Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and its...

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 solving...

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...

cases where neither of these are possible. The classic example is Pollard's rho algorithm for integer factorization, which searches for a factor p of a given...

Several algorithms created by British mathematician John Pollard: Pollard's kangaroo algorithm Pollard's p − 1 algorithm Pollard's rho algorithm Pollard (coin)...

Baby-step giant-step Index calculus algorithm Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Euclidean algorithm: computes the greatest common...

algorithms such as Pollard's rho algorithm. Functional programming languages often discourage or do not support explicit in-place algorithms that overwrite...

efficient algorithm since, for example, the Pollard's rho algorithm is able to find a collision in SHA-2 more efficiently than Grover's algorithm. Grover's...

example, naive trial division is a Category 1 algorithm. Trial division Wheel factorization Pollard's rho algorithm, which has two common flavors to identify...

calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's lambda...

logarithm of 2 Neper Offset logarithmic integral pH Pollard's kangaroo algorithm Pollard's rho algorithm for logarithms Polylogarithm Polylogarithmic function...

ρ, spectral radius of a square matrix Pollard's rho algorithm, for integer factorization Pollard's rho algorithm for logarithms ρ, prime constant ρ, plastic...

first step of the algorithm. Doing so increases the running time, which then is O(n/m). Alternatively one can use Pollard's rho algorithm for logarithms...

factorization algorithms are known, they are slower than the fastest primality testing methods. Trial division and Pollard's rho algorithm can be used to...

Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning...

essential step in several integer factorization algorithms, such as Pollard's rho algorithm, Shor's algorithm, Dixon's factorization method and the Lenstra...

order where the discrete logarithm solution lies unlike with the Pollard's rho or Pollard's kangaroo. Input: Discrete logarithm generator g {\displaystyle...

for the calculation of discrete logarithms. His factorization algorithms include the rho, p − 1, and the first version of the special number field sieve...

parameters, except for the arbitrary choice of base point—for example, Pollard's rho algorithm for logarithms is expected to take approximately ℓ π / 4 {\displaystyle...

contract, not just the fraudulent one. Pollard's rho algorithm for logarithms is an example for an algorithm using a birthday attack for the computation...

perform exponentiation in a quadratic field. It is analogous to Pollard's p − 1 algorithm. Choose some integer A greater than 2 which characterizes the...

Lucas–Lehmer test for Mersenne numbers AKS primality test Pollard's p − 1 algorithm Pollard's rho algorithm Lenstra elliptic curve factorization Quadratic sieve...

John Pollard 1974 – Quadtree developed by Raphael Finkel and J.L. Bentley 1975 – Genetic algorithms popularized by John Holland 1975 – Pollard's rho algorithm...

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...

than 1015000). In 1980 he and John Pollard factored the eighth Fermat number using a variant of the Pollard rho algorithm. He later factored the tenth and...

multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient...

curve, using an optimized FPGA implementation of a parallel version of Pollard's rho method. The attack ran for about six months on 64 to 576 FPGAs in parallel...

primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena...

requires about O ( p 1 / 2 ) {\displaystyle O(p^{1/2})} time using the Pollards rho algorithm. The most famous example of Montgomery curve is Curve25519 which...

currently best known discrete logarithm attack is the generic Pollard's rho algorithm, requiring about 2 122.5 {\displaystyle 2^{122.5}} group operations...