Abstract
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.
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T. Matsumoto and H. Imai, “Public quadratic polynomial-tuples for efficient signature-verification and message-encryption”, EUROCRYPT’88, Springer Verlag, pp. 419–453.
J. Patarin, “Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt’88”, CRYPTO’95, Springer Verlag, pp. 248–261.
J. Patarin, “Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new Families of Asymmetric Algorithms”, EUROCRYPT’96, Springer Verlag, pp. 33–48.
F.R. Gantmacher, “The theory of matrices”, Chelsea Publishing Company, Volume one, chapter VII.
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© 1996 Springer-Verlag Berlin Heidelberg
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Patarin, J. (1996). Asymmetric Cryptography with a Hidden Monomial. In: Koblitz, N. (eds) Advances in Cryptology — CRYPTO ’96. CRYPTO 1996. Lecture Notes in Computer Science, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68697-5_4
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DOI: https://doi.org/10.1007/3-540-68697-5_4
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