Area-time efficient point multiplication architecture on twisted Edwards curve over general prime field GF(p)$$ GF(p) $$

Elliptic curve point multiplication is the main primitive required in almost all security schemes using elliptic curve cryptography (ECC). It is the leading computationally intensive operation that sets the overall performance of the associated cryptosystem. This work presents a highly novel area-time efficient elliptic curve point multiplier over a general prime field GF(p)$$ GF(p) $$. It is based on an efficient radix-2(3) parallel GF(p)$$ GF(p) $$ multiplier, which performs a k$$ k $$-bit GF(p)$$ GF(p) $$ multiplication in (k3)$$ \left(\frac{k}{3}\right) $$ clock cycles. On the system level, the twisted Edwards curves with unified point addition using projective coordinates are adopted, where an efficient scheduling technique is presented to schedule several GF(p)$$ GF(p) $$ operations on deployed modular arithmetic units. Due to the introduced optimization at different stages of the design, latency, hardware resource requirement, and total clock cycle count are reduced significantly. Synthesis, and implementation of the proposed design over different Xilinx FPGA platforms are completed using the Xilinx ISE Design Suite tool for key sizes of 192, 224, and 256 bits. The 256-bit Xilinx Virtex-7 FPGA implementation reveals that it completes a single point multiplication operation in 0.8 ms and occupies 6.7K FPGA slices in a clock cycle count of 132.2K. It produces significantly better area-time product and throughput per slice than the contemporary designs. The proposed design also has the potential to counter simple power analysis and timing attacks. Thus, it is an elegant solution to develop ECC-based cryptosystems for applications, where both speed and hardware resource consumption are important.