New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem

We consider the decoding problem or the problem of finding low weight codewords for rank metric codes. We show how additional information about the codeword we want to find under the form of certain linear combinations of the entries of the codeword leads to algorithms with a better complexity. This is then used together with a folding technique for attacking a McEliece scheme based on LRPC codes. It leads to a feasible attack on one of the parameters suggested in \cite{GMRZ13}.Comment: A shortened version of this paper will be published in the proceedings of the IEEE International Symposium on Information Theory 2015 (ISIT 2015

Code-Based Cryptography: New Security Solutions Against a Quantum Adversary

International audienceCryptography is one of the key tools for providing security in our quickly evolving technological society. An adversary with the ability to use a quantum computer would defeat most of the cryptographic solutions that are deployed today to secure our communications. We do not know when quantum computing will become available, but nevertheless, the cryptographic research community must get ready for it now. Code-based cryptography is among the few cryptographic techniques which are known to resist to a quantum adversary

The problem with the SURF scheme

There is a serious problem with one of the assumptions made in the security proof of the SURF scheme. This problem turns out to be easy in the regime of parameters needed for the SURF scheme to work. We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the SURF scheme. We explain this problem here and give the old version of the paper afterward

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

The Blockwise Rank Syndrome Learning problem and its applications to cryptography

Recently the notion of blockwise error in a context of rank based cryptography has been introduced by Sont et al. at AsiaCrypt 2023 . This notion of error, very close to the notion sum-rank metric, permits, by decreasing the weight of the decoded error, to greatly improve parameters for the LRPC and RQC cryptographic schemes. A little before the multi-syndromes approach introduced for LRPC and RQC schemes had also allowed to considerably decrease parameters sizes for LRPC and RQC schemes, through in particular the introduction of Augmented Gabidulin codes. In the present paper we show that the two previous approaches (blockwise errors and multi-syndromes) can be combined in a unique approach which leads to very efficient generalized RQC and LRPC schemes. In order to do so, we introduce a new problem, the Blockwise Rank Support Learning problem, which consists of guessing the support of the errors when several syndromes are given in input, with blockwise structured errors. The new schemes we introduce have very interesting features since for 128 bits security they permit to obtain generalized schemes for which the sum of public key and ciphertext is only 1.4 kB for the generalized RQC scheme and 1.7 kB for the generalized LRPC scheme. The new approach proposed in this paper permits to reach a 40 % gain in terms of parameters size when compared to previous results, obtaining even better results in terms of size than for the KYBER scheme whose total sum is 1.5 kB. Besides the description of theses new schemes the paper provides new attacks for the l-RD problem introduced in the paper by Song et al. of AsiaCrypt 2023, in particular these new attacks permit to cryptanalyze all blockwise LRPC parameters they proposed (with an improvement of more than 40bits in the case of structural attacks). We also describe combinatorial attacks and algebraic attacks, for the new Blockwise Rank Support Learning problem we introduce

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper

Wave: A New Code-Based Signature Scheme

preprint IACR disponible sur https://eprint.iacr.org/2018/996/20181022:154324We present here Wave the first "hash-and-sign" code-based signature scheme which strictly follows the GPV strategy [GPV08]. It uses the family of ternary generalized (U, U + V) codes. We prove that Wave achieves existential unforgeability under adaptive chosen message attacks (EUF-CMA) in the random oracle model (ROM) with a tight reduction to two assumptions from coding theory: one is a distinguishing problem that is related to the trapdoor we insert in our scheme, the other one is DOOM, a multiple target version of syndrome decoding. The algorithm produces uniformly distributed signatures through a suitable rejection sampling. Our scheme enjoys efficient signature and verification algorithms. For 128 bits of classical security, signature are 8 thousand bits long and the public key size is slightly smaller than one megabyte. Furthermore, with our current choice of parameters, the rejection rate is limited to one rejection every 3 or 4 signatures

New results for rank-based cryptography

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