Cryptanalysis of SFLASH with Slightly Modified Parameters

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.