Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
A course in computational algebraic number theory
Elliptic curves and their applications to cryptography: an introduction
Elliptic curves and their applications to cryptography: an introduction
Elliptic curves in cryptography
Elliptic curves in cryptography
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress 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
Selecting Cryptographic Key Sizes
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
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
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Address-Bit Differential Power Analysis of Cryptographic Schemes OK-ECDH and OK-ECDSA
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Montgomery Ladder for All Genus 2 Curves in Characteristic 2
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Differential addition in generalized Edwards coordinates
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery form elliptic curve over any nonbinary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods in Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementations with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.