Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Improving SSL Handshake Performance via Batching
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Finding Optimum Parallel Coprocessor Design for Genus 2 Hyperelliptic Curve Cryptosystems
ITCC '04 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'04) Volume 2 - Volume 2
Field inversion and point halving revisited
IEEE Transactions on Computers
| Hi-index | 0.00 |
Inversion is the costliest of all finite field operations. Some algorithms require computation of several finite field elements simultaneously (elliptic curve factorization for example). Montgomery’s trick is a well known technique for performing the same in a sequential set up with little scope for parallelization. In the current work we propose an algorithm which needs almost same computational resources as Montgomery’s trick, but can be easily parallelized. Our algorithm uses binary tree structures for computation and using 2r−1 multipliers, it can simultaneously invert 2r elements in 2r multiplication rounds and one inversion round. We also describe how the algorithm can be used when 2, 4, ... number of multipliers are available. To exhibit the utility of the method, we apply it to obtain a parallel algorithm for elliptic curve point multiplication. The proposed method is immune to side-channel attacks and compares favourably to many parallel algorithms existing in literature.