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Williams's p + 1 algorithm
Integer factorization algorithm
In computational number theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982.
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In computational number theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982. It works well if the number N to be factored contains one or more prime factors p such that p + 1 is smooth, i.e. p + 1 contains only small factors. It uses Lucas sequences to perform exponentiation in a quadratic field. It is analogous to Pollard's p − 1 algorithm. In fact, it is also able to find p if p − 1 is smooth, in which case it degenerates into a slow version of Pollard's algorithm.
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