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Front. Inform. Technol. Electron. Eng.  2010, Vol. 11 Issue (9): 724-736    DOI: 10.1631/jzus.C0910660
    
A low-power and low-energy flexible GF(p) elliptic-curve cryptography processor
Hamid Reza Ahmadi, Ali Afzali-Kusha
School of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395-515, Tehran, Iran
A low-power and low-energy flexible GF(p) elliptic-curve cryptography processor
Hamid Reza Ahmadi, Ali Afzali-Kusha
School of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395-515, Tehran, Iran
 全文: PDF 
摘要： We investigate the use of two integer inversion algorithms, a modified Montgomery modulo inverse and a Fermat’s Little Theorem based inversion, in a prime-field affine-coordinate elliptic-curve crypto-processor. To perform this, we present a low-power/energy GF(p) affine-coordinate elliptic-curve cryptography (ECC) processor design with a simplified architecture and complete flexibility in terms of the field and curve parameters. The design can use either of the inversion algorithms. Based on the implementations of this design for 168-, 192-, and 224-bit prime fields using a standard 0.13 μm CMOS technology, we compare the efficiency of the algorithms in terms of power/energy consumption, area, and calculation time. The results show that while the Fermat’s theorem approach is not appropriate for the affine-coordinate ECC processors due to its long computation time, the Montgomery modulo inverse algorithm is a good candidate for low-energy implementations. The results also show that the 168-bit ECC processor based on the Montgomery modulo inverse completes one scalar multiplication in only 0.4 s at a 1 MHz clock frequency consuming only 12.92 μJ, which is lower than the reported values for similar designs.
关键词： Elliptic-curve cryptography (ECC);  Prime field;  Montgomery multiplication;  Montgomery inverse;  Low-energy    
Abstract: We investigate the use of two integer inversion algorithms, a modified Montgomery modulo inverse and a Fermat’s Little Theorem based inversion, in a prime-field affine-coordinate elliptic-curve crypto-processor. To perform this, we present a low-power/energy GF(p) affine-coordinate elliptic-curve cryptography (ECC) processor design with a simplified architecture and complete flexibility in terms of the field and curve parameters. The design can use either of the inversion algorithms. Based on the implementations of this design for 168-, 192-, and 224-bit prime fields using a standard 0.13 μm CMOS technology, we compare the efficiency of the algorithms in terms of power/energy consumption, area, and calculation time. The results show that while the Fermat’s theorem approach is not appropriate for the affine-coordinate ECC processors due to its long computation time, the Montgomery modulo inverse algorithm is a good candidate for low-energy implementations. The results also show that the 168-bit ECC processor based on the Montgomery modulo inverse completes one scalar multiplication in only 0.4 s at a 1 MHz clock frequency consuming only 12.92 μJ, which is lower than the reported values for similar designs.
Key words: Elliptic-curve cryptography (ECC)    Prime field    Montgomery multiplication    Montgomery inverse    Low-energy
收稿日期: 2009-10-30 出版日期: 2010-09-07
CLC:  TN4  
基金资助: Project supported in part by the  Iran Telecommunication Research Center (ITRC) and the Research Council of University of Tehran
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Hamid Reza Ahmadi
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Hamid Reza Ahmadi, Ali Afzali-Kusha. A low-power and low-energy flexible GF(p) elliptic-curve cryptography processor. Front. Inform. Technol. Electron. Eng., 2010, 11(9): 724-736.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/jzus.C0910660    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2010/V11/I9/724

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