[PDF] Top 20 A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem

... our algorithm slightly faster: allow multiplicities of intersection between the curve C and the elliptic curve E ...the elliptic curve is smooth at the points one is interested ... See full document

... Giant-step algorithm [6], the Pollard Rho algorithm [7] and the Pohlig-Hellman algorithm[8] are some of the well known generic algorithms to find discrete log while the Index Calculus ... See full document

... At present, our best explanation for the remarkable decrease in Gr¨ obner basis calculation time offered by the Delta method is that decreasing n 0 gives a system with the same number of equations, but in fewer ... See full document

... to solve around 3(k/3) 2 = k 2 /3 instances of the ...basic algorithm but not to match the “ideal” lower ...the algorithm has slightly better average-case running time than Pollard rho, perhaps ... See full document

... the elliptic curve discrete logarithm ...based elliptic curves, done by Mon- ico et ...field-based elliptic curves, also done by Monico et ... See full document

... for elliptic curves by Semaev has opened up new avenues of investigation in index calcu- lus type algorithms for the elliptic curve discrete logarithm problem, and several recent ... See full document

... that Elliptic Curve cryptography (ECC) techniques and encoding technique on images to enhance the security of the communication ...the Elliptic Curve cryptography (ECC) of the cover image with ... See full document

... Finding solutions to algebraic equations is a fundamental task. A common approach is a Gr¨ obner basis computation via an algorithm such as Faug` ere’s F 4 and F 5 (see [4, 5]). In recent applications Gr¨ obner ... See full document

... using elliptic curves, we need to find a “hard ...mathematical problem for their security ...mathematical problem, the notion of an algorithm is ...an algorithm takes, computer ... See full document

... detection algorithm called hair and tortoise algorithm [10], Brent’s cycle detection algorithm using two pointer techniques and Nivasch’s cycle finding algorithm using ...finding ... See full document

... an elliptic curve group is equivalent to solving a particular system of multivariate non-linear system of equations derived from the so called Semaev summation ...type algorithm which is more ... See full document

... For Discrete Logarithm based cryptography, it is desirable to find efficiently implementable groups for which sub-exponential algorithms for the Discrete Logarithm Problem are not ...on ... See full document

... this problem is denoted PDP. In this paper, we will apply this algorithm to the case of Edwards curves, the well-known family of elliptic curves that al- low faster arithmetic as shown by Bernstein ... See full document

... cryptographic problem, that is, hardness against such generic algorithms, was studied for many group-based cryptographic ...a problem, at least it serves as a sanity check, in the sense that if a ... See full document

... our algorithm, which differs slightly from the traditional ICM as described in Section 1 in that it does not first compute the logarithms of the factor base elements and then apply a descent ...the ... See full document

... BSGS algorithm is useful for a number of variants of the dis- crete logarithm ...This problem makes sense even when the order of P is much larger than N ...of discrete logarithms in small ... See full document

... on Elliptic Curves in order to find distinguished points that can then be used to solve the discrete logarithm problem on a chosen ... See full document

... basis algorithm F4 is [n(m − 1)] 4ω ...basis algorithm, where the block size was k, rather than the standard ...to solve the equations coming from (5) as well, with the block size ... See full document

... quantum algorithm in (expected) polynomial time in log 2 (p), s, |G|. In Section 2 we give the definition of a group ring and describe the Kahrobaei et al. protocol. In Section 3 we recall the Meneses-Wu reduction ... See full document

... The rest of the paper is organized as follows: We begin with the description of the algorithm and present complexity analysis in Section 2. In Section 3, we present a fast multipoint evaluation method on ... See full document