Optimization of elliptic curve scalar multiplication using constraint based scheduling

Abstract

Elliptic Curve Cryptography is public key cryptography that features smaller keys, ciphertexts, and signatures and is faster than RSA at the same security level. Scalar multiplication is the main and the most compute-intensive operation in the generation of keys. Point Addition, Doubling and Inversion are the basic operations for scalar multiplication. Inversion is a very expensive operation as compared to multiplication, addition and squaring in the finite fields with an affine coordinate system. López-Dahab coordinates are the best alternative to reduce the inversion overhead in scalar computation. Area, Delay and Power trade-offs are the main constraints in hardware implementations of scalar multiplication. In this paper, optimization of elliptic curve scalar multiplication using constraint-based scheduling for the López-Dahab coordinate system is proposed. Data dependency graphs of point addition and doubling are modified for optimization of area and delay. The proposed architecture is implemented on Altera Stratix-II FPGA. The constraint is applied on the field multiplication operation and the considerable area is reduced. The proposed architecture computes scalar multiplication in 11.43 μs and takes 9856 ALMs. The performance comparison with state of the art shows that area is reduced by 41.21%, delay is reduced by 2.4% and Area-Delay-Product is improved.