Advances in Applied Mathematics
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
A New Addition Formula for Elliptic Curves over GF(2^n)
IEEE Transactions on Computers
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in 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
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
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic Curves: Number Theory and Cryptography
Elliptic Curves: Number Theory and Cryptography
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
The Jacobi model of an elliptic curve and side-channel analysis
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
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
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
Finite Fields and Their Applications
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Another elliptic curve model for faster pairing computation
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
On the implementation of unified arithmetic on binary huff curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
| Hi-index | 0.00 |
This paper considers a generalized form for Hessian curves. The family of generalized Hessian curves covers more isomorphism classes of elliptic curves. Over a finite field $\mathbb{F}_q$, it is shown to be equivalent to the family of elliptic curves with a torsion subgroup isomorphic to ℤ/3ℤ. This paper provides efficient unified addition formulas for generalized Hessian curves. The formulas even feature completeness for suitably chosen parameters. This paper also presents extremely fast addition formulas for generalized binary Hessian curves. The fastest projective addition formulas require 9M+3S, where M is the cost of a field multiplication and S is the cost of a field squaring. Moreover, very fast differential addition and doubling formulas are provided that need only 5M+4S when the curve is chosen with small curve parameters.