[Resource Topic] 2010/221: Solving Generalized Small Inverse Problems

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Title:
Solving Generalized Small Inverse Problems

Authors: Noboru Kunihiro

Abstract:

We introduce a ``generalized small inverse problem (GSIP)‘’ and present an algorithm for solving this problem. GSIP is formulated as finding small solutions of f(x_0, x_1, \ldots , x_n)=x_0 h(x_1, \ldots , x_n)+C=0 (\bmod \; M) for an n-variate polynomial h, non-zero integers C and M. Our algorithm is based on lattice-based Coppersmith technique. We provide a strategy for construction of a lattice basis for solving f=0, which are systematically transformed from a lattice basis for solving h=0. Then, we derive an upper bound such that the target problem can be solved in polynomial time in \log M in an explicit form. Since GSIPs include some RSA related problems, our algorithm is applicable to them. For example, the small key attacks by Boneh and Durfee are re-found automatically.

ePrint: https://eprint.iacr.org/2010/221

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