. A zero knowledge identification scheme based on the q-ary SD problem. Selected Areas in Cryptography, Aug 2010, Waterloo, Canada. pp.171-186, 10.1007 A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem Abstract. At CRYPTO'93, Stern proposed a 3-pass code-based identification scheme with a cheating probability of 2/3. In this paper, we propose a 5-pass code-based protocol with a lower communication complexity, allowing an impersonator to succeed with only a probability of 1/2. Furthermore, we propose to use double-circulant construction in order to dramatically reduce the size of the public key. The proposed scheme is zero-knowledge and relies on an NP-complete coding theory problem (namely the q-ary Syndrome Decoding problem). The parameters we suggest for the instantiation of this scheme take into account a recent study of (a generalization of) Stern's information set decoding algorithm, applicable to linear codes over arbitrary fields Fq; the public data of our construction is then 4 Kbytes, whereas that of Stern's scheme is 15 Kbytes for the same level of security. This provides a very practical identification scheme which is especially attractive for light-weight cryptography.

Abstract.As it is often the case in public-key cryptography, the first practical identification schemes were based on hard problems from number theory (factoring, discrete logarithms). The security of the proposed scheme depends on an NPcomplete problem from the theory of error correcting codes: the syndrome decoding problem which relies on the hardness of decoding a binary word of given weight and given syndrome. Starting from Stern's scheme [18], we define a dual version which, unlike the other schemes based on the SD problem, uses a generator matrix of a random linear binary code. This allows, among other things, an improvement of the transmission rate with regards to the other schemes. Finally, by using techniques of computation in a finite field, we show how it is possible to considerably reduce: -the complexity of the computations done by the prover (which is usually a portable device with a limited computing power), -the size of the data stored by the latter.

The Adapted Modular Number System (AMNS) is a sytem of representation of integers to speed up arithmetic operations modulo a prime p. Such a system can be defined by a tuple (p, n, γ, ρ, E) where E ∈ Z[X]. In [13] conditions are given to build AMNS with E(X) = X n + 1. In this paper, we generalize their results and show how to generate multiple AMNS for a given prime p with E(X) = X n − λ and λ ∈ Z. Moreover, we propose a complete set of algorithms without conditional branching to perform arithmetic and conversion operations in the AMNS, using a Montgomerylike method described in [15].

No abstract

To cite this version:Fangan-Yssouf Dosso, Fabien Herbaut, Nicolas Méloni, Pascal Véron. Euclidean addition chains scalar multiplication on curves with efficient endomorphism. Journal of Cryptographic Engineering, Springer, In press, <10.1007/s13389-018-0190-0>. Noname manuscript No. (will be inserted by the editor) Euclidean addition chains scalar multiplication on curves with efficient endomorphismThis is a pre-print of an article published in "Journal of Cryptographic Engineering". The final authenticated version is available online at: https://doi.org/10.1007/s13389-018-0190-0.the date of receipt and acceptance should be inserted later Abstract Random Euclidean addition chain generation has proven to be an efficient low memory and SPA secure alternative to standard ECC scalar multiplication methods in the context of fixed base point [21]. In this work, we show how to generalize this method to random point scalar multiplication on elliptic curves with an efficiently computable endomorphism. In order to do so we generalize results from [21] on the relation of random Euclidean chains generation and elliptic curve point distribution obtained from those chains. We propose a software implementation of our method on various platforms to illustrate the impact of our approach. For that matter, we provide a comprehensive study of the practical computational cost of the modular multiplication when using Java and C standard libraries developed for the arithmetic over large integers.