可扩展双域模乘器设计与研究
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摘要
提出一种可扩展同时支持双域的模乘单元体系结构,通过调整内部运算单元的相关参数,可以满足侧重于性能或成本的不同应用.首先从基于字的双域蒙哥马利算法出发,提出模乘单元的基本体系结构;然后考虑了性能优化的两种不同思路与提高工作频率之间的相互折衷和平衡.由于高度统一的算法和紧密结合的模块结构,使得该可扩展双域模乘单元可以同时支持素数域与二进制域两个域的模乘运算,这一点在进行椭圆曲线密码(ECC)运算时尤为重要.最后以256bit素域模乘为例验证本设计,结果表明该可扩展双域模乘单元既可以降低开销,保持合理的可接受性能,又可以提高硬件开销以完全发挥性能潜力.
The architecture of high-performance scalable modular multiplier on dual-field was proposed.Various applications focused on either performance or cost could be satisfied by adjusting the parameter of scalable arithmetic units.Firstly the basic architecture of multiplier was proposed based on the word-based Montgomery algorithm,and then the two approaches of performance improvement and their trade-off between working frequencies were discussed.Moreover,with integration of dualfield from algorithm to structure,modular multiplication over both prime and binary fields could be supported,which was valuable to elliptic curve cryptography(ECC).At last,evaluation shows that for 256 bit modular multiplication over prime field,low cost with reasonable performance or ultra high performance with additional cost both can be achieved according to different configurations.
The architecture of high-performance scalable modular multiplier on dual-field was proposed.Various applications focused on either performance or cost could be satisfied by adjusting the parameter of scalable arithmetic units.Firstly the basic architecture of multiplier was proposed based on the word-based Montgomery algorithm,and then the two approaches of performance improvement and their trade-off between working frequencies were discussed.Moreover,with integration of dualfield from algorithm to structure,modular multiplication over both prime and binary fields could be supported,which was valuable to elliptic curve cryptography(ECC).At last,evaluation shows that for 256 bit modular multiplication over prime field,low cost with reasonable performance or ultra high performance with additional cost both can be achieved according to different configurations.
引文
[1]Diffie W,Hellman M E.New directions in cryptography[J].IEEE Trans Information Theory,1976,22:644-654.
[2]IEEE.IEEE 1363—2000standard specifications for public-key cryptography[S].New York:IEEE Computer Society,2000.
[3]Lopez J,Dahab R.Improved algorithms for elliptic curve arithmetic in GF(2m)[C]∥Proceedings of the Selected Areas in Cryptography.Heidelberg:Springer-Verlag,1998:201-212.
[4]Montgomery P L.Modular multiplication without trial division[J].Math Computation,1985,44(7):519-521.
[5]Wallace C S.A suggestion for a fast multiplier[J].IEEE Transactions on Electronic Computers,1964,EC-13(1):14-17.
[6]陈光化,朱景明,刘名,等.双有限域模乘和模逆算法及其硬件实现[J].电子与信息学报,2010,32(9):2095-2010.
[7]邬贵明,谢向辉,吴东,等.高基Montgomery模乘阵列结构设计与实现[J].计算机工程与科学,2014,36(2):201-205.
[8]郭晓,蒋安平,宗宇.SM2高速双域Montgomery模乘的硬件设计[J].微电子学与计算机,2013,30(9):17-21.
[9]韩炼冰,黄锐,段俊红,等.基于FPGA的素域模乘快速实现方法[J].信息安全与通信保密,2013(9):76-78.
[10]Shieh M D,Lin W C.Word-based montgomery modular multiplication algorithm for low-latency scalable architectures[J].IEEE Transactions on Computers,2010,59(8):1145-1151.
[11]邹雪城,张丽,黎明,等.一种高性能可扩展双域模乘器的研究与设计[J].华中科技大学学报:自然科学版,2011,39(4):25-28.
[2]IEEE.IEEE 1363—2000standard specifications for public-key cryptography[S].New York:IEEE Computer Society,2000.
[3]Lopez J,Dahab R.Improved algorithms for elliptic curve arithmetic in GF(2m)[C]∥Proceedings of the Selected Areas in Cryptography.Heidelberg:Springer-Verlag,1998:201-212.
[4]Montgomery P L.Modular multiplication without trial division[J].Math Computation,1985,44(7):519-521.
[5]Wallace C S.A suggestion for a fast multiplier[J].IEEE Transactions on Electronic Computers,1964,EC-13(1):14-17.
[6]陈光化,朱景明,刘名,等.双有限域模乘和模逆算法及其硬件实现[J].电子与信息学报,2010,32(9):2095-2010.
[7]邬贵明,谢向辉,吴东,等.高基Montgomery模乘阵列结构设计与实现[J].计算机工程与科学,2014,36(2):201-205.
[8]郭晓,蒋安平,宗宇.SM2高速双域Montgomery模乘的硬件设计[J].微电子学与计算机,2013,30(9):17-21.
[9]韩炼冰,黄锐,段俊红,等.基于FPGA的素域模乘快速实现方法[J].信息安全与通信保密,2013(9):76-78.
[10]Shieh M D,Lin W C.Word-based montgomery modular multiplication algorithm for low-latency scalable architectures[J].IEEE Transactions on Computers,2010,59(8):1145-1151.
[11]邹雪城,张丽,黎明,等.一种高性能可扩展双域模乘器的研究与设计[J].华中科技大学学报:自然科学版,2011,39(4):25-28.