Solving Generalized Small Inverse Problems

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(x0, x1,..., xn) = x0h(x1,..., xn) + C = 0(mod M) for an n-variate polynomial h, non-zero integers C and M. Our algorithm is based on lattice-based Coppersmith technique. We pro-vide 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 logM in an explicit form. Since GSIPs in-clude some RSA-related problems, our algorithm is applicable to them. For example, the small key attacks by Boneh and Durfee are re-found automatically. This is a full version of [13]