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...

analogous to Pollard's p − 1 algorithm. Choose some integer A greater than 2 which characterizes the Lucas sequence: V 0 = 2 , V 1 = A , V j = A V j − 1 − V j...

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...

and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm...

for p and q is trivial. Furthermore, if either p − 1 or q − 1 has only small prime factors, n can be factored quickly by Pollard's p − 1 algorithm, and...

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

to rapidly eliminate many Mersenne numbers with small factors. Pollard's p − 1 algorithm is also used to search for smooth factors. In 2018, GIMPS adopted...

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...

John M. Pollard (born 1941) is a British mathematician who has invented algorithms for the factorization of large numbers and for the calculation of discrete...

single-stranded DNA as well as RNA Period 1 of the periodic table Pollard's p − 1 algorithm for integer factorization P-ONE - a proposed neutrino detector P1...

Brent. Algebraic-group factorization algorithms, among which are Pollard's p − 1 algorithm, Williams' p + 1 algorithm, and Lenstra elliptic curve factorization...

factor. As of 2024, test candidates are mainly filtered using Pollard's p − 1 algorithm. Trial division is implemented, but Prime95 is rarely used for...

Dixon's algorithm Fermat's factorization method General number field sieve Lenstra elliptic curve factorization Pollard's p − 1 algorithm Pollard's rho algorithm...

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

march algorithm developed by R. A. Jarvis 1973 – Hopcroft–Karp algorithm developed by John Hopcroft and Richard Karp 1974 – Pollard's p − 1 algorithm developed...

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

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

n-powersmooth numbers have applications in number theory, such as in Pollard's p − 1 algorithm and ECM. Such applications are often said to work with "smooth...

prevent the system being broken by some factorization algorithms such as Pollard's p − 1 algorithm. However, with the current factorization technology,...

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...

The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a...

Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv n{\pmod {p}},} where x , n ∈ F p {\displaystyle...

Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2 ≡ n (mod p), where...

two strong primes. This makes the factorization of n = pq using Pollard's p − 1 algorithm computationally infeasible. For this reason, strong primes are...

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

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

A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or...

theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms...

The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor...

or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar...