Software Implementation of the NIST Elliptic Curves Over Prime Fields
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Fast Implementation of Elliptic Curve Arithmetic in GF(pn)
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Fast and Flexible Elliptic Curve Point Arithmetic over Prime Fields
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Improved techniques for fast exponentiation
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Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Affine precomputation with sole inversion in elliptic curve cryptography
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ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
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CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
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 techniques for high-speed elliptic curve cryptography
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
Efficient precomputation schemes of kP+lQ
Information Processing Letters
A duality in space usage between left-to-right and right-to-left exponentiation
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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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Designs, Codes and Cryptography
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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We present a new methodology to derive faster composite operations of the form dP + Q, where d is a small integer ≥ 2, for generic ECC scalar multiplications over prime fields. In particular, we present an efficient Doubling-Addition (DA) operation that can be exploited to accelerate most scalar multiplication methods, including multiscalar variants. We also present a new precomputation scheme useful for window-based scalar multiplication that is shown to achieve the lowest cost among all known methods using only one inversion. In comparison to the remaining approaches that use none or several inversions, our scheme offers higher performance for most common I/M ratios. By combining the benefits of our precomputation scheme and the new DA operation, we can save up to 6.2% on the scalar multiplication using fractional wNAF.