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There are two other well known algorithms that solve the discrete logarithm problem in sub-exponential time: the index calculus algorithm and a version of the Number Field Sieve. [5] In their easiest forms both solve the DLP in a finite field of prime order but they can be expanded to solve the DLP in as well.
Let be a cyclic group of order , and given ,, and a partition =, let : be the map = {and define maps : and : by (,) = {() + (,) = {+ ()input: a: a generator of G b: an element of G output: An integer x such that a x = b, or failure Initialise i ← 0, a 0 ← 0, b 0 ← 0, x 0 ← 1 ∈ G loop i ← i + 1 x i ← f(x i−1), a i ← g(x i−1, a i−1), b i ← h(x i−1, b i−1) x 2i−1 ← ...
In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that b x = a.Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a.
The computation solve DLP in the 1551-bit field GF(3 6 · 163), taking 1201 CPU hours. [ 21 ] [ 22 ] in 2012 by a joint Fujitsu, NICT, and Kyushu University team, that computed a discrete logarithm in the field of 3 6 · 97 elements and a size of 923 bits, [ 23 ] using a variation on the function field sieve and beating the previous record in a ...
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms.Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves.