منابع مشابه
A hidden number problem in small subgroups
Boneh and Venkatesan have proposed a polynomial time algorithm for recovering a hidden element α ∈ Fp, where p is prime, from rather short strings of the most significant bits of the residue of αt modulo p for several randomly chosen t ∈ Fp. González Vasco and the first author have recently extended this result to subgroups of Fp of order at least p 1/3+ε for all p and to subgroups of order at ...
متن کاملHidden Number Problem in Small Subgroups
Boneh and Venkatesan have proposed a polynomial time algorithm for recovering a ”hidden” element α ∈ IFp, where p is prime, from rather short strings of the most significant bits of the residue of αt modulo p for several randomly chosen t ∈ IFp. González Vasco and the first author have recently extended this result to subgroups of IFp of order at least p 1/3+ε for all p and to subgroups of orde...
متن کاملA Nonuniform Algorithm for the Hidden Number Problem in Subgroups
Boneh and Venkatesan have proposed a polynomial time algorithm in a non-uniform model for recovering a ”hidden” element α ∈ IFp, where p is prime, from very short strings of the most significant bits of the residue of αt modulo p for several randomly chosen t ∈ IFp. Here we modify the scheme and amplify the uniformity of distribution of the ‘multipliers’ t and thus extend this result to subgrou...
متن کاملThe Multivariate Hidden Number Problem
This work extends the line of research on the hidden number problem. Motivated by studying bit security in finite fields, we define the multivariate hidden number problem. Here, the secret and the multiplier are vectors, and partial information about their dot product is given. Using tools from discrete Fourier analysis introduced by Akavia, Goldwasser and Safra, we show that if one can find th...
متن کاملOn 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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2005
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-05-01797-7