Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A fast addition algorithm for elliptic curve arithmetic in GF(2n) using projective coordinataes
Information Processing Letters
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
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
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
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient representations on koblitz curves with resistance to side channel attacks
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Efficient precomputation schemes of kP+lQ
Information Processing Letters
Improved precomputation scheme for scalar multiplication on elliptic curves
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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We present an innovative technique to add elliptic curve points with the form P ±Q , and discuss its application to the generation of precomputed tables for the scalar multiplication. Our analysis shows that the proposed schemes offer, to the best of our knowledge, the lowest costs for precomputing points on both single and multiple scalar multiplication and for various elliptic curve forms, including the highly efficient Jacobi quartics and Edwards curves.