A SIMD multiplier-accumulator design for pairing cryptography

Finite field arithmetic is the base of cryptography algorithms like Elliptic Curves Cryptography (ECC) and RSA. In this paper, We have designed an arithmetic unit to implement the operation (A ± αB)mod N, where α is a small number compared with N. In our design, the coefficient α is smaller than 128. The basic motivation of designing this multiply-accumulate (MAC) unit is to support some high security ECC algorithms such as Optimal Ate Pairings. The well-known Optimal Ate Pairing based on Barreto-Naehrig elliptic curve is famous for it´s efficient implementation. In those cryptography algorithms, the calculation of αB mod N is required, where α is a small number. It is unefficient to use modular multiplication to calculate it. This is the basic motivation of implementing the operation (A ± αB)mod N with α <;<; N. Considering that the Barreto-Naehrig elliptic curve for pairing are defined in F_P12, we implement the arithmetic unit to be a Single Instruction Multiple Data (SIMD) unit with pipelined structure. Thus, the design is suitable for arithmetic in extensions of finte fields. We have modified the Barrett reduction algorithm to make it suitable for the design. The design is synthesized with SMIC 65nm CMOS process. Compared with using modular multiplication to calculate (A ± αB)mod N, Our work shows better performance with small latency and high throughput.