6 research outputs found
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
An algebraic approach to the Rank Support Learning problem
Rank-metric code-based cryptography relies on the hardness of decoding a
random linear code in the rank metric. The Rank Support Learning problem (RSL)
is a variant where an attacker has access to N decoding instances whose errors
have the same support and wants to solve one of them. This problem is for
instance used in the Durandal signature scheme. In this paper, we propose an
algebraic attack on RSL which clearly outperforms the previous attacks to solve
this problem. We build upon Bardet et al., Asiacrypt 2020, where similar
techniques are used to solve MinRank and RD. However, our analysis is simpler
and overall our attack relies on very elementary assumptions compared to
standard Gr{\"o}bner bases attacks. In particular, our results show that key
recovery attacks on Durandal are more efficient than was previously thought
An algebraic approach to the Rank Support Learning problem
Rank-metric code-based cryptography relies on the hardness of decoding a random linear code in the rank metric. The Rank Support Learning problem (RSL) is a variant where an attacker has access to N decoding instances whose errors have the same support and wants to solve one of them. This problem is for instance used in the Durandal signature scheme. In this paper, we propose an algebraic attack on RSL which clearly outperforms the previous attacks to solve this problem. We build upon Bardet et al., Asiacrypt 2020, where similar techniques are used to solve MinRank and RD. However, our analysis is simpler and overall our attack relies on very elementary assumptions compared to standard Gröbner bases attacks. In particular, our results show that key recovery attacks on Durandal are more efficient than was previously thought