Abstract
The function decomposition problem can be stated as: Given the algebraic expression of the composition of two mappings, how can we identify the two factors? This problem is believed to be in general intractable [1]. Based on this belief, J. Patarin and L. Goubin designed a new family of candidates for public key cryptography, the so called “2R—schemes” [10], [11]. The public key of a “2R”-scheme is a composition of two quadratic mappings, which is given by n polynomials in n variables over a finite field K with q elements. In this paper, we contend that a composition of two quadratic mappings can be decomposed in most cases as long as q > 4. Our method is based on heuristic arguments rather than rigorous proofs. However, through computer experiments, we have observed its effectiveness when applied to the example scheme “D**” given in [10].
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© 1999 Springer-Verlag Berlin Heidelberg
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Ding-Feng, Y., Kwok-Yan, L., Zong-Duo, D. (1999). Cryptanalysis of “2R” Schemes. In: Wiener, M. (eds) Advances in Cryptology — CRYPTO’ 99. CRYPTO 1999. Lecture Notes in Computer Science, vol 1666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48405-1_20
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DOI: https://doi.org/10.1007/3-540-48405-1_20
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