Cryptanalysis of Imai and Matsumoto Scheme B Asymmetric Cryptosystem

Imai and Matsumoto introduced alternative algebraic methods for constructing public key cryptosystems. An obvious advantage of theses public key cryptosystems is that the private side computations can be made very efficient with a simple hardware. Almost all of these proposals and variants of them were broken. However, scheme “B” in [3] is still unbroken. In this paper we show some statistical weaknesses of this scheme. In particular, we show that trying to minimize the size of the public key facilitates a cryptanalytic attack that enables the cryptanalyst to decrypt, with high probability of success, a given ciphertext by performing a very limited number of encryption operations using the public encryption function.