Hidden Number Problem and Its Applications in Crypto Scheme
نویسندگان
چکیده
منابع مشابه
Extended Hidden Number Problem and Its Cryptanalytic Applications
Since its formulation in 1996, the Hidden Number Problem (HNP) plays an important role in both cryptography and cryptanalysis. It has a strong connection with proving security of Diffie-Hellman and related schemes as well as breaking certain implementations of DSA-like signature schemes. We formulate an extended version of HNP (EHNP) and present a polynomial time algorithm for solving its insta...
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We consider a generalisation of the hidden number problem recently introduced by Boneh and Venkatesan. The initial problem can be stated as follows: recover a number a ∈ Fp such that for many known random t ∈ Fp approximations to the values of batcp are known. Here we study a version of the problem where the “multipliers” t are not known but rather certain approximations to them are given. We p...
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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 کاملA 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...
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ژورنال
عنوان ژورنال: DEStech Transactions on Engineering and Technology Research
سال: 2017
ISSN: 2475-885X
DOI: 10.12783/dtetr/sste2016/6491