On the Number of Trace-One Elements in Polynomial Bases for $$\mathbb{F}_{2^n}$$
Designs, Codes and Cryptography
Formulas for cube roots in F3m
Discrete Applied Mathematics
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Parallel Itoh---Tsujii multiplicative inversion algorithm for a special class of trinomials
Designs, Codes and Cryptography
Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Software Implementation of Arithmetic in
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
On the application of pairing based cryptography to wireless sensor networks
Proceedings of the second ACM conference on Wireless network security
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Delaying and merging operations in scalar multiplication: applications to curve-based cryptosystems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Another look at square roots (and other less common operations) in fields of even characteristic
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
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
Transactions on computational science XI
A correlation power analysis attack against tate pairing on FPGA
ARC'11 Proceedings of the 7th international conference on Reconfigurable computing: architectures, tools and applications
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
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
Efficient simultaneous inversion in parallel and application to point multiplication in ECC
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Advances in alternative non-adjacent form representations
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Accelerating inverse of GF(2n) with precomputation
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
High-speed parallel software implementation of the ηT pairing
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Typing a core binary-field arithmetic in a light logic
FOPARA'11 Proceedings of the Second international conference on Foundational and Practical Aspects of Resource Analysis
ISC'07 Proceedings of the 10th international conference on Information Security
Speeding up elliptic curve discrete logarithm computations with point halving
Designs, Codes and Cryptography
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel and compare these methods to traditional algorithms that use point doubling. The performance advantage of halving methods is clearest in the case of point multiplication kP, where P is not known in advance and smaller field inversion to multiplication ratios generally favor halving. Although halving essentially operates on affine coordinate representations, we adapt an algorithm of Knuth to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.