Fast cryptanalysis of the Matsumoto-Imai public key scheme
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ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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In 1 Matsumoto and Imai developeda new public key scheme, called C^*, for encipheringor signing. (This scheme is completely different from and shouldnot be mistaken with another scheme of Matsumoto and Imai developedin 1983 in 7 and broken in 1984 in 8). No attacks have beenpublished as yet for this scheme. However, in this paper, wewill see that—for almost all keys—almost every cleartextcan be found from its ciphertext after only approximately m^{2}n^{4} \log n computations, where m is thedegree of the chosen field K and mnis the number of bits of text. Moreover, for absolutely all keysthat give a practical size for the messages, it will be possibleto find almost all cleartexts from the corresponding ciphertextsafter a feasible computation. Thus the algorithm of 1 is insecure.