Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in 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
Exceptional Procedure Attackon Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: 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 Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Embedded Cryptographic Hardware: Methodologies & Architectures
Embedded Cryptographic Hardware: Methodologies & Architectures
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
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
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Toric forms of elliptic curves and their arithmetic
Journal of Symbolic Computation
To infinity and beyond: combined attack on ECC using points of low order
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded 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
Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity
Quantum Information & Computation
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This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n茂戮驴 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over .This paper also presents dedicated doubling formulas for these curves using 2M+ 6S+ 3D, where Mis the cost of a field multiplication, Sis the cost of a field squaring, and Dis the cost of multiplying by a curve parameter. These doubling formulas are also the first complete doubling formulas in the literature, with no exceptions for the neutral element, points of order 2, etc.Finally, this paper presents complete formulas for differential addition, i.e., addition of points with known difference. A differential addition and doubling, the basic step in a Montgomery ladder, uses 5M+ 4S+ 2Dwhen the known difference is given in affine form.