[PDF] Top 20 New algorithm for the discrete logarithm problem on elliptic curves

... basis algorithm F4[4]. The algorithm successively constructs Macaulay type matrices of increasing sizes, compute row echelon forms of them, produce some new polynomials and use them in the next step ... See full document

... Detection Algorithm: Stack is an ordinary method used for abstract data type in many programming languages associated with two operations push and ...Rho algorithm cycle detection algorithm using ... 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 ... See full document

... A new factoring algorithm proposed in this paper is based on the analysis of several modular elliptic equa- tions {called elliptic curves} and counting how many integer points {integer ... See full document

... basic algorithm but not to match the “ideal” lower ...the algorithm has slightly better average-case running time than Pollard rho, perhaps around ...the algorithm in the case of elliptic ... 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

... introduced elliptic curve cryptog- raphy based on the DLP in the group formed by rational points of an elliptic curve defined over a finite ...particular problem is denoted ...of elliptic ... 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 efficient than ... 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

... There are two kinds of attack on the discrete logarithm problem. One is generic. This kind of attack works in any group. Examples of such attacks are the baby-step giant-step attack [7, Proposition ... 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

... employing elliptic curve discrete logarithm problem ...the elliptic curve discrete logarithm assumption in the random oracle ... See full document

... The recent developments therefore raise the question of whether analogous improvements can be made to the index calculus algorithm for curves, thus producing an L(1/4) or even quasi-polynomial ... See full document

... The new modified algorithm uses only 15 giant steps where as the Classical Shanks’ algorithm would use atmost 25    n   600 = 25  giant ...the new modified algorithm when ... See full document

... of new quantum computer algorithms. It also facilitates research on new cryptosystems that are secure against quantum computers, collectively called post-quantum ... See full document

... From the observations, it is easy to obtain a fast multipoint evaluation method on the exponentiated elements. A similar method is used in [17], where the coeffi- cients of the polynomial being encrypted by an additive ... See full document

... A remarkable property of the above descent method is that it does not require any smooth- ness assumptions about non-uniformly distributed polynomials, in contrast to all previous index calculus algorithms, including the ... See full document

... computational problem is hard when a certain number of points of the random oracle are fixed (“presampled”), then the problem is hard in the random-oracle model against preprocessing adversaries using a ... 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

... 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