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In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the group of rational points of an elliptic curve an...
This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an "advice" string about a specific group (e.g., ...
In their foundational paper on pseudorandom bit generation, Blum and Micali showed that the discrete logarithm problem could be solved efficiently given a ``magic box'' oracle that computes the most s...
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multiv...
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives.
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multip...
The Discrete Logarithm Problem over Prime Fields can be transformed to a Linear Multivariable Chinese Remainder Theorem.
The aim of this work is to investigate the hardness of the discrete logarithm problem in fields GF(pn) where n is a small integer greater than 1. Though less studied than the small characteristic case...
In this paper I propose the new fully homomorphic public-key encryption scheme without bootstrapping that is based on the discrete logarithm assumption and computational DiffieHellman assumption of...
We study generic hardness of the multiple discrete logarithm problem, where the solver has to solve n instances of the discrete logarithm problem simultaneously. There are known generic algorithms w...
The function field sieve, a subexponential algorithm of complexity L(1/3) that computes discrete logarithms in finite fields, has recently been improved to an algorithm of complexity L(1/4) and subs...
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic c...
For q a prime power, the discrete logarithm problem (DLP) in F×q consists in finding, for any g∈F×q and h∈⟨g⟩, an integer x such that gx=h. For each prime p we exhibit infinitely many ex...

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