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The modular inversion hidden number problem

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2001) 2248 36-51
DOI: 10.1007/3-540-45682-1_3
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Abstract

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 (Formula presented)xi, MSBk ((α + xi)−1 mod p)(Formula presented) for random xi ∈ (Formula presented)p the problem is to find α ∈ (formulapresented)p (here msbk(x) refers to the k most significant bits of x). We describe an algorithm for this problem when k > (log2p)/3 and conjecture that the problem is hard whenever k

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Boneh, D., Halevi, S., & Howgrave-Graham, N. (2001). The modular inversion hidden number problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2248, pp. 36–51). Springer Verlag. https://doi.org/10.1007/3-540-45682-1_3

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