Abstract
At Eurocrypt’96, J.Patarin proposed a signature and authentication scheme whose security relies on the difficulty of the Isomorphism of Polynomials problem [P]. In this paper, we study a variant of this problem, namely the Isomorphism of Polynomials with one secret problem and we propose new algorithms to solve it, which improve on all the previously known algorithms. As a consequence, we prove that, when the number of polynomials (u) is close to the number of variables (n), the instances considered in [P] and [P1] can be broken. We point out that the case n-u small is the most relevant one for cryptographic applications. Besides, we show that a large class of instances that have been presumed difficult in [P] and [P1] can be solved in deterministic polynomial time. We also give numerical results to illustrate our methods.
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Levy-dit-Vehel, F., Perret, L. (2003). Polynomial Equivalence Problems and Applications to Multivariate Cryptosystems. In: Johansson, T., Maitra, S. (eds) Progress in Cryptology - INDOCRYPT 2003. INDOCRYPT 2003. Lecture Notes in Computer Science, vol 2904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24582-7_18
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DOI: https://doi.org/10.1007/978-3-540-24582-7_18
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