Abstract
This article describes the particular parameter choice and implementation details of one of the rare published, but not broken signature schemes, that allow signatures to be computed and checked by a low-cost smart card. The security is controversial, since we have no proof of security, but the best known attacks require more than 280 computations. We called FLASH our algorithm and we also proposed SFLASH, a version that has a smaller public key and faster verification though one should be even more careful about it’s security.
FLASH and SFLASH have been accepted as submissions to NESSIE (New European Schemes for Signatures, Integrity, and Encryption), a project within the Information Societies Technology (IST) Programme of the European Commission.
Part of this work is an output of project “Turbo-signatures”, supported by the french Ministry of Research.
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References
Nicolas Courtois, Asymmetric cryptography with algebraic problems MQ, Min-Rank, IP and HFE. PhD thesis, Paris 6 University, to appear soon.
Tsutomu Matsumoto and Hideki Imai, Public Quadratic Polynomial-tuples for efficient signature-verification and message-encryption, Proceedings of EUROCRYPT’88, Springer-Verlag, pp. 419–453.
Jacques Patarin, Cryptanalysis of the Matsumoto and Imai public Key Scheme of Eurocrypt’88, Proceedings of CRYPTO’95, Springer-Verlag, pp. 248–26
Jacques Patarin, Louis Goubin, and Nicolas Courtois, C✻–+ and HM: Variations around two schemes of T. Matsumoto and H. Imai, in Advances in Cryptology, Proceedings of ASIACRYPT’98, LNCS n∘ 1514, Springer Verlag, 1998, pp. 35–49.
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Patarin, J., Courtois, N., Goubin, L. (2001). FLASH, a Fast Multivariate Signature Algorithm. In: Naccache, D. (eds) Topics in Cryptology — CT-RSA 2001. CT-RSA 2001. Lecture Notes in Computer Science, vol 2020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45353-9_22
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DOI: https://doi.org/10.1007/3-540-45353-9_22
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