International Association for Cryptologic Research

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2012-12-10
13:17 [Pub][ePrint]

In the setting of secure multiparty computation, a set of parties wish to compute a joint function of their inputs, while preserving properties like privacy, correctness, and independence of inputs. One security property that has typically not been considered in the past relates to the length or size of the parties inputs. This is despite the fact that in many cases the size of a party\'s input can be confidential. The reason for this omission seems to have been the folklore belief that, as with encryption, it is impossible to carry out non-trivial secure computation while hiding the size of parties\' inputs. However some recent results (e.g., Ishai and Paskin at TCC 2007, Ateniese, De Cristofaro and Tsudik at PKC 2011) showed that it is possible to hide the input size of one of the parties for some limited class of functions, including secure two-party set intersection. This suggests that the folklore belief may not be fully accurate.

In this work, we initiate a theoretical study of input-size hiding secure computation, and focus on the two-party case. We present definitions for this task, and deal with the subtleties that arise in the setting where there is no a priori polynomial bound on the parties\' input sizes. Our definitional study yields a multitude of classes of input-size hiding computation, depending on whether a single party\'s input size remains hidden or both parties\' input sizes remain hidden, and depending on who receives output and if the output size is hidden from a party in the case that it does not receive output. We prove feasibility and impossibility results for input-size hiding secure two-party computation. Some of the highlights are as follows:

Under the assumption that fully homomorphic encryption (FHE) exists, there exist non-trivial functions (e.g., the millionaire\'s problem) that can be securely computed while hiding the input size of both parties.

Under the assumption that FHE exists, every function can be securely computed while hiding the input size of one party, when both parties receive output (or when the party not receiving output does learn the size of the output). In the case of functions with fixed output length, this implies that every function can be securely computed while hiding one party\'s input size.

There exist functions that cannot be securely computed while hiding both parties\' input sizes. This is the first formal proof that, in general, some information about the size of the parties\' inputs must be revealed.

Our results are in the semi-honest model. The problem of input-size hiding is already challenging in this scenario. We discuss the additional difficulties that arise in the malicious setting and leave this extension for future work.

13:17 [Pub][ePrint]

We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over

every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure

the proofs for the existence of ideal secret sharing schemes for them.

13:17 [Pub][ePrint]

The stream cipher WG-7 is a lightweight variant of the well-known Welch-Gong (WG) stream cipher family, targeting for resource-constrained devices like RFID tags, smart cards, and wireless sensor nodes. Recently, a distinguishing attack was discovered against the stream cipher WG-7 by Orumiehchiha, Pieprzyk and Steinfeld. In this paper, we

extend their work to a general distinguishing attack and suggest criteria to protect the WG stream cipher family from this attack. Our analysis shows that by properly choosing the minimal polynomial of the linear feedback shift register for a WG stream cipher, the general distinguishing attack can be easily thwarted.

13:17 [Pub][ePrint]

For data storage outsourcing services, it is important to allow data owners to efficiently and securely verify that the storage sever stores their data correctly. To address this issue, several proof-of-retrievability(POR) schemes have been proposed wherein a storage sever must prove to a verifier that all of a client\'s data is stored correctly. While existing POR schemes offer decent solutions addressing various practical issues, they either have a non-trivial (linear or quadratic) communication complexity, or only support private verication - only the data owner can verify the remotely stored data. It remains open to design a POR scheme that achieves both public verifiability and constant communication cost simultaneously.

In this paper, we solve this open problem and propose the first POR scheme with public verifiability and constant communication cost. In our proposed scheme, the message exchanged between the prover and verifier is composed of a const number of the underlying group elements. Different from existing private POR construction, our scheme allows public verification and releases the data owners from burden of being staying online. Thorough analysis and experiments on Amazon S3 show that our proposed scheme is efficient and practical. We prove the security of our scheme based on Computational Diffie-Hellman Assumption, Strong Diffie-Hellman Assumption and Bilinear Strong Diffie-Hellman Assumption.

13:17 [Pub][ePrint]

Cryptanalytic time-memory trade-offs were introduced by Hellman in 1980 in order to perform key-recovery attacks on cryptosystems. A major advance was presented at Crypto 2003 by Oechslin, with the rainbow table variant that outperforms Hellman\'s seminal work.

This paper introduces the fingerprint tables, which drastically reduce the number of false alarms during the attack compared to the rainbow tables. The key point of our technique consists in storing in the tables the fingerprints of the chains instead of their endpoints. The fingerprint tables provide a time-memory trade-off that is about two times faster than the rainbow tables on usual problem sizes. We experimentally illustrate the performance of our technique, and demonstrate that it is faster than Ophcrack, a Windows LM Hash password cracker considered so far to be the fastest one ever implemented.

13:17 [Pub][ePrint]

In this article we describe new generic distinguishing and forgery attacks in the related-key scenario (using only a single related-key) for the HMAC construction. When HMAC uses a k-bit key, outputs an n-bit MAC, and is instantiated with an l-bit inner iterative hash function processing m-bit message blocks where m=k, our distinguishing-R attack requires about 2^{n/2} queries which improves over the currently best known generic attack complexity 2^{l/2} as soon as l>n. This means that contrary to the general belief, using wide-pipe hash functions as internal primitive will not increase the overall security of HMAC in the related-key model when the key size is equal to the message block size.

