Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures

In this paper, we address the problem of achieving efficient code-based digital signatures with small public keys. The solution we propose exploits sparse syndromes and randomly designed low-density generator matrix codes. Based on our evaluations, the proposed scheme is able to outperform existing solutions, permitting to achieve considerable security levels with very small public keys.Comment: 16 pages. The final publication is available at springerlink.co

Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes

We present here a new family of trapdoor one-way Preimage Sampleable Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is one-way under two computational assumptions: the hardness of generic decoding for high weights and the indistinguishability of generalized $(U,U+V)$-codes. Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we ensure the proper distribution for the trapdoor inverse output. The domain sampling property of our family is ensured by using and proving a variant of the left-over hash lemma. We instantiate the new Wave-PSF family with ternary generalized $(U,U+V)$-codes to design a "hash-and-sign" signature scheme which achieves existential unforgeability under adaptive chosen message attacks (EUF-CMA) in the random oracle model. For 128 bits of classical security, signature sizes are in the order of 15 thousand bits, the public key size in the order of 4 megabytes, and the rejection rate is limited to one rejection every 10 to 12 signatures.Comment: arXiv admin note: text overlap with arXiv:1706.0806

An Efficient Attack on All Concrete KKS Proposals

International audienceKabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on a couple of random error-correcting codes. A variation of this scheme was proposed recently and was proved to be EUF-1CMA secure in the random oracle model. In this paper we investigate the security of these schemes and suggest a simple attack based on (essentially) Stern's algorithm for finding low weight codewords. It efficiently recovers the private key of all schemes of this type existing in the literature. This is basically due to the fact that we can define a code from the available public data with unusual properties: it has many codewords whose support is concentrated in a rather small subset. In such a case, Stern's algorithm performs much better and we provide a theoretical analysis substantiating this claim. Our analysis actually shows that the insecurity of the proposed parameters is related to the fact that the rates of the couple of random codes used in the scheme were chosen to be too close. This does not compromise the security of the whole KKS scheme. It just points out that the region of weak parameters is really much larger than previously thought

A digital signature scheme based on random error-correcting codes

Over the past years there have been few attempts to construct digital signature schemes based on the intractability of the decoding of linear error-correcting codes. Unfortunately all these attempts failed. In this paper we suggest a new approach based on a seemingly unknown before fact that the set of correctable syndroms being nonlinear nevertheless contains a rather large linear subspace

On the construction of universal families of hash functions via geometric codes and concatenation

In this paper we use coding theory to give simple explanations of some recent results on universal hashing. We first apply our approach to give a precise and elegant analysis of the Wegman-Carter construction for authentication codes. Using Reed-Solomon codes and the well known concept of concatenated codes we can then give some new constructions, which require much less key size than previously known constructions. The relation to coding theory allows the use of codes from algebraic curves for the construction of hash functions. Particularly, we show how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield good classes of universal hash functions

Software performance of universal hash functions

Abstract. This paper compares the parameters sizes and software performance of several recent constructions for universal hash functions: bucket hashing, polynomial hashing, Toeplitz hashing, division hashing, evaluation hashing, and MMH hashing. An objective comparison between these widely varying approaches is achieved by defining constructions that offer a comparable security level. It is also demonstrated how the security of these constructions compares favorably to existing MAC algorithms, the security of which is less understood.

Identity-based Encryption from Codes with Rank Metric

International audienceCode-based cryptography has a long history, almost as long as the history of public-key encryption (PKE). While we can construct almost all primitives from codes such as PKE, signature, group signature etc, it is a long standing open problem to construct an identity-based encryption from codes. We solve this problem by relying on codes with rank metric. The concept of identity-based encryption (IBE), introduced by Shamir in 1984, allows the use of users' identifier information such as email as public key for encryption. There are two problems that makes the design of IBE extremely hard: the requirement that the public key can be an arbitrary string and the possibility to extract decryption keys from the public keys. In fact, it took nearly twenty years for the problem of designing an efficient method to implement an IBE to be solved. The known methods of designing IBE are based on different tools: from elliptic curve pairings by Sakai, Ohgishi and Kasahara and by Boneh and Franklin in 2000 and 2001 respectively; from the quadratic residue problem by Cocks in 2001; and finally from the Learning-with-Error problem by Gentry, Peikert, and Vaikuntanathan in 2008. Among all candidates for post-quantum cryptography, there only exist thus lattice-based IBE. In this paper, we propose a new method, based on the hardness of learning problems with rank metric, to design the first code-based IBE scheme. In order to overcome the two above problems in designing an IBE scheme, we first construct a rank-based PKE, called RankPKE, where the public key space is dense and thus can be obtained from a hash of any identity. We then extract a decryption key from any public key by constructing an trapdoor function which relies on RankSign-a signature scheme from PQCrypto 2014. In order to prove the security of our schemes, we introduced a new problem for rank metric: the Rank Support Learning problem (RSL). A high technical contribution of the paper is devoted to study in details the hardness of the RSL problem