椭圆曲线密码的优化设计方法

doi:10.3969/j.issn.1001-2400.2015.01.011

Abstract

Abstract:

Elliptic Curve Cryptography algorithm, which depends on the difficulty of the discrete logarithm problem, has some characteristics of low computational overhead and high security. The main operation of Elliptic Curve Cryptography is point multiplication which is the most time-consuming part in the encryption and decryption process. This paper optimizes the point multiplication, proposes a hardware architecture to implement Elliptic Curve Cryptography algorithm and designs encryption and decryption system basing on FGPA. The proposed method improves the encryption and decryption efficiency by the multiplication, squaring and division optimization in the finite binary field. Analysis and testing show that the proposed architecture has some advantages with low hard resource consumption, low complexity of module interface and scalability, the designed encryption and decryption system supports key length of 113bit, 163bit, 193bit and so on, and relative to the software Elliptic Curve Cryptography system running on embedded processor, this encryption and decryption processor can achieve thousands of times faster.

Key words: FPGA, ECC, elliptic curve, point multiplication

CUI Xining;YANG Jingwei;YE Hong;DAI Xiaodi. Optimized design method on elliptic curve cryptography[J].J4, 2015, 42(1): 69-74.

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Optimized design method on elliptic curve cryptography

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