Cryptanalysis of the Hidden Matrix Cryptosystem

Abstract. In this paper, we present an efficient cryptanalysis of the socalled HM cryptosystem which was published at Asiacrypt’1999, and one perturbed version of HM. Until now, this scheme was exempt from cryptanalysis. We first present a distinguisher which uses a differential property of the public key. This distinguisher permits to break one perturbed version of HM. After that, we describe a practical message-recovery attack against HM using Gr¨obner bases. The attack can be mounted in few hundreds seconds for recommended parameters. It turns out that algebraic systems arising in HM are easier to solve than random systems of the same size. Note that this fact provides another distinguisher for HM. Interestingly enough, we offer an explanation why algebraic systems arising in HM are easy to solve in practice. Briefly, this is due to the apparition of many new linear and quadratic equations during the Gr¨obner basis computation. More precisely, we provide an upper bound on th...

• Type: Journal
• Year: 2010
• Where: LATINCRYPT
• Authors: Jean-Charles Faugère, Antoine Joux, Ludovic Perret, Joana Treger
• Keywords: Algebraic Systems, Cryptology, Gr¨obner Basis Computation, LATINCRYPT 2010, Socalled Hm Cryptosystem