On the modular inversion hidden number problem
نویسندگان
چکیده
منابع مشابه
On the modular inversion hidden number problem
We give a rigorous deterministic polynomial time algorithm for the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N. A. Howgrave-Graham in 2001. For our algorithm we need to be given about 2/3 of the bits of the output, which matches one of the heuristic algorithms of D. Boneh, S. Halevi and N. A. Howgrave-Graham and answers one of their open questions. However th...
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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 〈 xi, msbk ( (α+ xi) −1 mod p )〉 for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(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 wh...
متن کاملModular Inversion Hidden Number Problem- A Lattice Approach
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 th...
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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 i...
متن کاملSolving a Class of Modular Polynomial Equations and its Relation to Modular Inversion Hidden Number Problem and Inversive Congruential Generator
In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently. We consider systems of modular polynomial equations of the form aij + bijxi + cijxj + xixj = 0 (mod p) and show the relation between solving such equations and attacking MIHNP and ICG. We present three heuristic strategies ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2012
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2011.09.002