A course in number theory and cryptography
A course in number theory and cryptography
A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
Use of Elliptic Curves in Cryptography
CRYPTO '85 Advances in Cryptology
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Finding good random elliptic curves for cryptosystems defined over IF2n
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Counting the number of points on elliptic curves over finite fields: strategies and performances
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
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A family of elliptic curves for cryptographic use is proposed for which the determination of the order of the corresponding algebraic group is much easier than in the general case. This makes it easier to meet the cryptographic requirement that this order have a large prime factor. Another advantage of this familiy is that the group operation simplifies slightly. Explicit numerical examples are given that are suitable for practical use.