Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Theoretical Computer Science
An advanced method for joint scalar multiplications on memory constraint devices
ESAS'05 Proceedings of the Second European conference on Security and Privacy in Ad-Hoc and Sensor Networks
Hi-index | 0.00 |
The joint sparse form (JSF) is a representation of a pair of integers, which is famous for accelerating a multi-scalar multiplication in elliptic curve cryptosystems. Solinas’ original paper showed three unsolved problems on the enhancement of JSF. Whereas two of them have been solved, the other still remains to be done. The remaining unsolved problem is as follows: To design a representation of a pair of integers using a larger digit set such as a set involving ±3, while the original JSF utilizes the digit set that consists of 0, ±1 for representing a pair of integers. This paper puts an end to the problem; width-3 JSF. The proposed enhancement satisfies properties that are similar to that of the original. For example, the enhanced representation is defined as a representation that satisfies some rules. Some other properties are the existence, the uniqueness of such a representation, and the optimality of the Hamming weight. The non-zero density of the width-3 JSF is 563/1574(=0.3577) and this is ideal. The conversion algorithm to the enhanced representation takes O(logn) memory and O(n) computational cost, which is very efficient, where n stands for the bit length of the integers.