A unified, scalable dual-field Montgomery multiplier architecture for ECCs

This paper proposes a unified, scalable dual-field Montgomery multiplier architecture which can operate in both prime GF(p) and binary extension fields GF(2ⁿ) for arbitrary prime numbers and irreducible polynomials. The Montgomery multiplier architecture has advantages in speed and flexibility for operator size compared with conventional architectures using long adders or long-bit × short-bit multipliers by introducing using a balanced r-bit×r-bit dual field multiplier. Finally, the hardware size of multipliers on GF(2ⁿ) for various r, are investigated. The Montgomery multiplier provides efficient execution of Montgomery multiplication in either field for different operand lengths, which suitable be applied to elliptic curve cryptographic (ECC) processors.