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Security Estimates for Quadratic Field Based Cryptosystems

Abstract : We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used algorithms, and extensive numerical results are presented demonstrating their efficiency. This data is used as the basis for extrapolations, used to provide recommendations for parameter sizes providing approximately the same level of security as block ciphers with $80,$ $112,$ $128,$ $192,$ and $256$-bit symmetric keys.
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Contributor : Jean-François Biasse Connect in order to contact the contributor
Submitted on : Friday, April 30, 2010 - 2:08:42 PM
Last modification on : Wednesday, February 2, 2022 - 3:54:46 PM
Long-term archiving on: : Thursday, September 30, 2010 - 4:42:35 PM


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  • HAL Id : inria-00477949, version 1
  • ARXIV : 1004.5512



Jean-François Biasse, Jacobson Michael, Silverster Alan. Security Estimates for Quadratic Field Based Cryptosystems. Lecture Notes in Computer Science, 2010. ⟨inria-00477949⟩



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