deviate from the protocol. Even in this model, it seems to be unavoidable that for every multiplication gate every player must send a value to every other player, and hence the complexity of our protocol may well be optimal. The constant overhead factor for robustness is small and the protocol is practical.
2001
EPRINT
Secure Multiparty Computation of Approximations
Approximation algorithms can sometimes be used to obtain efficient solutions where no efficient exact computation is known. In particular, approximations are often useful in a distributed setting where the inputs are held by different parties and are extremely large. Furthermore, for some applications, the parties want to cooperate to compute a function of their inputs without revealing more information than they have to. Suppose the function $\fhat$ is an approximation to the function $f$. Secure multiparty computation of $f$ allows the parties to compute $f$ without revealing more than they have to, but it requires some additional overhead in computation and communication. Hence, if computation of $f$ is inefficient or just efficient enough to be practical, then secure computation of $f$ may be impractically expensive. Furthermore, a secure computation of $\fhat$ is not necessarily as private as a secure computation of $f$, because the output of $\fhat$ may reveal more information than the output of $f$. In this paper, we present definitions and protocols of secure multiparty approximate computation that show how to realize most of the cost savings available by using $\fhat$ instead of $f$ without losing the privacy of a secure computation of $f$. We make three contributions. First, we give formal definitions of secure multiparty approximate computations. Second, we present an efficient, sublinear-communication, private approximate computation for the Hamming distance; we also give an efficient, polylogarithmic-communication solution for the $L^{2}$ distance in a relaxed model. Finally, we give an efficient private approximation of the permanent and other related \#P-hard problems.
2001
EPRINT
Cryptanalysis of some elliptic curve based cryptosystems of Paillier
Two public key encryption schemes based on anomalous elliptic curves over rings are studied. It is argued that these schemes are not secure.
2001
EPRINT
OCB Mode
This paper was prepared for NIST, which is considering new block-cipher modes of operation. It describes a parallelizable mode of operation that simultaneously provides both privacy and authenticity. "OCB mode" encrypts-and-authenticates an arbitrary message $M\in\bits^*$ using only $\lceil |M|/n\rceil + 2$ block-cipher invocations, where $n$ is the block length of the underlying block cipher. Additional overhead is small. OCB refines a scheme, IAPM, suggested by Jutla [IACR-2000/39], who was the first to devise an authenticated-encryption mode with minimal overhead compared to standard modes. Desirable new properties of OCB include: very cheap offset calculations; operating on an arbitrary message $M\in\bits^*$; producing ciphertexts of minimal length; using a single underlying cryptographic key; making a nearly optimal number of block-cipher calls; avoiding the need for a random IV; and rendering it infeasible for an adversary to find "pretag collisions". The paper provides a full proof of security for OCB.
2001
EPRINT
A Block-Cipher Mode of Operation for Parallelizable Message Authentication
We define and analyze a simple and fully parallelizable block-cipher mode of operation for message authentication. Parallelizability does not come at the expense of serial efficiency: in a conventional, serial environment, the algorithm's speed is within a few percent of the (inherently sequential) CBC~MAC. The new mode, PMAC, is deterministic, resembles a standard mode of operation (and not a Carter-Wegman MAC), works for strings of any bit length, employs a single block-cipher key, and uses just max{1, ceiling(|M|/n)} block-cipher calls to MAC any string M using an n-bit block cipher. We prove PMAC secure, quantifying an adversary's forgery probability in terms of the quality of the block cipher as a pseudorandom permutation.
2001
EPRINT
Efficient Encryption for Rich Message Spaces Under General Assumptions
We present a new family of public-key encryption schemes which combine modest computational demands with provable security guarantees under only general assumptions. The schemes may be realized with any one-way trapdoor permutation, and provide a notion of security corresponding to semantic security under the condition that the message space has sufficient entropy. Furthermore, these schemes can be implemented with very few applications of the underlying one-way permutation: schemes which provide security for message spaces in $\{0,1\}^n$ with minimum entropy $n - \ell$ can be realized with $\ell + w(k)\log k$ applications of the underlying one-way trapdoor permutation. Here $k$ is the security parameter and $w(k)$ is any function which tends to infinity. In comparison, extant systems offering full semantic security require roughly $n$ applications of the underlying one-way trapdoor permutation. Finally, we give a simplified proof of a fundamental ``elision lemma'' of Goldwasser and Micali.
2001
EPRINT
On multivariate signature-only public key cryptosystems
In a paper published at Asiacrypt 2000 a signature scheme that (apparently) cannot be abused for encryption is published. The problem is highly non-trivial and every solution should be looked upon with caution. What is especially hard to achieve is to avoid that the public key should leak some information, to be used as a possible "shadow" secondary public key. In the present paper we argument that the problem has many natural solutions within the framework of the multivariate cryptography. First of all it seems that virtually any non-injective multivariate public key is inherently unusable for encryption. Unfortunately having a lot of leakage is inherent to multivariate cryptosystems. Though it may appear hopeless at the first sight, we use this very property to remove leakage. In our new scenario the Certification Authority (CA) makes extensive modifications of the public key such that the user can still use the internal trapdoor, but has no control on any publicly verifiable property of the actual public key equations published by CA. Thus we propose a very large class of multivariate non-encryption PKI schemes with many parameters $q,d,h,v,r,u,f,D$. The paper is also of independent interest, as it contains all variants of the HFE trapdoor public key cryptosystem. We give numerous and precise security claims that HFE achieves or appears to achieve and establish some provable security relationships.
2001
EPRINT
On the Power of Nonlinear Secret-Sharing
A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f:{0,1}^n --> {0,1}. A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n. Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure. Prior to this work there was no evidence that nonlinear schemes can be significantly more efficient than linear schemes, and in particular there were no candidates for schemes efficiently realizing access structures which do not lie in NC. The main contribution of this work is the construction of two efficient nonlinear schemes: (1) A scheme with perfect privacy whose access structure is conjectured not to lie in NC; (2) A scheme with statistical privacy whose access structure is conjectured not to lie in P/poly. Another contribution is the study of a class of nonlinear schemes, termed quasi-linear schemes, obtained by composing linear schemes over different fields. We show that while these schemes are possibly (super-polynomially) more powerful than linear schemes, they cannot efficiently realize access structures outside NC.
2001
EPRINT
Efficient Password-Authenticated Key Exchange Using Human-Memorable Passwords
We present an efficient password-authenticated key exchange protocol which is secure against off-line dictionary attacks even when users choose passwords from a very small space (say, a dictionary of English words). We prove security in the standard model under the decisional Diffie-Hellman assumption, assuming public parameters generated by a trusted party. Compared to the recent work of Goldreich and Lindell (which was the first to give a secure construction, under general assumptions, in the standard model), our protocol requires only 3 rounds and is efficient enough to be used in practice.
2001
EPRINT
Efficient and Non-Interactive Non-Malleable Commitment
We present new constructions of non-malleable commitment schemes, in the public parameter model (where a trusted party makes parameters available to all parties), based on the discrete logarithm or RSA assumptions. The main features of our schemes are: they achieve near-optimal communication for arbitrarily-large messages and are non-interactive. Previous schemes either required (several rounds of) interaction or focused on achieving non-malleable commitment based on general assumptions and were thus efficient only when committing to a single bit. Although our main constructions are for the case of perfectly-hiding commitment, we also present a communication-efficient, non-interactive commitment scheme (based on general assumptions) that is perfectly binding.
2001
EPRINT
Dual of New Method for Upper Bounding the Maximum Average Linear Hull Probability for SPNs
In [3], we present a new algorithm for computing an upper bound on the maximum average linear hull probability (MALHP) for the SPN symmetric cipher structure, a value required to make claims about provable security against linear cryptanalysis. This algorithm improves on existing work in that the resulting upper bound is a function of the number of encryption rounds (other upper bounds known to the authors are not), and moreover, it can be computed for an SPN with any linear transformation layer (the best previous result, that of Hong et.al [4], applies only to SPNs with highly diffusive linear transformations). It is well known that there exists a duality between linear cryptanalysis and differential cryptanalysis which allows certain results related to one of the attacks to be translated into the corresponding results for the other attack [1,5]. Since this duality applies to our work in [3], we immediately obtain an algorithm for upper bounding the maximum average differential probability (MADP) for SPNs (required to make claims about provable security against differential cryptanalysis). Note: In what follows, we assume familiarity with the notation and results of [3].
