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(Fp) 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...
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 ...
LetHbe ahyperelliptic curvedefined over afinite fieldFq, and letDa∈PicH0(F)be a divisor of ordern. GivenDb ∈〈Da〉, thehyperelliptic discrete logarithm problemconsists in finding an integerλ, 0 ≤ λ ≤ n − 1 such thatDb = λDa. Thehyperelliptic discrete ...
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...
If that doesn't work, please contact support so we can address the problem.Abstract Computing discrete logarithms takes time. It takes time to develop new algorithms, choose the best algorithms, implement these algorithms correctly and efficiently, keep the system running for several months, and, ...
well-known and widely accepted conjectures concerning the expected ranks of elliptic curves over the ra- tionals. 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 ...
The Elliptic Curve Cryptography (ECC) is modern family of public-key cryptosystems, which is based on the algebraic structures of the elliptic curves over finite fields and on the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP). ECC implements all major capabilities of the asymm...
The introduction of elliptic curve cryptography by Koblitz [3] and Miller [4] in the mid-1980s has yielded new public key algorithms based on the discrete logarithm problem. Under Quantum Computer Attack: Is Rainbow a Replacement of RSA and Elliptic Curves on Hardware? Elliptic curve cryptography...
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 ...
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 ...