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 〈x i, msb k ((α + x i)-1 mod p〉 for random x i ∈ ℤp the problem is to find α ∈ ℤp (here msb k(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.
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Boneh, D., Halevi, S., Howgrave-Graham, N. (2001). The Modular Inversion Hidden Number Problem. In: Boyd, C. (eds) Advances in Cryptology — ASIACRYPT 2001. ASIACRYPT 2001. Lecture Notes in Computer Science, vol 2248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45682-1_3
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DOI: https://doi.org/10.1007/3-540-45682-1_3
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