Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The Design of Rijndael
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the 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
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
High-Speed Software Multiplication in F2m
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
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
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Fast Parallel Table Lookups to Accelerate Symmetric-Key Cryptography
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Accelerating the Whirlpool Hash Function Using Parallel Table Lookup and Fast Cyclical Permutation
Fast Software Encryption
Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
IEEE Transactions on Computers
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
SSE Implementation of Multivariate PKCs on Modern x86 CPUs
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Compact McEliece Keys from Goppa Codes
Selected Areas in Cryptography
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
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
High-speed parallel software implementation of the ηT pairing
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
Field inversion and point halving revisited
IEEE Transactions on Computers
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Efficient software implementations of large finite fields GF(2n) for secure storage applications
ACM Transactions on Storage (TOS)
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
Hi-index | 0.00 |
In this paper we describe an efficient software implementation of characteristic 2 fields making extensive use of vector instruction sets commonly found in desktop processors. Field elements are represented in a split form so performance-critical field operations can be formulated in terms of simple operations over 4-bit sets. In particular, we detail techniques for implementing field multiplication, squaring, square root extraction and present a constant-memory lookup-based multiplication strategy. Our representation makes extensive use of the parallel table lookup (PTLU) instruction recently introduced in popular desktop platforms and follows the trend of accelerating implementations of cryptography through PTLU-style instructions. We present timings for several binary fields commonly employed for curve-based cryptography and illustrate the presented techniques with executions of the ECDH and ECDSA protocols over binary curves at the 128-bit and 256-bit security levels standardized by NIST. Our implementation results are compared with publicly available benchmarking data.