Cryptanalysis of Okamoto cryptosystems with continued fraction algorithm

Okamoto cryptosystems have drawn attention for their properties of fast encryption and decryption. A probabilistic attack based on the L/sup 3/ algorithm was proposed by Vallee et al. (1988). Other attacks have also been proposed. In the letter, a very simple and fast attack with continued fractions is given, which can completely break the Okamoto cryptosystems.<>