Close values of shifted modular inversions and the decisional modular inversion hidden number problem

Abstract

We give deterministic polynomialtime algorithms for two different decision version the modularinversion hidden number problemintroduced by D. Boneh, S. Halevi and N. A. Howgrave-Grahamin 2001. For example, for one of our algorithms we need to be given about $1/2$ of thebits of each inversion, while for the computationalversion the best known algorithm requires about $2/3$ of the bitsand is probabilistic.