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A new efficient algorithm for computing Gröbner bases without reduction to zero ( F 5 )
Abstract
This paper introduces a new efficient algorithm for computing Gröbner bases. We replace the Buchberger criteria by an optimal criteria. We give a proof that the resulting algorithm (called F5) generates no useless critical pairs if the input is a regular sequence. This a new result by itself but a first implementation of the algorithm F5 shows that it is also very efficient in practice: for instance previously untractable problems can be solved (cyclic 10). In practice for most examples there is no reduction to zero. We illustrate this algorithm by one detailed example.
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Cites
A new efficient algorithm for computing Gröbner bases (F4)
Faugére, J.-C. (1999) · Journal of Pure and Applied Algebra · doi:10.1016/s0022-4049(99)00005-5 · Cited by 1,145
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Cited by
Extending SAT Solvers to Cryptographic Problems
Soos, M., Nohl, K., & Castelluccia, C. (2009) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-02777-2_24 · Cited by 484
Status report on the third round of the NIST Post-Quantum Cryptography Standardization process
Alagic, G., Apon, D., Cooper, D., Dang, Q., Dang, T., Kelsey, J., Lichtinger, J., Liu, Y.-K., Miller, C., Moody, D., et al. (2022) · doi:10.6028/nist.ir.8413-upd1 · Cited by 301
(2009) · Cited by 54
Structural cryptanalysis of McEliece schemes with compact keys
Faugère, J.-C., Otmani, A., Perret, L., de Portzamparc, F., & Tillich, J.-P. (2016) · Designs, Codes and Cryptography · doi:10.1007/s10623-015-0036-z · Cited by 49
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Metadata
- Authors
- Faugère, J. C.
- Venue
- Proceedings of the 2002 international symposium on Symbolic and algebraic computation
- Publisher
- ACM
- Published
- 2002-07-10
- Pages
- 75-83
- OpenAlex
- W2038345254
- Cited by
- 785
- References
- 1
- FWCI
- 11.33
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Faugère, J. C. (2002). A new efficient algorithm for computing Gröbner bases without reduction to zero ( F 5 ). Proceedings of the 2002 international symposium on Symbolic and algebraic computation. https://doi.org/10.1145/780506.780516
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