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The number field sieve
Open accessAbstract
The number field sieve is an algorithm to factor integers of the form r, 4-s for small positive r and s.This note is intended as a 'report on work in progress' on this algorithm.We informally describe the algorithm, discuss several implementation related aspects, and present some of the factorizations obtained so far.We also mention some solutions to the problems encountered when generalizing the algorithm to general integers using an idea of Buhler and Pomerance.It is not unlikely that this leads to a general purpose factoring algorithm that is asymptotically substantially faster than the fastest factoring algorithms known so far, like the multiple polynomial quadratic sieve.
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Cited by
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Gidney, C., & Ekerå, M. (2021) · Quantum · doi:10.22331/q-2021-04-15-433 · Cited by 830
Reducing elliptic curve logarithms to logarithms in a finite field
Menezes, A., Vanstone, S., & Okamoto, T. (1991) · Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91 · doi:10.1145/103418.103434 · Cited by 337
Factoring integers with the number field sieve
Buhler, J. P., Lenstra, H. W., & Pomerance, C. (1993) · Lecture Notes in Mathematics · doi:10.1007/bfb0091539 · Cited by 188
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Metadata
- Authors
- Lenstra, A. K., Lenstra, H. W., Manasse, M. S., & Pollard, J. M.
- Venue
- Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
- Publisher
- ACM Press
- Published
- 1990
- Pages
- 564-572
- OpenAlex
- W2142778315
- Cited by
- 285
- References
- 0
- FWCI
- 30.77
- Type
- conference paper
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: The number field sieve. https://app.cochat.ai/papers/10.1145/100216.100295
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- Lenstra, A. K., Lenstra, H. W., Manasse, M. S., & Pollard, J. M. (1990). The number field sieve. Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90. https://doi.org/10.1145/100216.100295
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