International Association
for Cryptologic Research

Imai and Matsumoto introduced a public key cryptosystem based on

multivariate quadratic polynomials. In a simplified way, the essence of their cryptosystem can be described in the following way: Start with a central monomial F. The secret key comprises

two invertible linear transformations T and L such that TFL is the public key. In order to study equivalent public keys it is natural to ask for the \"invariant\" secret keys (T,L), i.e. TFL=F. Lin, Faugere, Perret and Wang give a partial answer to this question by considering such L which fulfill FL=F. In this paper we will determine all invariant invertible linear transformations (T,L).