**Modular Inversion Hidden Number Problem- A Lattice Approach**

*Pranjal Dutta*

**Abstract: **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.

**Category / Keywords: **public-key cryptography /

**Date: **received 25 Nov 2015

**Contact author: **duttpranjal at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20151126:194100 (All versions of this report)

**Short URL: **ia.cr/2015/1140

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