The Modular Inversion Hidden Number Problem

We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs xi, msbk (α + xi)−1 mod p for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits of x). We describe an algorithm for this problem when k > (log2 p)/3 and conjecture that the problem is hard whenever k < (log2 p)/3. We show that assuming hardness of some variants of this MIHNP problem leads to very efficient algebraic PRNGs and MACs.

• Type: Conference
• Year: 2001
• Where: ASIACRYPT
• Authors: Dan Boneh, Shai Halevi, Nick Howgrave-Graham
• Keywords: ASIACRYPT 2001, Basic Problem, Cryptology, Inverse Hidden Number, Random Xi