International Association for Cryptologic Research

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2012-04-30
18:17 [Pub][ePrint]

In Secure Message Transmission (SMT) problem, a sender $\\cal S$ is connected to a

receiver $\\cal R$ through $N$ node disjoint bidirectional paths in the network, $t$ of

which are controlled by an adversary with \\textit{unlimited computational power}.

$\\cal{S}$ wants to send a message $m$ to $\\cal{R}$ in a \\textit{reliable} and \\textit{private} way. It is proved that SMT is possible if and only if $N\\ge2t+1$. In Reliable Message Transmission (RMT) problem, the network setting is the same and the goal is to provide reliability for communication, only.

In this paper we focus on 1-round $\\delta$-RMT and $(0,\\delta)$-SMT where the chance of protocol failure (receiver cannot decode the sent message) is at most $\\delta$, and in the case of SMT, privacy is perfect.

We propose a new approach to the construction of 1-round $\\delta$-RMT and (0, $\\delta$)-SMT for all connectivities $N \\ge 2t+1$, using list decodable codes and message authentication codes. Our concrete constructions use folded Reed-Solomon codes and multireceiver message authentication codes. The protocols have optimal transmission rates and provide the highest reliability among all known comparable protocols. Important advantages of these constructions are, (i) they can be adapted to all connectivities, and (ii) have simple and direct security (privacy and reliability) proofs using properties of the underlying codes, and $\\delta$ can be calculated from parameters of the underlying codes.

We discuss our results in relation to previous work in this area and propose directions for future research.

18:17 [Pub][ePrint]

We implement asymmetric pairings derived from Kachisa-Schaefer-Scott (KSS), Barreto-Naehrig (BN), and Barreto-Lynn-Scott (BLS) elliptic curves at the 192-bit security level. Somewhat surprisingly, we find pairings derived from BLS curves with embedding degree 12 to be the fastest for our serial as well as our parallel implementations. Our serial implementations provide a factor-3 speedup over the previous state-of-the-art, demonstrating that pairing computation at the 192-bit security level is not as expensive as previously thought. We also present a general framework for deriving a Weil-type pairing that is well-suited for computing a single pairing on a multi-processor machine.

18:17 [Pub][ePrint]

Hummingbird-2 is one recent design of lightweight block ciphers targeting constraint devices, which not only enables a compact hardware implementation and ultra-low power consumption but also meets the stringent response time as specified in ISO18000-6C.

In this paper, we present the first cryptanalytic result on the full version of this cipher using two pairs of related keys. We discover that the differential sequences for the last invocation of the round function can be computed by running the full cipher, due to which the search space for the key can be reduced. Base upon this observation, we propose a probabilistic attack encompassing two phases, preparation phase and key recovery phase. The preparation phase, requiring $2^{80}$ effort in time, aims to reach an internal state, with $0.5$ success probability, that satisfies particular conditions. In the key recovery phase, by attacking the last invocation of the round function of the encryption (decryption resp.) using the proposed differential sequence analysis (DSA), we are able to recover $36$ bits (another $44$ bits resp.) of the $128$-bit key. In addition, the rest $48$ bits of the key can be exhaustively searched and the overall time complexity of the key recovery phase is $2^{49.63}$.

Note that the proposed attack, though exhibiting an interesting tradeoff between the success probability and time complexity, is only of a theoretical interest at the moment and does not affect the security of the Hummingbird-2 in practice.

18:17 [Pub][ePrint]

Collision resistance is a fundamental property required for cryptographic hash functions. One way to ensure collision resistance is to use hash functions based on public key cryptography (PKC) which reduces collision resistance to a hard mathematical problem, but such primitives are usually slow. A more practical approach is to use symmetric-key design techniques which lead to faster schemes, but collision resistance can only be heuristically inferred from the best probability of a single differential characteristic path. We propose a new hash function design with variable hash output sizes of 128, 256, and 512 bits, that reduces this gap. Due to its inherent Substitution-Permutation Network (SPN) structure and JH mode of operation, we are able to compute its differential collision probability using the concept of differentials. Namely, for each possible input differences, we take into account all the differential paths leading to a collision and this enables us to prove that our hash function is secure against a differential collision attack using a single input difference. None of the SHA-3 finalists could prove such a resistance. At the same time, our hash function design is secure against pre-image, second pre-image and rebound attacks, and is faster than PKC-based hashes. Part of our design includes a generalization of the optimal diffusion used in the classical wide-trail SPN construction from Daemen and Rijmen, which leads to near-optimal differential bounds when applied to non-square byte arrays. We also found a novel way to use parallel copies of a serial matrix over the finite field GF(2^4), so as to create lightweight and secure byte-based diffusion for our design. Overall, we obtain hash functions that are fast in software, very lightweight in hardware (about 4625 GE for the $256$-bit hash output) and that provide much stronger security proofs regarding collision resistance than any of the SHA-3 finalists.

18:17 [Pub][ePrint]

The Ring-LWE problem, introduced by Lyubashevsky, Peikert, and Regev

(Eurocrypt 2010), has been steadily finding many uses in numerous

cryptographic applications. Still, the Ring-LWE problem defined

in [LPR10] involves the

fractional ideal $R^\\vee$, the dual of the ring $R$, which is the

source of many theoretical and implementation technicalities. Until

now, getting rid of $R^\\vee$, required some relatively complex

transformation that substantially increase the magnitude of the

error polynomial and the practical complexity to sample it.