We also present generic related-key distinguishing-H, internal state recovery and forgery attacks. Our method is new and elegant, and uses a simple cycle-size detection criterion. The issue in the HMAC construction (not present in the NMAC construction) comes from the non-independence of the two inner hash layers and we provide a simple patch in order to avoid this generic attack. Our work finally shows that the choice of the opad and ipad constants value in HMAC is important.

13:17 [Pub][ePrint]

This paper presents a comprehensive study of the computation of square roots over finite extension fields.

We propose two novel algorithms for computing square roots over even field extensions

of the form $\\F_{q^{2}}$, with $q=p^n,$ $p$ an odd prime and $n\\geq 1$. Both algorithms have an associate

computational cost roughly equivalent to one exponentiation in $\\F_{q^{2}}$.

The first algorithm is devoted to the case when $q\\equiv 1 \\bmod 4$, whereas the second one handles the case when

$q\\equiv 3 \\bmod 4$. Numerical comparisons show that the two algorithms presented in this paper are competitive

and in some cases more efficient than the square root methods previously known.

13:17 [Pub][ePrint]

Gr{\\o}stl is one of the five finalists in the third round of SHA-3

competition hosted by NIST. In this paper, we use many techniques to

improve the pseudo preimage attack on Gr{\\o}stl hash function, such

as subspace preimage attack and guess-and-determine technique. We

present improved pseudo preimage attacks on 5-round Gr{\\o}stl-256

and 8-round Gr{\\o}stl-512 respectively. The complexity of the above

two attacks are ($2^{239.90},2^{240.40}$) (in time and memory) and

($2^{499.50},2^{499}$) respectively. Furthermore, we propose pseudo

preimage attack and pseudo second preimage attack on 6-round

Gr{\\o}stl-256. The complexity of our 6-round pseudo preimage and

second preimage attack is ($2^{253.26},2^{253.67}$) and

($2^{251.0},2^{252.0}$) respectively. As far as we know, these are

the best known attacks on round-reduced Gr{\\o}stl hash function.

13:17 [Pub][ePrint]

Over the past decade bilinear maps have been used to build a large variety of cryptosystems.

In addition to new functionality, we have concurrently seen the emergence of many strong assumptions.

In this work, we explore how to build bilinear map cryptosystems under progressively weaker assumptions.

We propose $k$-BDH, a new family of progressively

weaker assumptions that generalizes the decisional bilinear

Diffie-Hellman (DBDH) assumption. We give evidence in the generic

group model that each assumption in our family is strictly weaker

than the assumptions before it. DBDH has been used for proving many

schemes secure, notably identity-based and functional encryption

schemes; we expect that our $k$-BDH will lead to generalizations of

many such schemes.

To illustrate the usefulness of our $k$-BDH family, we

construct a family of selectively secure Identity-Based Encryption (IBE) systems based on it. Our system can be viewed

as a generalization of the Boneh-Boyen IBE, however, the construction and proof require new ideas to

fit the family. We then extend our methods to produces hierarchical IBEs and CCA

security; and give a fully secure variant. In addition, we discuss the opportunities and challenges of building

new systems under our weaker assumption family.

13:17 [Pub][ePrint]

We use a variant of learning with errors (LWE) problem, a simple and direct extension of the original LWE problem to the case of a small secret, which we call

a small LWE problem (SLWE), to build a new simple and provably secure key exchange scheme. The basic idea behind the construction can be viewed as certain type of bilinear pairing with errors (PE). We build a more efficient implementation of our scheme using a similar LWE problem but solely based on matrices, and we extend our construction further using the ring LWE problem, where the provable security is based on the hardness of the ring LWE problem.

13:17 [Pub][ePrint]

A \\captcha is a puzzle that is easy for humans but hard to solve for computers.

A formal framework,

modelling \\captcha puzzles (as hard AI problems), was introduced by

Ahn, Blum, Hopper, and Langford (\\cite{AhnBHL03}, Eurocrypt 2003). Despite their

attractive features and wide adoption in practice, the use of \\captcha puzzles

for general cryptographic applications has been limited.

In this work, we explore various ways to formally model \\captcha puzzles and their human component

and

explore new applications for \\captcha. We show that by defining \\captcha with

it is possible to broaden \\captcha applicability, including using it to learning a machine\'s

secret internal state.\'\'

To facilitate this, we introduce

the notion of an human-extractable \\captcha, which we believe may be of independent interest.

We show that this type of \\captcha yields a \\emph{constant round} protocol for \\emph{fully}

concurrent non-malleable zero-knowledge. To enable this we also define and

construct a \\captcha -based commitment scheme which admits straight line\'\' extraction.

We also explore

\\captcha definitions in the setting of Universal Composability (UC). We show that there are two (incomparable) ways to

In particular, we show that in the so called

\\emph{indirect access model}, for every polynomial time functionality $\\calf$

there exists a protocol that UC-realizes $\\calf$ using human-extractable \\captcha, while for the so-called

\\emph{direct access model}, UC is impossible, even with the help of human-extractable \\captcha.

The security of our constructions using human-extractable \\captcha

is proven against the (standard) class of

all polynomial time adversaries. In contrast, most previous works guarantee

security only against a very limited class of adversaries, called the