Security Estimates for Quadratic Field Based Cryptosystems

Details Security Estimates for Quadratic Field Based Cryptosystems Security Estimates for Quadratic Field Based Cryptosystems

2010-04-30

arxiv.org/abs/1004.5512v1

Lecture notes in computer science (2010)

Computer Science

Cryptography and Security

Scientific paper

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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