Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for uP + vQ on a Family of Elliptic Curves
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 17 - Volume 18
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
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The computational performance of cryptographic protocols using an elliptic curve strongly depends on the efficiency of the scalar multiplication. Some elliptic curve based cryptographic protocols, such as signature verification, require computation of multi scalar multiplications of kP + lQ, where P and Q are points on an elliptic curve. An efficient way to compute kP + lQ is to compute two scalar multiplications simultaneously, rather than computing each scalar multiplication separately. We introduce new efficient algorithms for simultaneous scalar multiplication on an elliptic curve. We also give a detailed analysis of the computational efficiency of our proposed algorithms.