2001
EPRINT
Composition and Efficiency Tradeoffs for Forward-Secure Digital Signatures
Forward-secure digital signatures, initially proposed by Anderson in CCS 97 and formalized by Bellare and Miner in Crypto 99, are signature schemes which enjoy the additional guarantee that a compromise of the secret key at some point in time does not help forge signatures allegedly signed in an earlier time period. Consequently, if the secret key is lost, then the key can be safely revoked without invalidating previously-issued signatures. Since the introduction of the concept, several forward-secure signature schemes have been proposed, with varying performance both in terms of space and time. Which scheme is most useful in practice typically depends on the requirements of the specific application. In this paper we propose and study some general composition operations that can be used to combine existing signature schemes (whether forward-secure or not) into new forward-secure signature schemes. Our schemes offer interesting trade-offs between the various efficiency parameters, achieving a greater flexibility in accommodating the requirements of different applications. As an extension of our techniques, we also construct the first efficient forward-secure signature scheme where the total number of time periods for which the public key is used does not have to be fixed in advance. The scheme can be used for practically unbounded time, and the performance depends (minimally) only on the time elapsed so far. Our scheme achieves excellent performance overall, is very competitive with previous schemes with respect to all parameters, and outperforms each of the previous schemes in at least one parameter. Moreover, the scheme can be based on any underlying digital signature scheme, and does not rely on specific assumptions. Its forward security is proven in the standard model, without using a random oracle.
2001
EPRINT
Forward-Security in Private-Key Cryptography
This paper provides a comprehensive treatment of forward-security in the context of shared-key based cryptographic primitives, as a practical means to mitigate the damage caused by key-exposure. We provide definitions of security, practical proven-secure constructions, and applications for the main primitives in this area. We identify forward-secure pseudorandom bit generators as the central primitive, providing several constructions and then showing how forward-secure message authentication schemes and symmetric encryption schemes can be built based on standard schemes for these problems coupled with forward-secure pseudorandom bit generators. We then apply forward-secure message authentication schemes to the problem of maintaining secure access logs in the presence of break-ins.
2001
EPRINT
Anti-persistence: History Independent Data Structures
Many data structures give away much more information than they were intended to. Whenever privacy is important, we need to be concerned that it might be possible to infer information from the memory representation of a data structure that is not available through its ``legitimate'' interface. Word processors that quietly maintain old versions of a document are merely the most egregious example of a general problem. We deal with data structures whose current memory representation does not reveal their history. We focus on dictionaries, where this means revealing nothing about the order of insertions or deletions. Our first algorithm is a hash table based on open addressing, allowing $O(1)$ insertion and search. We also present a history independent dynamic perfect hash table that uses space linear in the number of elements inserted and has expected amortized insertion and deletion time $O(1)$. To solve the dynamic perfect hashing problem we devise a general scheme for history independent memory allocation. For fixed-size records this is quite efficient, with insertion and deletion both linear in the size of the record. Our variable-size record scheme is efficient enough for dynamic perfect hashing but not for general use. The main open problem we leave is whether it is possible to implement a variable-size record scheme with low overhead.
2001
EPRINT
EMpowering Side-Channel Attacks
In this paper, we report preliminary results obtained as a result of a systematic investigation of leakage of compromising information via EM emanations from chipcards and other devices. Our findings show that the EM side--channel is more powerful than other side--channels such as timing and power analysis. Specifically, in some cases, one can obtain much more compromising information about computations and one can use this information to defeat the protection provided by countermeasures to the other side--channel attacks.
2001
EPRINT
Flaws in differential cryptanalysis of Skipjack
This paper is motivated by some results presented by Knudsen, Robshaw and Wagner at Crypto'99, that described many attacks of reduced versions of Skipjack, some of them being erroneous. Differential cryptanalysis is based on distinguishers, any attack should prove that the events that triggers the analysis has not the same probability for the cipher than for a random function. In particular, the composition of differential for successive parts of a cipher should be done very carefully to lead to an attack. This revised version of the paper includes the exact computations of some probabilities and repairs the attack of the first half of Skipjack.
2001
EPRINT
Robust Software Tokens: Towards Securing a Digital Identity
This paper presents a new method called the robust software token for providing users with a stable and portable container in which a private key is stored and kept from adversaries, by simple software-only techniques. The proposed scheme is comparable with the related noble work such as a cryptographic camouflage scheme and a networked cryptographic device, but equipped with several advantages; (1) it uniquely supports both closed and open domains on public key infrastructures, (2) it supports more protocol setup, (3) and it is more efficient than the others. This paper handles the new RSA-based scheme only. The DSA-based scheme sharing the basic idea can be found in our previous work.
2001
EPRINT
Analysis of Key-Exchange Protocols and Their Use for Building Secure Channels
We present a formalism for the analysis of key-exchange protocols that combines previous definitional approaches and results in a definition of security that enjoys some important analytical benefits: (i) any key-exchange protocol that satisfies the security definition can be composed with symmetric encryption and authentication functions to provide provably secure communication channels; and (ii) the definition allows for simple modular proofs of security: one can design and prove security of key-exchange protocols in an idealized model where the communication links are perfectly authenticated, and then translate them using general tools to obtain security in the realistic setting of adversary-controlled links. We exemplify the usability of our results by applying them to obtain the proof of two main classes of key-exchange protocols, Diffie-Hellman and key-transport, authenticated via symmetric or asymmetric techniques. Further contributions of the paper include the formalization of ``secure channels'' in the context of key-exchange protocols, and establishing sufficient conditions on the symmetric encryption and authentication functions to realize these channels.
2001
EPRINT
Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent
We provide a concrete instance of the discrete logarithm problem on an elliptic curve over F_{2^{155}} which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index-calculus methods for hyperelliptic curves over characteristic two finite fields, and discuss the cryptographic implications of our results.
2001
EPRINT
Simple Forward-Secure Signatures From Any Signature Scheme
In Crypto'99, Bellare and Miner introduced {\em forward-secure signatures} as digital signature schemes with the attractive property that exposure of the signing key at certain time period does not allow for the forgery of signatures from previous time periods. That paper presented the first full design of an efficient forward-secure signatures scheme, but left open the question of building efficient and practical schemes based on standard signatures such as RSA or DSS. In particular, they called for the development of schemes where the main size-parameters (namely, the size of the private key, public key, and signature) do not grow with the total number of periods for which the public key is to be in use. We present an efficient and extremely simple construction of forward-secure signatures based on {\em any} regular signature scheme (e.g., RSA and DSS); the resultant signatures enjoy size-parameters that are independent of the number of periods (except for the inclusion of an index to the period in which a signature is issued). The only parameter that grows (linearly) with the number of periods is the total size of local non-secret memory of the signer. The forward-security of our schemes is directly implied by the unforgeability property of the underlying signature scheme and it requires no extra assumptions. Our approach can also be applied to some signature schemes with special properties, such as undeniable signatures, to obtain forward-secure signatures that still enjoy the added special property.
2001
EPRINT
Cryptanalysis of the Vesta-2M Stream Cipher
In this paper the security of the stream cipher Vesta-2M is investigated. Cryptanalytic algorithm is developed for a known plaintext attack where only a small segment of plaintext is assumed to be known. The complexity the attack is estimated the time of searching through the square root of all possible initial states.
2001
EPRINT
Optimistic Asynchronous Multi-Party Contract Signing with Reduced Number of Rounds
Optimistic asynchronous multi-party contract signing protocols have received attention in recent years as a compromise between efficient protocols and protocols avoiding a third party as a bottleneck of security. ``Optimistic'' roughly means: in case all participants are honest and receive the messages from the other participants as expected, the third party is not involved at all. The best solutions known so far terminate within $t+2$ rounds in the optimistic case, for any fixed set of $n$ signatories and allowing up to $t<n$ dishonest signatories. The protocols presented here achieve a major improvement compared to the state of the art: The number of rounds $R$ is reduced from $O(t)$ to $O(1)$ for all $n \ge 2t+1$, and for $n < 2t+1$, $R$ grows remarkably slowly compared with numbers of rounds in $O(t)$: If $t \approx \frac{k}{k+1} n $ then $R \approx 2k$.
