Performance Evaluation of Elliptic Curve Projective Coordinates with Parallel GF(p) Field Operations and Side-Channel Atomicity

This paper presents performance analysis and evaluation of elliptic curve projective coordinates with parallel field operations over GF( p ). Side-channel atomicity has been used in these comparisons. The field computations of point operations are segmented into atomic blocks that are indistinguishable from each other to resist against simple power analysis attacks. These atomic blocks are executed in parallel using 2, 3 and 4 multipliers. Comparisons between the Homogeneous, Jacobian and Edwards coordinate systems using parallel field operations over GF( p ) are presented. Results show that Edwards coordinate system outperforms both the Homogeneous and Jacobian coordinate systems and gives better area-time (AT) and area-time 2 (AT 2 ) complexities.