It is only for rings $R=\\Z[X]/(X^n+1)$ where $n$ a power of

$2$, that this transformation is simple and benign.

In this work we show that by applying a different, and much simpler

transformation, one can transfer the results from [LPR10] into an easy-to-use\'\' Ring-LWE setting ({\\em i.e.} without the dual ring $R^\\vee$), with only a very

slight increase in the magnitude of the noise coefficients.

Additionally, we show that creating the correct noise distribution

can also be simplified by generating a Gaussian distribution over a

particular extension ring of $R$, and then performing a reduction

modulo $f(X)$. In essence, our results show that one does not need

to resort to using any algebraic structure that is more complicated

than polynomial rings in order to fully utilize the hardness of the

Ring-LWE problem as a building block for cryptographic applications.

18:17 [Pub][ePrint]

We exhibit the precise security guarantees that a public key encryption scheme needs to satisfy to guarantee ballot privacy when used in a large class of voting systems. We also identify new security notions for public key encryption that characterize the number of times that a public key can be used in different elections, and show that the most common ballot preparation approach that consists in encrypting the vote and adding a NIZK proof of its validity is sound, even without hardwiring the voter identity in the proof. Our results provide important steps towards proving the privacy of the ballot submission procedure in the widely deployed Helios voting system.

18:17 [Pub][ePrint]

We present in these papers a scheme, which bypasses the weakness presented in the existed scheme of IBE with random oracle. We propose, a secure scheme which project into Zp contrary to elliptic

curve as with Boneh and Franklin. More, our scheme is basing in its study of simulation in the problem 4-EBDHP which is more efficient than q-BDHIP used by Skai Kasarah. We provide the prove of security of our scheme and we show its efficiency by comparison with the scheme declared

above. Even if it we have a little cost in complexity, but as in the field cryptography we are more interested to the security, this makes our proposition more efficient.

18:17 [Pub][ePrint]

The hash function Skein is one of the five finalists of the NIST SHA-3 competition;it is based on the block cipher Threefish which only uses three primitive operations: modular addition, rotation and bitwise XOR (ARX). This paper studies the boomerang attacks on Skein-512. Boomerang distinguishers on the compression function reduced to 32 and 36 rounds are proposed, with complexities 2^{104.5} and 2^{454} respectively. Examples of the distinguishers on 28-round and 31-round are also given. In addition, the boomerang distinguishers are applicable to the key-recovery attacks on reduced Threefish-512. The complexities for key-recovery attacks reduced to 32-/33-/34-round are about 2^{181}, 2^{305} and 2^{424}. Because Laurent et al. [14] pointed out that the previous boomerang distinguishers for Threefish-512 are in fact not compatible, our attacks are the first valid boomerang attacks for the final round Skein-512.

18:17 [Pub][ePrint]

In~\\cite{SSH} a Zero-Knowledge scheme $ZK(2)$ was designed from a solution of a set of multivariate quadratic equations over a finite field. In this paper we will give two methods to generalize this construction for polynomials of any degree $d$, i.e. we will design two Zero-Knowledge schemes $ZK(d)$ and $\\tilde {ZK}(d)$ from a set of polynomial equations of degree $d$. We will show that $\\tilde {ZK} (d)$ is optimal in term of the number of computations to be performed and that $ZK(d)$ is optimal in term of the number of bits to be send. Moreover this

property is still true for all kinds of polynomials: for example if the polynomials are sparse or dense. Finally, we will present two examples of applications: with

Brent equations, or with morphisms of polynomials.

18:17 [Pub][ePrint]

BGV-style homomorphic encryption schemes over polynomial rings, rely for their security on rings of very large dimension. This large dimension is needed because of the large modulus-to-noise ratio in the key-switching matrices that are used for the top few levels of the evaluated circuit. However, larger noise (and hence smaller modulus-to-noise ratio) is used in lower levels of the circuit, so from a security standpoint it is permissible to switch to lower-dimension rings. Switching to a smaller ring, if possible, can help speeding up the homomorphic operations for the lower levels of the circuit. However, implementing such ring-switching is nontrivial, since these schemes rely on the ring algebraic structure for their homomorphic properties.

A basic ring-switching operation was introduced by Brakerski, Gentry and Vaikuntanathan, in the context of bootstrapping over polynomial rings of the form $\\Z[X]/(X^{2^n}+1)$. In this work we first extend this technique to work over any cyclotomic ring. Then we build on the extended technique and show how it can be used not only for bootstrapping but also during the computation itself, in conjunction with the packed ciphertext\'\' techniques of Gentry, Halevi and Smart.

18:17 [Pub][ePrint]

I propose the new key distribution system and attribute-based encryption scheme on non-commutative ring where the complexity required for enciphering and deciphering is small. As in this system encryption keys and decryption keys involve the attributes of each user, the system is adaptive for cloud computing systems. The security of this system is based on the complexity for solving the multivariate algebraic equations of high degree over finite field, that is, one of NP complete problems. So this system is immune from the Gröbner basis attacks. The key size of this system becomes to be small enough to handle.