Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Fast and Flexible Elliptic Curve Point Arithmetic over Prime Fields
IEEE Transactions on Computers
New Point Addition Formulae for ECC Applications
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Novel Precomputation Schemes for Elliptic Curve Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
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Many efficient multiple scalar multiplications have to compute the form kP+lQ. And if the points P and Q are unknown before the computation of multiple scalar multiplications, we have to precompute and store some points as fast as possible. This paper proposes an efficient precomputation scheme of kP+lQ by using conjugate and co-Z addition formulas where k and l are integers, and P and Q are points on a curve. To compute c"iP+/-d"iQ where c"i,d"i@?{1,3,5,...,m}, our scheme is more efficient than others.