2001
EPRINT
The order of encryption and authentication for protecting communications (Or: how secure is SSL?)
We study the question of how to generically compose {\em symmetric} encryption and authentication when building ``secure channels'' for the protection of communications over insecure networks. We show that any secure channels protocol designed to work with any combination of secure encryption (against chosen plaintext attacks) and secure MAC must use the encrypt-then-authenticate method. We demonstrate this by showing that the other common methods of composing encryption and authentication, including the authenticate-then-encrypt method used in SSL, are not generically secure. We show an example of an encryption function that provides (Shannon's) perfect secrecy but when combined with any MAC function under the authenticate-then-encrypt method yields a totally insecure protocol (for example, finding passwords or credit card numbers transmitted under the protection of such protocol becomes an easy task for an active attacker). The same applies to the encrypt-and-authenticate method used in SSH. On the positive side we show that the authenticate-then-encrypt method is secure if the encryption method in use is either CBC mode (with an underlying secure block cipher) or a stream cipher (that xor the data with a random or pseudorandom pad). Thus, while we show the generic security of SSL to be broken, the current standard implementations of the protocol that use the above modes of encryption are safe.
2001
EPRINT
The simple ideal cipher system
We address the problem of how to construct ideal cipher systems when the length of a key is much less than the length of an encrypted message. We suggest a new secret key cipher system in which firstly the message is transformed into two parts in such a way that the biggest part consists of independent and equiprobable letters. Secondly the relatively small second part is enciphered wholly by the Vernam cipher whereas only few bits from the biggest part are enciphered. This transformation is based on the fast version of the Elias construction of an unbiased random sequence. The time required for encoding and decoding and the memory size of the encoder and decoder are presented as functions of the ratio of the key length and the message length. The suggested scheme can be applied to sources with unknown statistics.
2001
EPRINT
ON THE METHOD OF "XL" AND ITS INEFFICIENCY TO TTM
We will show that the paper "Efficient Algorithm for solving over- defined systems of multivariate polynomials equations" published in Eurocrypt 2000 by N. Courtois, A. Shamir, J. Patarin and A.Klimov ignors the intersection property at infinity of the system and the program proposed by them can not achieve their desired results. In fact, we produce very simple example to show that in some cases, their program always fails.
2001
EPRINT
Forward-Secure Signatures with Optimal Signing and Verifying
Ordinary digital signatures have an inherent weakness: if the secret key is leaked, then all signatures, even the ones generated before the leak, are no longer trustworthy. Forward-secure digital signatures were recently proposed to address this weakness: they ensure that past signatures remain secure even if the current secret key is leaked. We propose the first forward-secure signature scheme for which both signing and verifying are as efficient as for one of the most efficient ordinary signature schemes (Guillou-Quisquater): each requiring just two modular exponentiations with a short exponent. All previously proposed forward-secure signature schemes took significantly longer to sign and verify than ordinary signature schemes. Our scheme requires only fractional increases to the sizes of keys and signatures, and no additional public storage. Like the underlying Guillou-Quisquater scheme, our scheme is provably secure in the random oracle model.
2001
EPRINT
A known plaintext attack on the ISAAC keystream generator
Stream ciphers are often used in applications where high speed and low delay are a requirement. The ISAAC keystream generator is a fast software-oriented encryption algorithm. In this papers the security of the ISAAC keystream generator is investigated. Cryptanalytic algorithm is developed for a known plaintext attack where only a small segment of plaintext is assumed to be known. Keywords. ISAAC. Keystream generator. Cryptanalysis.
2001
EPRINT
Elliptic curve Paillier schemes
This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes are not secure. A more natural generalisation of Paillier's scheme to elliptic curves is given.
2001
EPRINT
Black-Box Concurrent Zero-Knowledge Requires $\tilde\Omega(\log n)$ Rounds
We show that any concurrent zero-knowledge protocol for a non-trivial language (i.e., for a language outside $\BPP$), whose security is proven via black-box simulation, must use at least $\tilde\Omega(\log n)$ rounds of interaction. This result achieves a substantial improvement over previous lower bounds, and is the first bound to rule out the possibility of constant-round concurrent zero-knowledge when proven via black-box simulation. Furthermore, the bound is polynomially related to the number of rounds in the best known concurrent zero-knowledge protocol for languages in $\NP$.
2001
EPRINT
Differential Probability of Modular Addition with a Constant Operand
In this article I analyze the function f(X) = A + X (mod 2**n) exclusive-or differential probability. The result, regarding differential cryptanalysis, is a better understanding of ciphers that use f(X) as a primitive operation. A simple O(n) algorithm to compute the probability is given.
2001
EPRINT
Security Proofs for the RSA-PSS Signature Scheme and Its Variants
We analyze the security of different versions of the adapted RSA-PSS signature scheme, including schemes with variable salt lengths and message recovery. We also examine a variant with Rabin-Williams (RW) as the underlying verification primitive. Our conclusion is that the security of RSA-PSS and RW-PSS in the random oracle model can be tightly related to the hardness of inverting the underlying RSA and RW primitives, at least if the PSS salt length is reasonably large. Our security proofs are based on already existing work by Bellare and Rogaway and by Coron, who examined signature schemes based on the original PSS encoding method.
2001
EPRINT
Extending the GHS Weil Descent Attack
In this paper we extend the Weil descent attack due to Gaudry, Hess and Smart (GHS) to a much larger class of elliptic curves. This extended attack still only works for fields of composite degree over $\F_2$. The principle behind the extended attack is to use isogenies to find a new elliptic curve for which the GHS attack is effective. The discrete logarithm problem on the target curve can be transformed into a discrete logarithm problem on the new isogenous curve. One contribution of the paper is to give an improvement to an algorithm of Galbraith for constructing isogenies between elliptic curves, and this is of independent interest in elliptic curve cryptography. We conclude that fields of the form $\F_{q^7}$ should be considered weaker from a cryptographic standpoint than other fields. In addition we show that a larger proportion than previously thought of elliptic curves over $\F_{2^{155}}$ should be considered weak.
2001
EPRINT
Universally Composable Commitments
We propose a new security measure for commitment protocols, called /universally composable/ (UC) Commitment. The measure guarantees that commitment protocols behave like an "ideal commitment service," even when concurrently composed with an arbitrary set of protocols. This is a strong guarantee: it implies that security is maintained even when an unbounded number of copies of the scheme are running concurrently, it implies non-malleability (not only with respect to other copies of the same protocol but even with respect to other protocols), it provides resilience to selective decommitment, and more. Unfortunately two-party UC commitment protocols do not exist in the plain model. However, we construct two-party UC commitment protocols, based on general complexity assumptions, in the /common reference string model/ where all parties have access to a common string taken from a predetermined distribution. The protocols are non-interactive, in the sense that both the commitment and the opening phases consist of a single message from the committer to the receiver.
2001
EPRINT
On the Complexity of Matsui's Attack
Linear cryptanalysis remains the most powerful attack against DES at this time. Given $2^{43}$ known plaintext-ciphertext pairs, Matsui expected a complexity of less than $2^{43}$ DES evaluations in 85% of the cases for recovering the key. In this paper, we present a theoretical and experimental complexity analysis of this attack, which has been simulated 21 times using the idle time of several computers. The experimental results suggest a complexity upper-bounded by $2^{41}$ DES evaluations in 85% of the case, while more than the half of the experiments needed less than $2^{39}$ DES evaluations. In addition, we give a detailed theoretical analysis of the attack complexity.
2001
EPRINT
On the Security of the SPEKE Password-Authenticated Key Exchange Protocol
In the most strict formal definition of security for password-authenticated key exchange, an adversary can test at most one password per impersonation attempt. We propose a slightly relaxed definition which restricts an adversary to testing at most a constant number of passwords per impersonation attempt. This definition seems useful, since there is currently a popular password-authenticated key exchange protocol called SRP that seems resistant to off-line dictionary attack, yet does allow an adversary to test two passwords per impersonation attempt. In this paper we prove (in the random oracle model) that a certain instantiation of the SPEKE protocol that uses hashed passwords instead of non-hashed passwords is a secure password-authenticated key exchange protocol (using our relaxed definition) based on a new assumption, the Decision Inverted-Additive Diffie-Hellman assumption. Since this is a new security assumption, we investigate its security and relation to other assumptions; specifically we prove a lower bound for breaking this new assumption in the generic model, and we show that the computational version of this new assumption is equivalent to the Computational Diffie-Hellman assumption.
