A High Performance FPGA Implementation of 256-bit Elliptic Curve Cryptography Processor Over GF(<i>p</i>)

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  • FENG Xiang
    Institute of Microelectronics, Tsinghua University
  • LI Shuguo
    Institute of Microelectronics, Tsinghua University

Description

Field Programmable Gate Array (FPGA) implementation of Elliptic Curve Cryptography (ECC) over GF(p) is commonly not fast enough to meet the request of high-performance applications. There are three critical factors to determine the performance of ECC processor over GF(p): multiplication structure, modular multiplication algorithm, and scalar point multiplication scheduling. This work proposes a novel multiplication structure which is a two-stage pipeline on the basis of Karatsuba-Ofman algorithm. With the proposed multiplication structure, we design a 256-bit modular multiplier based on Improved Barret Modular Multiplication algorithm. Upon the modular multiplier, we finish the scalar point multiplication scheduling and implement a high-performance ECC processor on FPGA. Compared with the previous modular multipliers, our modular multiplier reduces the 256-bit modular multiplication time by 28% at least. Synthesis result on Altera Stratix II shows that our ECC processor can complete a 256-bit ECC scalar point multiplication in 0.51ms, which is at least 1.3 times faster than the currently reported FPGA ECC processors over GF(p).

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