Hardware realization of fast elliptic curve point multiplication using balanced ternary representation and pre-computation over GF(p)

Abstract

We present a new hardware realization of fast elliptic curve Point Multiplication (PM) using the balanced ternary representation of the scalar multiplier. This hardware implementation uses multiple Elliptic Curve Point Tripler's (ECPT) and Elliptic Curve Point Adders (ECPA). Here, we pre-compute 3P, 9P, 27P, etc. using fast tripling and use them in calculating the final product over GF(p). However, to the best of our knowledge there exist no previous implementations of Balanced Ternary representation and pre-computation over GF(p) on FPGA platform. The FPGA synthesis results show that the proposed TPM6 and TPM24 methods can reach a speed up to 48.147 MHz and 50.814MHz; It needs 11.05µs and 49.45µs for the computation, consumes a power of 1.083W and 1.104W, occupies 2,657 and 5,449 slices respectively. The modular hardware approach used here provides high speed and scalability.