2001
EPRINT
Efficient Zero-knowledge Authentication Based on a Linear Algebra Problem MinRank
A Zero-knowledge protocol provides provably secure entity authentication based on a hard computational problem. Among many schemes proposed since 1984, the most practical rely on factoring and discrete log, but still they are practical schemes based on NP-hard problems. Among them, the problem SD of decoding linear codes is in spite of some 30 years of research effort, still exponential. We study a more general problem called MinRank that generalizes SD and contains also other well known hard problems. MinRank is also used in cryptanalysis of several public key cryptosystems such as birational schemes (Crypto'93), HFE (Crypto'99), GPT cryptosystem (Eurocrypt'91), TTM (Asiacrypt'2000) and Chen's authentication scheme (1996). We propose a new Zero-knowledge scheme based on MinRank. We prove it to be Zero-knowledge by black-box simulation. An adversary able to cheat with a given MinRank instance is either able to solve it, or is able to compute a collision on a given hash function. MinRank is one of the most efficient schemes based on NP-complete problems. It can be used to prove in Zero-knowledge a solution to any problem described by multivariate equations. We also present a version with a public key shared by a few users, that allows anonymous group signatures (a.k.a. ring signatures).
2001
EPRINT
Revocation and Tracing Schemes for Stateless Receivers
We deal with the problem of a center sending a message to a group of users such that some subset of the users is considered revoked and should not be able to obtain the content of the message. We concentrate on the stateless receiver case, where the users do not (necessarily) update their state from session to session. We present a framework called the Subset-Cover framework, which abstracts a variety of revocation schemes including some previously known ones. We provide sufficient conditions that guarantee the security of a revocation algorithm in this class. We describe two explicit Subset-Cover revocation algorithms; these algorithms are very flexible and work for any number of revoked users. The schemes require storage at the receiver of $\log N$ and $\frac{1}{2} \log^2 N$ keys respectively ($N$ is the total number of users), and in order to revoke $r$ users the required message lengths are of $r \log N$ and $2r$ keys respectively. We also provide a general traitor tracing mechanism that can be integrated with any Subset-Cover revocation scheme that satisfies a ``bifurcation property''. This mechanism does not need an a priori bound on the number of traitors and does not expand the message length by much compared to the revocation of the same set of traitors. The main improvements of these methods over previously suggested methods, when adapted to the stateless scenario, are: (1) reducing the message length to $O(r)$ regardless of the coalition size while maintaining a single decryption at the user's end (2) provide a seamless integration between the revocation and tracing so that the tracing mechanisms does not require any change to the revocation algorithm.
2001
EPRINT
The Security of Practical Two-Party RSA Signature Schemes
In a two-party RSA signature scheme, a client and server, each holding a share of an RSA decryption exponent $d$, collaborate to compute an RSA signature under the corresponding public key $N,e$ known to both. This primitive is of growing interest in the domain of server-aided password-based security, where the client's share of $d$ is based on its password. To minimize cost, designers are looking at very simple, practical protocols based on the early ideas of Boyd, but their security is unclear. We analyze a class of these protocols. We suggest two notions of security for two-party signature schemes and provide proofs of security for the schemes in our class based on assumptions about RSA and the hash function underlying the scheme.
2001
EPRINT
Clock-Controlled Shift Registers for Key-Stream Generation
In this paper we estimate the period of the sequence generated by a clock-controlled LFSR with an irreducible feedback polynomial and an arbitrary structure of the control sequence, as well as some randomness properties of this sequence including element distribution and the autocorrelation function. Also we construct and analyze a specific key-stream generator that applies clock-control. Finally, we present a comprehensive survey of known correlation attacks on clock-controlled registers and their memoryless combiners.
2001
EPRINT
Optimal security proofs for PSS and other signature schemes
The Probabilistic Signature Scheme (PSS) designed by Bellare and Rogaway is a signature scheme provably secure against chosen message attacks in the random oracle model, with a security level equivalent to RSA. In this paper, we derive a new security proof for PSS in which a much shorter random salt is used to achieve the same security level, namely we show that $\log_2 q_{sig}$ bits suffice, where $q_{sig}$ is the number of signature queries made by the attacker. When PSS is used with message recovery, a better bandwidth is obtained because longer messages can now be recovered. Moreover, we show that this size is optimal: if less than $\log_2 q_{sig}$ bits of random salt are used, PSS is still provably secure but no security proof can be tight. This result is based on a new technique which shows that other signature schemes such as the Full Domain Hash scheme and Gennaro-Halevi-Rabin's scheme have optimal security proofs.
2001
EPRINT
Resettably-Sound Zero-Knowledge and its Applications
Resettably-sound proofs and arguments remain sound even when the prover can reset the verifier, and so force it to use the same random coins in repeated executions of the protocol. We show that resettably-sound zero-knowledge {\em arguments} for NP exist if collision-resistant hash functions exist. In contrast, resettably-sound zero-knowledge {\em proofs} are possible only for languages in P/poly. We present two applications of resettably-sound zero-knowledge arguments. First, we construct resettable zero-knowledge arguments of knowledge for NP, using a natural relaxation of the definition of arguments (and proofs) of knowledge. We note that, under the standard definition of proofs of knowledge, it is impossible to obtain resettable zero-knowledge arguments of knowledge for languages outside BPP. Second, we construct a constant-round resettable zero-knowledge argument for NP in the public-key model, under the assumption that collision-resistant hash functions exist. This improves upon the sub-exponential hardness assumption required by previous constructions. We emphasize that our results use non-black-box zero-knowledge simulations. Indeed, we show that some of the results are {\em impossible} to achieve using black-box simulations. In particular, only languages in BPP have resettably-sound arguments that are zero-knowledge with respect to black-box simulation.
2001
EPRINT
An Integer Commitment Scheme based on Groups with Hidden Order
We present a commitment scheme allowing commitment to arbitrary size integers, based on any Abelian group with certain properties, most importantly that it is hard for the committer to compute its order. Potential examples include RSA and class groups. We also give efficient zero-knowledge protocols for proving knowledge of the contents of a commitment and for verifying multiplicative relations over the integers on committed values. This means that our scheme can support, for instance, the efficent interval proofs of Boudot. The scheme can be seen as a modification and a generalization of an earlier scheme of Fujisaki and Okamoto(FO), and in particular our results show that we can use a much larger class of RSA moduli than the safe prime products proposed by FO. Also, we correct some mistakes in the proofs of FO and give what appears to be the first multiplication protocol for a Fujisaki/Okamoto-like scheme with a complete proof of soundness.
2001
EPRINT
Analysis of chosen plaintext attacks on the WAKE Stream Cipher
Stream ciphers are an important class of encryption algorithms, which are widely used in practice. In this paper the security of the WAKE stream cipher is investigated. We present two chosen plaintext attacks on this cipher. The complexities of these attacks can be estimated as 10^^19.2 and 10^^14.4.
2001
EPRINT
IMPROVED PUBLIC KEY CRYPTOSYSTEM USING FINITE NON ABELIAN GROUPS
In the public key cryptosystem using finite non abelian groups which is suggested in CRYPTO 2001, the discrete logarithm problems in inner automorphism groups are used. In this paper, we generalize the system and give some examples of non abelian groups which is applicable to our system.
2001
EPRINT
An Attack on A Traitor Tracing Scheme
In Crypto'99, Boneh and Franklin proposed a public key traitor tracing scheme~\cite{Boneh}, which was believed to be able to catch all traitors while not accusing any innocent users (i.e., full-tracing and error-free). Assuming that Decision Diffie-Hellman problem is unsolvable in $G_{q}$, Boneh and Franklin proved that a decoder cannot distinguish valid ciphertexts from invalid ones that are used for tracing. However, our novel pirate decoder $P_{3}$ manages to make some invalid ciphertexts distinguishable without violating their assumption, and it can also frame innocent users to fool the tracer. Neither the single-key nor arbitrary pirate tracing algorithm presented in~\cite{Boneh} can identify all keys used by $P_{3}$ as claimed. Instead, it is possible for both algorithms to catch none of the traitors. We believe that the construction of our novel pirate also demonstrates a simple way to defeat some other black-box traitor tracing schemes in general.
