The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Selected papers on analysis of algorithms
Selected papers on analysis of algorithms
Elliptic curves in cryptography
Elliptic curves in cryptography
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
An Improved Implementation of Elliptic Curves over GF(2) when Using Projective Point Arithmetic
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
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
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
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
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: 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
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th 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
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
Finite Fields and Their Applications
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This paper discusses representations for computation on non-supersingular elliptic curves over binary fields, where computations are performed on the x-coordinates only. We discuss existing methods and present a new one, giving rise to a faster addition routine than previous Montgomery-representations. As a result a double exponentiation routine is described that requires 8.5 field multiplications per exponent bit, but that does not allow easy y-coordinate recovery. For comparison, we also give a briefu pdate oft he survey by Hankerson et al. and conclude that, for non-constrained devices, using a Montgomery-representation is slower for both single and double exponentiation than projective methods with y-coordinate.