International audienceThe McEliece cryptosystem is one of the oldest public-key cryptosystem ever designated. It is also the first public-key cryptosystem based on linear error-correcting codes. The main advantage of the McEliece cryptosystem is to have a very fast encryption and decryption functions but suffers from a major drawback. It requires a very large public key which makes it very difficult to use in many practical situations. In this paper we propose a new general way to reduce the public key size through quasi-cyclic codes. Our construction introduces a new method of hiding the structure of the secret generator matrix by first choosing a subfield subcode of a quasi-cyclic code that is defined over a large alphabet and then by randomly shortening the chosen subcode. The security of our variant is related to the hardness of decoding a random quasi-cyclic code. We introduce a new decisional problem that is associated to the decoding of an arbitrary quasi-cyclic code. We prove that it is an NP-complete problem. Starting from subfield subcodes of quasi-cyclic generalized Reed-Solomon codes, we propose a system with several size of parameters from 6,000 to 11,000 bits with a security ranging from 2 80 to 2 107 . Implementations of our proposal show that we can encrypt at a speed of 120 Mbits/s (or one octet for 120 cycles). Hence our new proposal represents the most competitive public-key cryptosystem

. 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.

Courtois-Finiasz-Sendrier (CFS) digital signatures critically depend on the ability to efficiently find a decodable syndrome by random sampling the syndrome space, previously restricting the class of codes upon which they could be instantiated to generic binary Goppa codes. In this paper we show how to construct terror correcting quasi-dyadic codes where the density of decodable syndromes is high, while also allowing for a reduction by a factor up to t in the key size.

Abstract. In this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device.