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 we identify that the claim in Method II is actually not correct and a detailed

calculation justifies that this method too requires two-third of the bits of the output, contrary to the claim in BHH\'01. Further, we show that using the same relations as in Boneh et al., one can reconstruct the lattice so that the problem can be heuristically solved by the knowledge of five-eighth of the bits. Finally, we could accumulate additional relations to solve the problem heuristically with only half of the output bits in asymptotic sense. Experimental results support the claim corresponding to our heuristics.