Journal of Cryptology
A course in computational algebraic number theory
A course in computational algebraic number theory
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th 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
Elliptic Scalar Multiplication Using Point Halving
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
On redundant T-adic expansions and non-adjacent digit sets
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
A note on the signed sliding window integer recoding and a left-to-right analogue
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Field inversion and point halving revisited
IEEE Transactions on Computers
On redundant T-adic expansions and non-adjacent digit sets
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Another look at square roots (and other less common operations) in fields of even characteristic
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Designs, Codes and Cryptography
A duality in space usage between left-to-right and right-to-left exponentiation
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Complete atomic blocks for elliptic curves in jacobian coordinates over prime fields
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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In this paper we introduce scalar multiplication algorithms for several classes of elliptic and hyperelliptic curves. The methods are variations on Yao's scalar multiplication algorithm where independent group operations are shown in an explicit way. We can thusmerge several group operations and reduce the number of field operations by means of Montgomery's trick. The results are that scalar multiplication on elliptic curves in even characteristic based on point halving can be improved by at least 10% and the performance of Koblitz curves by 25% to 32%.