高效能橢圓曲線密碼架構之設計

• Main Authors: Yang, Kai-Hsiang, 楊凱翔
• Other Authors: Huang, Chih-Tsun
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/88616034885897233614

碩士 === 國立清華大學 === 資訊工程學系 === 97 === Elliptic curve cryptography (ECC), a public-key cryptography, has raised much interests and attentions recently. Compared with RSA, ECC has short key length but provides the same security level as RSA. With this property, ECC is more suitable for the small and portable devices. Because the short key length reduces the storage and transmission power. In our approach, we try to accelerate the performance of scalar multiplication, which is an important point operation in ECC. Based on the Montgomery ladder method over binary field GF(2n), we address the operation scheduling results for different number of Arithmetic Units (AUs) with optimized amount of registers during the scalar multiplication. In order to do the modular reduction over GF(2163), we derive the closed form equations for pentanomial bit-parallel reduction. The AU is for the basic finite field operations, such as field multiplication, field squaring, and field addition. The multiplication inside the AU and the data transmission are well scheduled to speed up the critical operation effectively. Multipliers with various word lengths are designed and evaluated in terms of performance and area. The smaller word length makes the multiplier smaller but introduces more extra cycles, and vice versa. We also present an ECC core with different numbers of AU for the scalar multiplication. The implementation result with TSMC 0.13μm CMOS technology shows that we can perform a scalar multiplication in 20.9μs and 11.1μs with one-AU and three-AU ECC cores over GF(2163), respectively. At the last, the AT comparison between our approach and related works also shows that our approach is better than others.