John Pollard (mathematician)
Encyclopedia
John M. Pollard is a British
mathematician
who has invented algorithms for the factorization
of large numbers and for the calculation of discrete logarithm
s.
His factorization algorithms include the rho
, p − 1, and the first version of the special number field sieve
, which has since been improved by others.
His discrete logarithm algorithms include: the rho algorithm for logarithms
and the kangaroo algorithm.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who has invented algorithms for the factorization
Integer factorization
In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....
of large numbers and for the calculation of discrete logarithm
Discrete logarithm
In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga is a solution of the equation ax = b over the real or complex numbers...
s.
His factorization algorithms include the rho
Pollard's rho algorithm
Pollard's rho algorithm is a special-purpose integer factorization algorithm. It was invented by John Pollard in 1975. It is particularly effective at splitting composite numbers with small factors.-Core ideas:...
, p − 1, and the first version of the special number field sieve
Special number field sieve
In number theory, a branch of mathematics, the special number field sieve is a special-purpose integer factorization algorithm. The general number field sieve was derived from it....
, which has since been improved by others.
His discrete logarithm algorithms include: the rho algorithm for logarithms
Pollard's rho algorithm for logarithms
Pollard's rho algorithm for logarithms is an algorithm for solving the discrete logarithm problem analogous to Pollard's rho algorithm for solving the Integer factorization problem....
and the kangaroo algorithm.