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- Pollard's_p_−_1_algorithm abstract "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 that it is only suitable for integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm.The factors it finds are ones for which the number preceding the factor, p − 1, is powersmooth; the essential observation is that, by working in the multiplicative group modulo a composite number N, we are also working in the multiplicative groups modulo all of N's factors.The existence of this algorithm leads to the concept of safe primes, being primes for which p − 1 is two times a Sophie Germain prime q and thus minimally smooth. These primes are sometimes construed as "safe for cryptographic purposes", but they might be unsafe — in current recommendations for cryptographic strong primes (e.g. ANSI X9.31), it is necessary but not sufficient that p − 1 has at least one large prime factor. Most sufficiently large primes are strong; if a prime used for cryptographic purposes turns out to be non-strong, it is much more likely to be through malice than through an accident of random number generation. This terminology is considered obsolescent by the cryptography industry.[1]".
- Pollard's_p_−_1_algorithm wikiPageID "578753".
- Pollard's_p_−_1_algorithm wikiPageRevisionID "597640943".
- Pollard's_p_−_1_algorithm subject Category:Integer_factorization_algorithms.
- Pollard's_p_−_1_algorithm comment "Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974.".
- Pollard's_p_−_1_algorithm label "Algorithme p-1 de Pollard".
- Pollard's_p_−_1_algorithm label "Algoritmo p − 1 de Pollard".
- Pollard's_p_−_1_algorithm label "P-1 метод Полларда".
- Pollard's_p_−_1_algorithm label "Pollard's p − 1 algorithm".
- Pollard's_p_−_1_algorithm label "Pollard-p-1-Methode".
- Pollard's_p_−_1_algorithm label "Pollards p-1-methode".
- Pollard's_p_−_1_algorithm sameAs Pollard's_p_%E2%88%92_1_algorithm.
- Pollard's_p_−_1_algorithm sameAs Pollard-p-1-Methode.
- Pollard's_p_−_1_algorithm sameAs Algoritmo_p_−_1_de_Pollard.
- Pollard's_p_−_1_algorithm sameAs Algorithme_p-1_de_Pollard.
- Pollard's_p_−_1_algorithm sameAs Pollards_p-1-methode.
- Pollard's_p_−_1_algorithm sameAs Q1937853.
- Pollard's_p_−_1_algorithm sameAs Q1937853.
- Pollard's_p_−_1_algorithm wasDerivedFrom Pollard's_p_−_1_algorithm?oldid=597640943.