2001
EPRINT
SQUARE Attacks on Reduced-Round PES and IDEA Block Ciphers
This paper reports on variants of the Square attack applied to reduced-round versions of the PES and IDEA block ciphers. Attacks on 2.5 rounds of IDEA require $3\cdot 2^{16}$ chosen-plaintexts and recover 78 key bits. A new kind of attack, the Square related-key attack, is applied on 2.5 rounds of IDEA and recovers 32 key bits, with 2 chosen-plaintexts and $2^{17}$ related keys. Similar results hold for 2.5 rounds of PES. Implementations of the attacks on 32-bit block mini-versions of both ciphers confirmed the expected computational complexity. Although our attacks do not improve on previous approaches, this report shows new variants of the Square attack on word-oriented block ciphers like IDEA and PES.
2001
EPRINT
On the (Im)possibility of Obfuscating Programs
Informally, an {\em obfuscator} $O$ is an (efficient, probabilistic) ``compiler'' that takes as input a program (or circuit) $P$ and produces a new program $O(P)$ that has the same functionality as $P$ yet is ``unintelligible'' in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic and complexity-theoretic applications, ranging from software protection to homomorphic encryption to complexity-theoretic analogues of Rice's theorem. Most of these applications are based on an interpretation of the ``unintelligibility'' condition in obfuscation as meaning that $O(P)$ is a ``virtual black box,'' in the sense that anything one can efficiently compute given $O(P)$, one could also efficiently compute given oracle access to $P$. In this work, we initiate a theoretical investigation of obfuscation. Our main result is that, even under very weak formalizations of the above intuition, obfuscation is impossible. We prove this by constructing a family of functions $F$ that are {\em \inherently unobfuscatable} in the following sense: there is a property $\pi : F \rightarrow \{0,1\}$ such that (a) given {\em any program} that computes a function $f\in F$, the value $\pi(f)$ can be efficiently computed, yet (b) given {\em oracle access} to a (randomly selected) function $f\in F$, no efficient algorithm can compute $\pi(f)$ much better than random guessing. We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only {\em approximately} preserve the functionality, and (c) only need to work for very restricted models of computation ($TC_0$). We also rule out several potential applications of obfuscators, by constructing ``unobfuscatable'' signature schemes, encryption schemes, and pseudorandom function families.
2001
EPRINT
Security Assessment of Hierocrypt and Rijndael against the Differential and Linear Cryptanalysis (Extended Abstract)
The authors analyze the security of Hierocrypt-3(128-bit) and Hierocrypt-L1(64-bit) designed on the nested SPN(NSPN) structure against the differential and linear cryptanalysis, and found that they are sufficiently secure, e.g., the maximum average differential and linear hull probabilities (MACP and MALHP) are bounded by $2^{-96}$ for 4-round of Hierocrypt-3; those probabilities are bounded by $2^{-48}$ for 4-round of Hierocrypt-L1. The authors get these results by extending the provable security theorem by Hong et al.. Furthermore, the extended theory is applied to Rijndael, and found that MACP and MALHP of 4-round Rijndael are bounded by $2^{-96}$. This outperforms the best previous result by Keliher et al..
2001
EPRINT
Multi-Recipient Public-Key Encryption with Shortened Ciphertext
In the trivial $n$-recipient public-key encryption scheme, a ciphertext is a concatenation of independently encrypted messages for $n$ recipients. In this paper, we say that an $n$-recipient scheme has a ``{\it shortened ciphertext}'' property if the length of the ciphertext is almost a half (or less) of the trivial scheme and the security is still almost the same as the underlying single-recipient scheme. We first present (multi-plaintext, multi-recipient) schemes with the ``{\it shortened ciphertext}'' property for ElGamal scheme and Cramer-Shoup scheme. We next show (single-plaintext, multi-recipient) hybrid encryption schemes with the ``{\it shortened ciphertext}'' property.
2001
EPRINT
On the Goubin-Courtois Attack on TTM
In the paper [1] published in ``Asiacrypt 2000", L. Goubin and N.T. Courtois propose an attack on the TTM cryptosystem. In paper [1], they mispresent TTM cryptosystem. Then they jump an attack from an example of TTM to the general TTM cryptosystem. Finally they conclude:"There is very little hope that a secure triangular system (Tame transformation system in our terminology) will ever be proposed". This is serious challenge to many people working in the field. In this paper, we will show that their attack is full of gaps in section 5. Even their attack on one implementation of TTM is questionable. We write a lengthy introduction to restate TTM cryptosystem and point out many possible implementations. It will be clear that their attack on one implementation can not be generalized to attacks on other implementations. As one usually said: "truth is in the fine details", we quote and analysis their TPM system at the end of the introduction and $\S$ 2. We further state one implementations of TTM cryptosystem in $\S$ 3. We analysis their MiniRank(r) attack in $\S$ 4 and show that is infeasible. We conclude that the attack of [1] on the TTM cryptosystem is infeasible and full of gaps. There is no known attacks which can crack the TTM cryptosystem.
2001
EPRINT
Efficient oblivious transfer schemes
In this paper we propose a very efficient (string) $OT_n^1$ scheme for any $n\geq 2$. We build our $OT_n^1$ scheme from fundamental cryptographic techniques directly. It achieves optimal efficiency in the number of rounds and the total number of exchanged messages for the case that the receiver's choice is unconditionally secure. The computation time of our $OT_n^1$ scheme is very efficient, too. The receiver need compute 2 modular exponentiations only no matter how large $n$ is, and the sender need compute $2n$ modular exponentiations. Furthermore, the system-wide parameters need not change during the lifetime of the system and are {\em universally usable}. That is, all possible receivers and senders use the same parameters and need no trapdoors specific to each of them. For our $OT_n^1$ scheme, the privacy of the receiver's choice is unconditionally secure and the privacy of the un-chosen secrets is at least as strong as the hardness of the decisional Diffie-Hellman problem. \par We extend our $OT_n^1$ scheme to distributed oblivious transfer schemes. Our distributed $OT_n^1$ scheme takes full advantage of the research results of secret sharing and is conceptually simple. It achieves better security than Noar and Pinkas's scheme does in many aspects. For example, our scheme is secure against collusion of $R$ and $t$-$1$ servers and it need not restrict $R$ to contact at most $t$ servers, which is difficult to enforce. \par For applications, we present a method of transforming any single-database PIR protocol into a symmetric PIR protocol with only one extra unit of communication cost.
2001
EPRINT
On the Security of Randomized CBC-MAC Beyond the Birthday Paradox Limit - A New Construction
In this paper, we study the security of randomized CBC-MACs and propose a new construction that resists birthday paradox attacks and provably reaches full security. The size of the MAC tags in this construction is optimal, i.e., exactly twice the size of the block cipher. Up to a constant, the security of the proposed randomized CBC-MAC using an n-bit block cipher is the same as the security of the usual encrypted CBC-MAC using a 2n-bit block cipher. Moreover, this construction adds a negligible computational overhead compared to the cost of a plain, non-randomized CBC-MAC. We give a full standard proof of our construction using one pass of a block cipher with 2n-bit keys but there also is a proof for n-bit keys block ciphers in the ideal cipher model.
2001
EPRINT
Pseudo-Random Functions and Factoring
Factoring integers is the most established problem on which cryptographic primitives are based. This work presents an efficient construction of {\em pseudorandom functions} whose security is based on the intractability of factoring. In particular, we are able to construct efficient length-preserving pseudorandom functions where each evaluation requires only a {\em constant} number of modular multiplications per output bit. This is substantially more efficient than any previous construction of pseudorandom functions based on factoring, and matches (up to a constant factor) the efficiency of the best known factoring-based {\em pseudorandom bit generators}.
