Hidden Number Problem and Its Applications in Crypto Scheme

Abstract

This paper is based on the research result of Nguyen’s attacking against DSA .We extent the Hidden Number Method (HNM) from the univariate modular polynomials with one order to the univariate modular polynomials with higher order. There are many crypto schemes using the arithmetical and truncate operations. If the constant terms are partly known, these schemes can be written as the modular equations. We analysis a scheme using the arithmetical and truncate operations so as to improve the lattice model. On the supposed condition, we can recover the basic key with the probability 99%.