Advances in Applied Mathematics
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A New Addition Formula for Elliptic Curves over GF(2^n)
IEEE Transactions on Computers
Speeding Up Elliptic Scalar Multiplication with Precomputation
ICISC '99 Proceedings of the Second International Conference on Information Security and Cryptology
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the 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
Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Elliptic Scalar Multiplication Using Point Halving
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Exponent Recoding and Regular Exponentiation Algorithms
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
IEEE Transactions on Computers
A New Protocol for the Nearby Friend Problem
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Efficient software implementation of binary field arithmetic using vector instruction sets
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
Journal of Cryptology
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Field inversion and point halving revisited
IEEE Transactions on Computers
An implementation of elliptic curve cryptosystems over F2155
IEEE Journal on Selected Areas in Communications
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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In this work we present the λ-coordinates, a new system for representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and timing results of our software implementation over the field $\mathbb{F}_{2^{254}}$. As a result, we improve speed records for protected/unprotected single/multi-core software implementations of random-point elliptic curve scalar multiplication at the 128-bit security level. When implemented on a Sandy Bridge 3.4GHz Intel Xeon processor, our software is able to compute a single/multi-core unprotected scalar multiplication in 72,300 and 47,900 clock cycles, respectively; and a protected single-core scalar multiplication in 114,800 cycles. These numbers improve by around 2% on the newer Core i7 2.8GHz Ivy Bridge platform.