2001
EPRINT
Communication Complexity and Secure Function Evaluation
A secure function evaluation protocol allows two parties to jointly compute a function $f(x,y)$ of their inputs in a manner not leaking more information than necessary. A major result in this field is: ``any function $f$ that can be computed using polynomial resources can be computed securely using polynomial resources'' (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for $f$ to a secure protocol that evaluates $f$. Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of $f$. For the design of efficient secure protocols we suggest two new methodologies, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching program) representation of $f$. We start with an efficient (insecure) protocol for $f$ and transform it into a secure protocol. In other words, ``any function $f$ that can be computed using communication complexity $c$ can be can be computed securely using communication complexity that is polynomial in $c$ and a security parameter''. The second methodology uses the circuit computing $f$, enhanced with look-up tables as its underlying computational model. It is possible to simulate any RAM machine in this model with polylogarithmic blowup. Hence it is possible to start with a computation of $f$ on a RAM machine and transform it into a secure protocol. We show many applications of these new methodologies resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the ``millionaires problem'', where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation.
2001
EPRINT
A Time-Memory Tradeoff Attack Against LILI-128
In this note we discuss a novel but simple time-memory tradeoff attack against the stream cipher LILI-128. The attack defeats the security advantage of having an irregular stepping function. The attack requires $2^{46}$ bits of keystream, a lookup table of $2^{45}$ 89-bit words and computational effort which is roughly equivalent to $2^{48}$ DES operations.
2001
EPRINT
The COS Stream Ciphers are Extremely Weak
A new family of very fast stream ciphers called COS (for "crossing over system") has been proposed by Filiol and Fontaine, and seems to have been adopted for at least one commercial standard. In this note we show that the COS ciphers are very weak indeed ? it requires negligible effort to reconstruct the state of the keystream generator from a very small amount of known keystream.
2001
EPRINT
Authenticated Encryption in the Public-Key Setting: Security Notions and Analyses
This paper addresses the security of authenticated encryption schemes in the public key setting. We present two new notions of authenticity that are stronger than the integrity notions given in the symmetric setting \cite{bn00}. We also show that chosen-ciphertext attack security (IND-CCA) in the public key setting is not obtained in general from the combination of chosen-plaintext security (IND-CPA) and integrity of ciphertext (INT-CTXT), which is in contrast to the results shown in the symmetric setting \cite{ky00,bn00}. We provide security analyses of authenticated encryption schemes constructed by combining a given public key encryption scheme and a given digital signature scheme in a ``generic'' manner ---namely, Encrypt-and-Sign, Sign-then-Encrypt, and Encrypt-then-Sign--- and show that none of them, in general, provide security under all notions defined in this paper. We then present a scheme called {\em ESSR} that meets all security notions defined here. We also give security analyses on an efficient Diffie-Hellman based scheme called {\em DHETM}, which can be thought of as a transform of the encryption scheme ``DHIES'' \cite{abr01} into an {\em authenticated} encryption scheme in the public key setting.
2001
EPRINT
COS Ciphers are not "extremely weak"! - The Design Rationale of COS Ciphers
This note summarizes the results of Babbage's cryptanalysis of COS ciphers and shows that in fact COS ciphers are not weak as claimed. These ciphers have been designed according a novel concept of encryption directly determined by the context of use. This concept is here more precisely defined.
2001
EPRINT
A Sufficient Condition for Secure Ping--Pong Protocols
A sufficient condition for secure ping--pong protocols is repretsented. This condition, called \emph{name--suffixing}, is essentially to insert identities of participants in messages. We prove its sufficiency and discuss the feature of security in terms of name--suffixing.
2001
EPRINT
A Description of Protocols for Private Credentials
This document provides a short description of practical protocols for private credential systems. We explain the basic concepts and mechanisms behind issuing and showing of private credentials and e-cash. The goal is to describe concisely how practical private credential systems can be achieved and not to provide intuition or motivation for the technology; for information on these subjects, see [1,2,3]. We give the details of one specific type of practical protocols for private credentials; other choices of functionalities and optimizations are possible. The reader is assumed to have general knowledge of basic concepts of cryptography such as the Discrete Logarithm problem, basic group theory and hash functions. For security proofs and more elaborate descriptions of the techniques used we refer the reader to [2].
2001
EPRINT
On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound ${1\over\log_2(\sqrt{5}+1)}=0.5902...$ for the important ratio ${t\over t+k}$ of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of its parameters is equal to lower bound. By means of these matrices we construct $m$-resilient $n$-variable functions with maximum possible nonlinearity $2^{n-1}-2^{m+1}$ for $m=0.5902...n+O(\log_2 n)$. This result supersedes the previous record.
2001
EPRINT
Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree
In this paper, we analyze the Gaudry-Hess-Smart (GHS) Weil descent attack on the elliptic curve discrete logarithm problem (ECDLP) for elliptic curves defined over characteristic two finite fields of composite extension degree. For each such field $F_{2^N}$, $N \in [100,600]$, we identify elliptic curve parameters such that (i) there should exist a cryptographically interesting elliptic curve $E$ over $F_{2^N}$ with these parameters; and (ii) the GHS attack is more efficient for solving the ECDLP in $E(F_{2^N})$ than for solving the ECDLP on any other cryptographically interesting elliptic curve over $F_{2^N}$. We examine the feasibility of the GHS attack on the specific elliptic curves over $F_{2^{176}}$, $F_{2^{208}}$, $F_{2^{272}}$, $F_{2^{304}}$, and $F_{2^{368}}$ that are provided as examples inthe ANSI X9.62 standard for the elliptic curve signature scheme ECDSA. Finally, we provide several concrete instances of the ECDLP over $F_{2^N}$, $N$ composite, of increasing difficulty which resist all previously known attacks but which are within reach of the GHS attack.
2001
EPRINT
Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption
We present several new and fairly practical public-key encryption schemes and prove them secure against adaptive chosen ciphertext attack. One scheme is based on Paillier's Decision Composite Residuosity (DCR) assumption, while another is based in the classical Quadratic Residuosity (QR) assumption. The analysis is in the standard cryptographic model, i.e., the security of our schemes does not rely on the Random Oracle model. We also introduce the notion of a universal hash proof system. Essentially, this is a special kind of non-interactive zero-knowledge proof system for an NP language. We do not show that universal hash proof systems exist for all NP languages, but we do show how to construct very efficient universal hash proof systems for a general class of group-theoretic language membership problems. Given an efficient universal hash proof system for a language with certain natural cryptographic indistinguishability properties, we show how to construct an efficient public-key encryption schemes secure against adaptive chosen ciphertext attack in the standard model. Our construction only uses the universal hash proof systemas a primitive: no other primitives are required, although even more efficient encryption schemes can be obtained by using hash functions with appropriate collision-resistance properties. We show how to construct efficient universal hash proof systems for languages related to the DCR and QR assumptions. From these we get corresponding public-key encryption schemes that are secure under these assumptions. We also show that the Cramer-Shoup encryption scheme (which up until now was the only practical encryption scheme that could be proved secure against adaptive chosen ciphertext attack under a reasonable assumption, namely, the Decision Diffie-Hellman assumption) is also a special case of our general theory.
2001
EPRINT
Statistical Zero-Knowledge Proofs from Diophantine Equations
A family $(S_t)$ of sets is $p$-bounded Diophantine if $S_t$ has a representing $p$-bounded polynomial $R_{S,t}$, s.t. $x\in S_t \iff (\exists y)[R_{S}(x;y)=0]$. We say that $(S_t)$ is unbounded Diophantine if additionally, $R_{S,t}$ is a fixed $t$-independent polynomial. We show that $p$-bounded (resp., unbounded) Diophantine set has a polynomial-size (resp., constant-size) statistical zero-knowledge proof system that a committed tuple $x$ belongs to $S$. We describe efficient SZK proof systems for several cryptographically interesting sets. Finally, we show how to prove in SZK that an encrypted number belongs to $S$.
2001
EPRINT
A Linear Algebraic Approach to Metering Schemes
A metering scheme is a method by which an audit agency is able to measure the interaction between servers and clients during a certain number of time frames. Naor and Pinkas proposed metering schemes where any server is able to compute a proof, i.e., a value to be shown to the audit agency at the end of each time frame, if and only if it has been visited by a number of clients larger than or equal to some threshold $h$ during the time frame. Masucci and Stinson showed how to construct a metering scheme realizing any access structure, where the access structure is the family of all subsets of clients which enable a server to compute its proof. They also provided lower bounds on the communication complexity of metering schemes. In this paper we describe a linear algebraic approach to design metering schemes realizing any access structure. Namely, given any access structure, we present a method to construct a metering scheme realizing it from any linear secret sharing scheme with the same access structure. Besides, we prove some properties about the relationship between metering schemes and secret sharing schemes. These properties provide some new bounds on the information distributed to clients and servers in a metering scheme. According to these bounds, the optimality of the metering schemes obtained by our method relies upon the optimality of the linear secret sharing schemes for the given access structure.
