Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
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
Elliptic Curves with the Montgomery-Form and Their Cryptographic Applications
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
On the Performance of Signature Schemes Based on Elliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
ISC '02 Proceedings of the 5th International Conference on Information Security
On Montgomery-Like Representationsfor Elliptic Curves over GF(2k)
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
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We propose a new methodto compute x-coordinate of kP + lQ simultaneously on the elliptic curve with Montgomery form over Fp without precomputedp oints. To compute x-coordinate of kP +lQ is requiredin ECDSA signature verification. The proposedmetho dis about 25% faster than the methodusing scalar multiplication andthe recovery of Y -coordinate of kP and lQ on the elliptic curve with Montgomery form over Fp, and also slightly faster than the simultaneous scalar multiplication on the elliptic curve with Weierstrass form over Fp using NAF and mixedco ordinates. Furthermore, our methodis applicable to Montgomery methodon elliptic curves over F2n.