A Dual-Core High-Performance Processor for Elliptic Curve Cryptography in GF(p) Over Generic Weierstrass Curves
Yujun Xie, Yuan Liu, Xin Zheng, Wenhao Zhu, Junxian Li, Jianzhong Li, Shuting Cai, Xiaoming Xiong
Abstract
A dual-core high-performance processor for Elliptic Curve Cryptography (ECC) in GF( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${p}$ </tex-math></inline-formula> ) over Generic Weierstrass Curves was presented in this brief. Firstly, an optimized radix-128 Montgomery modular multiplication algorithm was proposed. It takes 6 clock cycles to calculate modular multiplication, which promotes the speed of elliptic curve point-addition (PA) and elliptic curve point-doubling (PD). Secondly, a dual-core hardware architecture which includes PD core and PA core to calculate elliptic curve point-multiplication (PM) was developed. It can speed up the PM by adopting parallelism with different levels and optimizing the scheduling. Finally, a data transfer architecture between PA and PD cores was proposed which requires only a 1024-bit register. It improves the speed of PM. The proposed design consumes 996k gates and compute the PM in 0.017 ms on ASIC with a 90 nm standard cell library. Moreover, the proposed design is also implemented on FPGA (Virtex-6 platform), which consumes 182k LUTs and compute the PM in 0.056 ms.