However, a number of attacks on ECDLP have been proposedIn this paper we analyze the generic attackson Elliptic Curve Discrete Log Problem. We present details of Pholig Hellman method and Pollard rho method and also mention the speed up by group automorphism, parallel methods and massive ...
arXiv:0803.0728v2 [math.NT] 4 Aug 2008The elliptic curve discrete logarithm problemand equivalent hard problems for ellipticdivisibility sequencesKristin E. Lauter 1 and Katherine E. Stange 2,⋆1Microsoft Research, One Microsoft Way, Redmond, WA 98052klauter@microsoft.com2Department of Mathematics...
Keyword: Elliptic curve cryptosystem, discrete logarithm, partial lift- ing. 1 Introduction The discrete logarithm problem over elliptic curves is a natural analog of the discrete logarithm problem over finite fields. It is the basis of elliptic curve cryp- tosystems proposed independently by Ko...
1.3 The Elliptic Curve Discrete Logarithm Problem 椭圆曲线的两点 Q,P∈E(Fp),Q=kP,求k, 记作 k=logpQ 最快的算法是Pohlig-Hellman attack 和 Pollard Rho Algorithm 2. Attacks on Weak Curves E(F_p) 在没有较大的素子群时,受 Pohlig-Hellman attack 影响 #E(Fp) = p 时,受Smart's attack 影...
Discrete log problemSummary: The security of the least significant bit (LSB) of the secret key in the Elliptic Curve Diffie-Hellman protocol (and of the message in the RSA) is related to the security of the whole key (and of the whole message, respectively). Algorithms to invert these ...
We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable in sub-exponential time if and only if the elliptic curve discrete logarithm problem is sol...
In this paper, we study the performance of ANNs on the computation of bits of discrete logarithms over elliptic curves. In particular, we consider a Boolean function that represents the problem at hand and study the ability of ANNs on the computation of the considered Boolean function. The ...
The improbability that an elliptic curve has subexponential discrete log problem under the Menezes–Okamoto–Vanstone algorithm J. Cryptology, 11 (1998), pp. 141-145 View in ScopusGoogle Scholar [5] M. Belenky, et al. Women's Ways of Knowing: The Development of Self, Voice, and Mind Basic...
Attacks on the hyperelliptic curve discrete logarithm problem can be divided into three main... This is a preview of subscription content,log in via an institutionto check access. Roberto Avanzi (ARM) Editor information Editors and Affiliations ...
logarithms Jinyoung Ha , Jonghyun Lee & Jun Heo * We estimate the number of physical qubits and execution time by decomposing an implementation of Shor's algorithm for elliptic curve discrete logarithms into universal gate units at the logical level when surface codes are used....