2001
EPRINT
Improving the trade-off between storage and communication in broadcast encryption schemes
The most important point in the design of broadcast encryption schemes (BESs) is obtain a good trade-off between the amount of secret information that must be stored by every user and the length of the broadcast message, which are measured, respectively, by the information rate $\rho$ and the broadcast information rate $\rho_B$. In this paper we present a simple method to combine two given BESs in order to improve the trade-off between $\rho$ and $\rho_B$ by finding BESs with good information rate $\rho$ for arbitrarily many different values of the broadcast information rate $\rho_B$. We apply this technique to threshold $(R,T)$-BESs and we present a method to obtain, for every rational value $1/R \le \rho_B \le 1$, a $(R,T)$-BES with optimal information rate $\rho$ among all $(R,T)$-BESs that can be obtained by combining two of the $(R,T)$-BESs proposed by Blundo et al.
2001
EPRINT
Linear broadcast encryption schemes
A new family of broadcast encryption schemes (BESs), which will be called linear broadcast encryption schemes (LBESs), is presented in this paper by using linear algebraic techniques. This family generalizes most previous proposals and provide a general framework to the study of broadcast encryption schemes. We present a method to construct LBESs for a general specification structure in order to find schemes that fit in situations that have not been considered before.
2001
EPRINT
Identity Based Encryption From the Weil Pairing
We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.
2001
EPRINT
Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor
Canetti and Fischlin have recently proposed the security notion {\em universal composability} for commitment schemes and provided two examples. This new notion is very strong. It guarantees that security is maintained even when an unbounded number of copies of the scheme are running concurrently, also it guarantees non-malleability, resilience to selective decommitment, and security against adaptive adversaries. Both of their schemes uses $\Theta(k)$ bits to commit to one bit and can be based on the existence of trapdoor commitments and non-malleable encryption. We present new universally composable commitment schemes based on the Paillier cryptosystem and the Okamoto-Uchiyama cryptosystem. The schemes are efficient: to commit to $k$ bits, they use a constant number of modular exponentiations and communicates $O(k)$ bits. Further more the scheme can be instantiated in either perfectly hiding or perfectly binding versions. These are the first schemes to show that constant expansion factor, perfect hiding, and perfect binding can be obtained for universally composable commitments. We also show how the schemes can be applied to do efficient zero-knowledge proofs of knowledge that are universally composable.
2001
EPRINT
BDD-based Cryptanalysis of Keystream Generators
Many of the keystream generators which are used in practice are LFSR-based in the sense that they produce the keystream according to a rule $y=C(L(x))$, where $L(x)$ denotes an internal linear bitstream, produced by a small number of parallel linear feedback shift registers (LFSRs), and $C$ denotes some nonlinear compression function. We present an $n^{O(1)} 2^{(1-\alpha)/(1+\alpha)n}$ time bounded attack, the FBDD-attack, against LFSR-based generators, which computes the secret initial state $x\in\booln$ from $cn$ consecutive keystream bits, where $\alpha$ denotes the rate of information, which $C$ reveals about the internal bitstream, and $c$ denotes some small constant. The algorithm uses Free Binary Decision Diagrams (FBDDs), a data structure for minimizing and manipulating Boolean functions. The FBDD-attack yields better bounds on the effective key length for several keystream generators of practical use, so a $0.656n$ bound for the self-shrinking generator, a $0.6403 n$ bound for the A5/1 generator, used in the GSM standard, a $0.6n$ bound for the $E_0$ encryption standard in the one level mode, and a $0.8823n$ bound for the two-level $E_0$ generator used in the Bluetooth wireless LAN system.
2001
EPRINT
Threshold Cryptosystems Based on Factoring
We consider threshold cryptosystems over a composite modulus $N$ where the \emph{factors} of $N$ are shared among the participants as the secret key. This is a new paradigm for threshold cryptosystems based on a composite modulus, differing from the typical treatment of RSA-based systems where a ``decryption exponent'' is shared among the participants. Our approach yields solutions to some open problems in threshold cryptography; in particular, we obtain the following: 1. \emph{Threshold homomorphic encryption}. A number of applications (e.g., electronic voting or efficient multi-party computation) require threshold homomorphic encryption schemes. We present a protocol for threshold decryption of the homomorphic Goldwasser-Micali encryption scheme \cite{GM84}, answering an open question of \cite{FPS00}. 2. \emph{Threshold cryptosystems as secure as factoring}. We describe a threshold version of a variant of the signature standards ISO 9796-2 and PKCS\#1 v1.5 (cf.\ \cite[Section 11.3.4]{MvOV}), thus giving the first threshold signature scheme whose security (in the random oracle model) is equivalent to the hardness of factoring \cite{C02}. Our techniques may be adapted to distribute the Rabin encryption scheme \cite{R79} whose semantic security may be reduced to the hardness of factoring. 3. \emph{Efficient threshold schemes without a trusted dealer.} Because our schemes only require sharing of $N$ --- which furthermore need not be a product of strong primes --- our schemes are very efficient (compared to previous schemes) when a trusted dealer is not assumed and key generation is done in a distributed manner. Extensions to achieve robustness and proactivation are also possible with our schemes.
2001
EPRINT
Slope packings and coverings, and generic algorithms for the discrete logarithm problem
We consider the set of slopes of lines formed by joining all pairs of points in some subset S of a Desarguesian affine plane of prime order, p. If all the slopes are distinct and non-infinite, we have a slope packing; if every possible non-infinite slope occurs, then we have a slope covering. We review and unify some results on these problems that can be derived from the study of Sidon sets and sum covers. Then we report some computational results we have obtained for small values of p. Finally, we point out some connections between slope packings and coverings and generic algorithms for the discrete logarithm problem in prime order (sub)groups. Our results provide a combinatorial characterization of such algorithms, in the sense that any generic algorithm implies the existence of a certain slope packing or covering, and conversely.
2001
EPRINT
Secure Vickrey Auctions without Threshold Trust
We argue that threshold trust is not an option in most of the real-life electronic auctions. We then propose two new cryptographic Vickrey auction schemes that involve, apart from the bidders and the seller $S$, an auction authority $A$ so that unless $S$ and $A$ collude the outcome of auctions will be correct, and moreover, $S$ will not get any information about the bids, while $A$ will learn bid statistics. Further extensions make it possible to decrease damage that colluding $S$ and $A$ can do, and to construct $(m+1)$st price auction schemes. The communication complexity between the $S$ and $A$ in medium-size auctions is at least one order of magnitude less than in the Naor-Pinkas-Sumner scheme.
2001
EPRINT
Constructing elliptic curves with a given number of points over a finite field
In using elliptic curves for cryptography, one often needs to construct elliptic curves with a given or known number of points over a given finite field. In the context of primality proving, Atkin and Morain suggested the use of the theory of complex multiplication to construct such curves. One of the steps in this method is the calculation of the Hilbert class polynomial $H_D(X)$ modulo some integer $p$ for a certain fundamental discriminant $D$. The usual way of doing this is to compute $H_D(X)$ over the integers and then reduce modulo $p$. But this involves computing the roots with very high accuracy and subsequent rounding of the coefficients to the closest integer. (Such accuracy issues also arise for higher genus cases.) We present a modified version of the Chinese remainder theorem (CRT) to compute $H_D(X)$ modulo $p$ directly from the knowledge of $H_D(X)$ modulo enough small primes. Our algorithm is inspired by Couveigne's method for computing square roots in the number field sieve, which is useful in other scenarios as well. It runs in heuristic expected time less than the CRT method in [CNST]. Moreover, our method requires very few digits of precision to succeed, and avoids calculating the exponentially large coefficients of the Hilbert class polynomial over the integers.
