Algorithmic number theory

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The algorithmic number theory is a branch of number theory , which in turn is a branch of mathematics . It deals with the question of efficient algorithmic solutions for number theoretic problems.

The most important areas of elementary algorithmic number theory are

For this one needs further procedures, which are also examined:

New research findings on algorithmic number theory are, among others, on the 1994 two-yearly conference ANTS presents (Algorithmic Number Theory Symposium).


The most important application of algorithmic number theory is cryptography . For example, the RSA method makes use of the fact that the prime number property of a number can be checked quickly, but so far no similarly fast methods are known to factor a composite number (that is a number that is not prime). The security of data transmission on the Internet is based on this fact. In this context, RSA Security offered larger sums of money to those who succeed in factoring certain numbers. Algorithms are also used in cryptography, for example when calculating discrete logarithms for other encryption and signature processes.

A much-studied problem with far-reaching applications is to find a base that generates the grid in a number grid, which base consists of base vectors that are as short as possible and as orthogonal as possible ( grid base reduction ).



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    • See also the associated ARIBAS program
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Individual evidence

  1. see RSA Challenge
  2. No. 129 of Mathematics of Computation , Volume 29, was dedicated to Lehmer in January 1975 on the occasion of his 70th birthday.
  3. No. 203 of Mathematics of Computation , Volume 61, was dedicated in July 1993 to the memory of Lehmer.
  4. On the occasion of the departure of Lenstra after 17 years at the University of Berkeley, a scientific conference took place in March 2003, the Lenstra Treurfeest - A Farewell Conference, March 21-23, 2003 ( Memento of February 13, 2003 in the Internet Archive )
  5. Issue 3 of Volume 18 (2006) of the Journal de Théorie des Nombres de Bordeaux was dedicated to Pohst on the occasion of his 60th birthday. Journal de théorie des nombres de Bordeaux Volume 18, number 3 (2006)
  6. Volume 12A (2012) of the journal Integers for combinatorial number theory and additive combinatorics ( [1] ) appeared as John Selfridge Memorial Volume .
  7. No. 177/178 of Mathematics of Computation , Volume 48, was dedicated to Shanks in January 1987 on the occasion of his 70th birthday.
  8. For Williams' 60th birthday, a scientific conference was held in his honor in Banff (Canada) in 2003 (see literature). Fields Institute - Conference in Number Theory - 2003 , Number Theory Conference in honor of Professor HC Williams | CISaC
  9. ^ A Computational Introduction to Number Theory and Algebra . Retrieved September 19, 2010.

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