Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
A course in computational algebraic number theory
A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Efficient Construction of Cryptographically Strong Elliptic Curves
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Efficient Computation of Singular Moduli with Application in Cryptography
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Generating prime order elliptic curves: difficulties and efficiency considerations
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
| Hi-index | 0.00 |
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Complex Multiplication. Furthermore, we demonstrate the efficiency of the algorithm in practice by giving practical running times. In addition, we present statistics on the number of cryptographically strong elliptic curves of prime order for Optimal Extension Fields of cardinality (232 + c)5 with c