Key Reduction of McEliece's Cryptosystem Using List Decoding

International audienceDifferent variants of the code-based McEliece cryptosystem were pro- posed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this paper, we show that the dyadic variant can be designed to resist all known attacks. In light of a new study on list decoding algorithms for binary Goppa codes, we explain how to increase the security level for given public keysizes. Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted dyadic variant

DAGS:Key encapsulation using dyadic GS codes

Code-based cryptography is one of the main areas of interest for NIST's Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization.</p

Re-encoding reformulation and application to Welch-Berlekamp algorithm

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm

Error-correcting pairs: a new approach to code-based cryptography

International audienceMcEliece proposed the first public-key cryptosystem based on linear error-correcting codes. A code with an efficient bounded distance decoding algorithm is chosen as secret key. It is assumed that the chosen code looks like a random code. The known efficient bounded distance decoding algorithms of the families of codes proposed for code-based cryptography, like Reed-Solomon codes, Goppa codes, alternant codes or algebraic geometry codes, can be described in terms of error-correcting pairs (ECP). That means that, the McEliece cryptosystem is not only based on the intractability of bounded distance decoding but also on the problem of retrieving an error-correcting pair from the public code. In this article we propose the class of codes with a t-ECP whose error-correcting pair that is not easily reconstructed from of a given generator matrix