Asymmetric Cryptography with a Hidden Monomial
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In [1]T. Matsumoto and H. Imai have presented a very efficient, "candidate" algorithm, called C*, for asymmetric cryptography. This algorithm was broken in [2]. Then in [3], I have suggested two algorithms, HFE and IP, to repair C*. However the secret key computations of HFE and IP are not as efficient as in the original algorithm C*. IS it possible to repair C* with the same kind of very easy secret key computations? This question is the subject of this paper. Unfortunately, we will see that for all the "easy" transformations of C* the answer is no. However one of the new ideas of this paper will enable us to suggest a candidate algorithm for assymetric signatures of length only 64 bits. An extended version of this paper can be obtained from the author.
[1] Jacques Patarin,et al. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms , 1996, EUROCRYPT.
[2] F. R. Gantmakher. The Theory of Matrices , 1984 .
[3] Jacques Patarin,et al. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88 , 1995, CRYPTO.
[4] Hideki Imai,et al. Public Quadratic Polynominal-Tuples for Efficient Signature-Verification and Message-Encryption , 1988, EUROCRYPT.