Cryptanalysis of a fast public key cryptosystem presented at SAC '91

At SAC '97, Itoh, Okamoto and Mambo presented a fast public key cryptosystem. After analyzing several attacks including lattice-reduction attacks, they claimed that its security was high, although the cryptosystem had some resemblances with the former knapsack cryptosystems, since decryption could be viewed as a multiplicative knapsack problem. In this paper, we show how to recover the private key from a fraction of the public key in less than 10 minutes for the suggested choice of parameters. The attack is based on a systematic use of the notion of the orthogonal lattice which we introduced as a cryptographic tool at Crypto '97. This notion allows us to attack the linearity hidden in the scheme.