Algebraic cryptanalysis of yasuda, takagi and sakurai’s signature scheme

Abstract

Recently Yasuda, Takagi and Sakurai proposed a new and interesting signature scheme from the classification of quadratic forms over finite fields of odd characteristic published in PQCrypto 2013. In this paper we propose two algebraic attacks to their scheme using only linear algebra. Both attacks are motivated by Kipnis and Shamir’s attack to the oil-vinegar signature scheme. Namely we first turn the original problem to a geometric problem and then apply the theory of invariant subspace intensively. We show that Yasuda, Takagi and Sakurai’s scheme can be broken by our attacks with complexity O{formal presented} where m is the number of variables and q is the size of the base field. Here d is expected generally to be 1 and is confirmed in our tests. We also compare our attacks with Y. Hashimoto’s attack which is just published in PQCrypto 2014.