2001
EPRINT
An Efficient MAC for Short Messages
HMAC is the internet standard for message authentication. What distinguishes HMAC from other MAC algorithms is that it provides proofs of security assuming that the underlying cryptographic hash (e.g. SHA-1) has some reasonable properties. HMAC is efficient for long messages, however, for short messages the nested construction results in a significant inefficiency. For example to MAC a message shorter than a block, HMAC requires at least two calls to the compression function rather than one. This inefficiency may be particularly high for some applications, like message authentication of signaling messages, where the individual messages may all fit within one or two blocks. Also for TCP/IP traffic it is well known that large number of packets (e.g. acknowledgment) have sizes around 40 bytes which fit within a block of most cryptographic hashes. We propose an enhancement that allows both short and long messages to be message authenticated more efficiently than HMAC while also providing proofs of security. In particular, for a message smaller than a block our MAC only requires one call to the compression function.
2001
EPRINT
Fast hashing onto elliptic curves over fields of characteristic 3
We describe a fast hash algorithm that maps arbitrary messages onto points of an elliptic curve defined over a finite field of characteristic 3. Our new scheme runs in time $O(m^2)$ for curves over $\GF{3^m}$. The best previous algorithm for this task runs in time $O(m^3)$. Experimental data confirms the speedup by a factor $O(m)$, or approximately a hundred times for practical $m$ values. Our results apply for both standard and normal basis representations of $\GF{3^m}$.
2001
EPRINT
Linear Code Implies Public-Key Traitor Tracing
In this paper, we first show that three public-key $(k,n)$-traceability schemes can be derived from an $[n,u,d]$-linear code ${\cal C}$ such that $d \geq 2k+1$. The previous schemes are obtained as special cases. This observation gives a more freedom and a new insight to this field. For example, we show that Boneh-Franklin scheme is equivalent to a slight modification of the corrected Kurosawa-Desmedt scheme. This means that BF scheme is redundant or overdesigned because the modified KD scheme is much simpler. It is also shown that the corrected KD scheme is the best among them.
2001
EPRINT
A Note on Girault's Self-Certified Model
In this paper, we describe an important shortcoming of the first self-certified model proposed by Girault, that may be exploited by the authority to compute users' secret keys. We also show, while it is possible to make the attack ineffective by taking additional precautions, the resulting model loses all merits of the original model and does no longer meet the primary contribution of the self-certified notion.
2001
EPRINT
Quasi-Efficient Revocation of Group Signatures
A group signature scheme allows any group member to sign on behalf of the group in an anonymous and unlinkable fashion. In the event of a dispute, a designated trusted entity can reveal the identity of the signer. Group signatures are claimed to have many useful applications such as voting and electronic cash. A number of group signature schemes have been proposed to-date. However, in order for the whole group signature concept to become practical and credible, the problem of secure and efficient group member revocation must be addressed. In this paper, we construct a new revocation method for group signatures based on the signature scheme by Ateniese et al. at Crypto 2000. This new method represents an advance in the state-of-the-art since the only revocation schemes proposed thus far are either: 1) based on implicit revocation and the use of fixed time periods, or 2) require the signature size to be linear in the number of revoked members. Our method, in contrast, does not rely on time periods, offers constant-length signatures and constant work for the signer.
2001
EPRINT
An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT is well-suited for generating large, random prime numbers since on a random input number, it takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability. EQFT extends QFT by verifying additional algebraic properties related to the existence of elements of order 3 and 4. We obtain a simple closed expression that upper bounds the probability of acceptance for any input number. This in turn allows us to give strong bounds on the average-case behaviour of the test: consider the algorithm that repeatedly chooses random odd $k$ bit numbers, subjects them to $t$ iterations of our test and outputs the first one found that passes all tests. We obtain numeric upper bounds for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most $2^{-143}$ for $k=500, t=2$. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point. While EQFT is slower than the average case on a small set of inputs, we present a variant that is always fast, i.e.takes time about 2 Miller-Rabin tests. The variant has slightly larger worst case error probability than EQFT, but still improves on previous proposed tests.
2001
EPRINT
Countermeasures against Side-Channel Attacks for Elliptic Curve Cryptosystems
Some attacks on cryptographic systems exploit the leakage of information through so-called ``side channels'', such as power consumption or time employed by a computation. For cryptosystems involving an exponentiation, a few possible countermeasures are suggested. In the case of elliptic curves over a binary finite field, we show how to split point addition into two blocks which, through the addition of a little overhead, can be made undistinguishable from a point doubling. This allows the whole exponentiation process to be performed as a sequence of homogeneous steps. To add some randomization to the exponentiation process in the ECC case, we suggest the use of points of small order, computed on the fly. This presents some disadvantages over known methods, but allows to avoid the storage of points in non-volatile RAM. A multiplicative variation of ``additive exponent blinding'' is suggested. This involves a two-phase exponentiation and is valid both for discrete log and RSA settings. Computer experiments implementing some of these ideas are described and analyzed.
2001
EPRINT
Concurrent Zero-Knowledge With Timing, Revisited
Following Dwork, Naor, and Sahai (30th STOC, 1998), we consider concurrent execution of protocols in a semi-synchronized network. Specifically, we assume that each party holds a local clock such that a constant bound on the relative rates of these clocks is a-priori known, and consider protocols that employ time-driven operations (i.e., time-out in-coming messages and delay out-going messages). We show that the constant-round zero-knowledge proof for NP of Goldreich and Kahan (Jour. of Crypto., 1996) preserves its security when polynomially-many independent copies are executed concurrently under the above timing model. We stress that our main result establishes zero-knowledge of interactive proofs, whereas the results of Dwork et al. are either for zero-knowledge arguments or for a weak notion of zero-knowledge (called $\epsilon$-knowledge) proofs. Our analysis identifies two extreme schedulings of concurrent executions under the above timing model: the first is the case of parallel execution of polynomially-many copies, and the second is of concurrent execution of polynomially-many copies such the number of copies that are simultaneously active at any time is bounded by a constant (i.e., bounded simultaneity). Dealing with each of these extreme cases is of independent interest, and the general result (regarding concurrent executions under the timing model) is obtained by combining the two treatments.
2001
EPRINT
Universal Arguments and their Applications
We put forward a new type of computationally-sound proof systems, called universal-arguments, which are related but different from both CS-proofs (as defined by Micali) and arguments (as defined by Brassard, Chaum and Crepeau). In particular, we adopt the instance-based prover-efficiency paradigm of CS-proofs, but follow the computational-soundness condition of argument systems (i.e., we consider only cheating strategies that are implementable by polynomial-size circuits). We show that universal-arguments can be constructed based on standard intractability assumptions that refer to polynomial-size circuits (rather than assumptions referring to subexponential-size circuits as used in the construction of CS-proofs). As an application of universal-arguments, we weaken the intractability assumptions used in the recent non-black-box zero-knowledge arguments of Barak. Specifically, we only utilize intractability assumptions that refer to polynomial-size circuits (rather than assumptions referring to circuits of some ``nice'' super-polynomial size).
2001
EPRINT
Cryptanalysis of the COS (2,128) Stream Ciphers
A new family of very fast stream ciphers called COS (for ?crossing over system?) has been proposed by Filiol and Fontaine, and seems to have been adopted for at least one commercial standard. COS(2,128) Mode I and COS(2,128) Mode II are particular members of this family for which the authors proposed a cryptanalysis challenge. The ciphers accept secret keys of 256, 192 or 128 bits. In this note we cryptanalyse both of these ciphers, using a small amount of known keystream ? with negligible effort in the case of Mode II, and with effort well below that required for a single DES key search in the case of Mode I.
2001
EPRINT
Parallel Coin-Tossing and Constant-Round Secure Two-Party Computation
In this paper we show that any {\em two-party} functionality can be securely computed in a {\em constant number of rounds}, where security is obtained against malicious adversaries that may arbitrarily deviate from the protocol specification. This is in contrast to Yao's constant-round protocol that ensures security only in the face of semi-honest adversaries, and to its malicious adversary version that requires a polynomial number of rounds. In order to obtain our result, we present a constant-round protocol for secure coin-tossing of polynomially many coins (in parallel). We then show how this protocol can be used in conjunction with other existing constructions in order to obtain a constant-round protocol for securely computing any two-party functionality. On the subject of coin-tossing, we also present a constant-round {\em perfect} coin-tossing protocol, where by ``perfect'' we mean that the resulting coins are guaranteed to be statistically close to uniform (and not just pseudorandom).