A survey of fast exponentiation methods
Journal of Algorithms
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key 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
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
ISC '02 Proceedings of the 5th International Conference on Information Security
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
Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
A Course in Computational Algebraic Number Theory
A Course in Computational Algebraic Number Theory
| Hi-index | 0.00 |
The computational performance of cryptographic protocols based on elliptic curves strongly depends on the efficiency of multi scalar multiplications of uP + vQ, where P and Q are points on an elliptic curve. An efficient way to compute uP + vQ is to compute two scalar multiplications simultaneously, rather than computing each scalar multiplications separately. Koblitz introduced a family of curves which admit especially fast elliptic multi scalar multiplication and Solinas brought forward an improved algorithm for kP using the 驴-expansion of Koblitz Curves. We give a new algorithm for uP +vQ on Koblitz Curves based on the 驴-expansion with the additional speedup of the new joint spare form,which is called 驴-NJSF, where P and Q are on an Koblitz Curve defined over F2m. We also present an efficient algorithm to obtain the 驴-NJSF and prove its average joint Hamming density (AJHD) is 27/56 via the method of stochastic process. Computing uP +vQby our algorithm can reduce the computational complexity in more than 95% cases, and the running time is reduced by 3.6% on average, while compared with computation that by using 驴-JSF.