International Association
for Cryptologic Research

The Modular Inversion Hidden Number Problem (MIHNP) was introduced by

Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001 (BHH\'01). They provided

two heuristics - in Method I, two-third of the output bits are required to solve the

problem, whereas the more efficient heuristic (Method II) requires only one-third of

the bits of the output. After more than a decade, here Sarkar in [28] identified that

the claim in Method II is actually not correct and a detailed calculation justified that

this method too requires two-third of the bits of the output, contrary to the claim in

BHH\'01. He reconstructed the lattice and give a bound which heuristically solve with

half of the output bits. Although J.Xu et al in [29] solved it with only one-third of the

output bits asymptotically but that technique is difficult to understand and implement.

Here we essentially use similar idea of [28] but in a clever way such that it is a better

bound although we solve the problem heuristically with only half of the output bits in

asymptotic sense. This is lot easier to understand and implement.

Also experimental results support the claim corresponding to our heuristics. In the last

section we actually talk about a variant of this which seems to be hard to solve under

lattice attack.