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Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.
In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard , in the same paper as his better-known Pollard's rho algorithm for ...
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. In number theory , the more commonly used term is index : we can write x = ind r a (mod m ) (read "the index of a to the base r modulo m ") for r x ≡ a (mod m ) if r is a primitive root of m and gcd ...
He used the same core ideas as Pollard but a different method of cycle detection, replacing Floyd's cycle-finding algorithm with the related Brent's cycle finding method. [3] CLRS gives a heuristic analysis and failure conditions (the trivial divisor is found). [2] A further improvement was made by Pollard and Brent.
The third stage searches for a power s of the generator g which, when multiplied by the argument h, may be factored in terms of the factor base g s h = (−1) f 0 2 f 1 3 f 2 ···p r f r. Finally, in an operation too simple to really be called a fourth stage, the results of the second and third stages can be rearranged by simple algebraic ...
In group theory, a branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. [1] The discrete log problem is of fundamental importance to the area of public key cryptography.
Steps of the Pohlig–Hellman algorithm. In group theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, [1] is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer.
The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons.. Shor's algorithm for factoring and for finding discrete logarithms (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite abelian groups.