Special Section on Discrete Mathematics and Its Applications
Solving Generalized Small Inverse Problems
2011 Volume E94.A Issue 6 Pages 1274-1284
Details
2011 Volume E94.A Issue 6 Pages 1274-1284
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 provide a strategy for construction of a lattice basis for solving f=0, which is 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.
