Handbook of Applied Cryptography
Handbook of Applied Cryptography
Speeding Up Elliptic Scalar Multiplication with Precomputation
ICISC '99 Proceedings of the Second International Conference on Information Security and Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Elliptic Curve Arithmetic Using SIMD
ISC '01 Proceedings of the 4th International Conference on Information Security
Fast Implementation of Elliptic Curve Arithmetic in GF(pn)
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Compressed jacobian coordinates for OEF
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Efficient, non-optimistic secure circuit evaluation based on the elgamal encryption
WISA'05 Proceedings of the 6th international conference on Information Security Applications
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This paper presents a new sliding window algorithm that is well-suited to an elliptic curve defined over an extension field for which the Frobenius map can be computed quickly, e.g., optimal extension field. The algorithm reduces elliptic curve group operations by approximately 15% for scalar multiplications for a practically used curve in comparison with Lim-Hwang's results presented at PKC2000, the fastest previously reported. The algorithm was implemented on computers. As a result, scalar multiplication can be accomplished in 573碌s, 595碌s, and 254碌s on Pentium II (450 MHz), 21164A (500 MHz), and 21264 (500 MHz) computers, respectively.