Cryptanalysis of SFLASH with Slightly Modified Parameters

Vivien Dubois 1 Pierre-Alain Fouque 2, 3, 4 Jacques Stern 4
1 DGA.MI - DGA Maîtrise de l'information
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
4 ENS Paris - École normale supérieure - Paris
Abstract : SFLASH is a signature scheme which belongs to a family of multivariate schemes proposed by Patarin et al. in 1998. The SFLASH scheme itself has been designed in 2001 and has been selected in 2003 by the NESSIE European Consortium as the best known solution for implementation on low cost smart cards. In this paper, we show that slight modifications of the parameters of SFLASH within the general family initially proposed renders the scheme insecure. The attack uses simple linear algebra, and allows to forge a signature for an arbitrary message in a question of minutes for practical parameters, using only the public key. Although SFLASH itself is not amenable to our attack, it is worrying to observe that no rationale was ever offered for this ?lucky? choice of parameters.
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Moni Naor. Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2007, Barcelona, Spain. Springer, 4515, pp.264-275, 2007, Lecture Notes in Computer Science. 〈10.1007/978-3-540-72540-4_15〉
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Vivien Dubois, Pierre-Alain Fouque, Jacques Stern. Cryptanalysis of SFLASH with Slightly Modified Parameters. Moni Naor. Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2007, Barcelona, Spain. Springer, 4515, pp.264-275, 2007, Lecture Notes in Computer Science. 〈10.1007/978-3-540-72540-4_15〉. 〈inria-00556692〉

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