computational number theory

computational number theory

1. (mathematics, number theory) The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry.

   Topics studied in computational number theory include algorithms for primality testing and integer factorisation, finding solutions to Diophantine equations and explicit methods in arithmetic geometry.

   Computational number theory has applications in cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis.

   • 1990, Carl Pomerance, editor, Proceedings of Symposia in Applied Mathematics, Volume 42: Cryptology and Computational Number Theory‎, American Mathematical Society:
   • 1994, Hari Krishna, Bal Krishna, Kuo-Yu Lin, Jenn-Dong Sun, Computational Number Theory and Digital Signal Processing: Fast Algorithms and Error Control Techniques, CRC Press, .
   • 2001, Kazimierz Alster, Jerzy Urbanowicz, Hugh C. Williams, editors, Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference‎, Walter de Gruyter:

• (field of study dealing with computational methods in number theory): algorithmic number theory