Abstract
As a possible new mathematical basis for authentication and signature schemes, at EUROCRYPT ’96 J. Patarin introduced the isomorphisms of polynomials (IP) problem [4, 5]. In this contribution, we describe an attack on the secret key of IP with one secret and demonstrate its efficiency through examples with realistic parameter sizes. The attack is carried out by means of a computer algebra system on “ordinary PCs”. Finally, we give a brief discussion of limits of our attack that points out possible directions for solving the mentioned security problems.
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Becker T, Weispfenning V (1993) Gröbner Bases: a computational approach to commutative algebra. In: Graduate texts in mathematics, vol 141. Springer, Berlin Heidelberg New York. (In cooperation with Heinz Kredel)
Bosma W, Cannon J, Playoust C (1997) The Magma algebra system. I: The user language. J Symb Comput 24:235–265
Matsumoto T, Imai H (1988) Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: Günther CG (ed) Advances in Cryptology – EUROCRYPT ’88; workshop on the theory and application of cryptographic techniques, Davos, Switzerland, May 1988. Lecture notes in computer science, vol 330. Springer, Berlin Heidelberg New York, pp 419–453
Patarin J (1996a) Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Maurer U (ed) Advances in Cryptology – EUROCRYPT ’96, Zaragoza, Spain, May 1996. Lecture notes in computer science, vol 1070. Springer, Berlin Heidelberg New York, pp 33–48
Patarin J (1996b) Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. Extended version of [4]. At the time of writing available at: http://www.minrank.org/hfe.pdf
Patarin J, Goubin L, Courtois N (1998a) Improved algorithms for isomorphisms of polynomials. In: Nyberg K (ed) Advances in Cryptology – EUROCRYPT ’98, Helsinki, May/June 1998. Lecture notes in computer science, vol 1403. Springer, Berlin Heidelberg New York, pp 184–200
Patarin J, Goubin L, Courtois N (1998b) Improved algorithms for isomorphisms of polynomials. Extended version of [6]. At the time of writing available at: http://www.minrank.org/ip6long.ps
Shor P (1997) Polynomial time algorithms for prime factorization and discrete logarithms on quantum computer. SIAM J Comput 26(5):1484–1509
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Geiselmann, W., Meier, W. & Steinwandt, R. An attack on the isomorphisms of polynomials problem with one secret. IJIS 2, 59–64 (2003). https://doi.org/10.1007/s10207-003-0025-5
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DOI: https://doi.org/10.1007/s10207-003-0025-5