The Development of the Number Field Sieve

1. Front Matter

   Pages i-viii

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2. The number field sieve: An annotated bibliography

   • H. W. Lenstra Jr.

   Pages 1-3

3. Factoring with cubic integers

   • J. M. Pollard

   Pages 4-10

4. The number field sieve

   • A. K. Lenstra, H. W. Lenstra Jr., M. S. Manasse, J. M. Pollard

   Pages 11-42

5. The lattice sieve

   • J. M. Pollard

   Pages 43-49

6. Factoring integers with the number field sieve

   • J. P. Buhler, H. W. Lenstra Jr., Carl Pomerance

   Pages 50-94

7. Computing a square root for the number field sieve

   • Jean-Marc Couveignes

   Pages 95-102

8. A general number field sieve implementation

   • Daniel J. Bernstein, A. K. Lenstra

   Pages 103-126

9. Back Matter

   Pages 127-131

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The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.

• Algebra
• Algebraic Number Fields
• Computational Number Theory
• Factoring algorithm
• Prime
• Prime Numbers
• number theory
• combinatorics

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