Constructing Elliptic Curve Cryptosystems in Characteristic 2
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
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ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
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CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
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A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstraß equation, in such a way that the resulting pair provides adequate security. Although the choice of Weierstraß equations allowed by this proposal is limited, the number of possible finite fields is unlimited. The proposed method allows each participant to select its elliptic curve cryptosystem parameters in such a way that the security is not affected by attacks on any other participant, unless unanticipated progress is made affecting the security for a particular Weierstraß equation irrespective of the underlying finite field. Thus the proposal provides more security than elliptic curve cryptosystems where all participants share the same Weierstraß equation and finite field. It also offers much faster and less complicated parameter initialization than elliptic curve cryptosystems where each participant randomly selects its own unique Weierstraß equation and thus has to solve the cumbersome point counting problem.