中国剩余定理模式下的1 024、2 048位RSA以及常规模式下1 024位RSA解密分别需要710 s、99 s、350 s
快于已发表的同类设计.
Abstract
In this paper
we implement RSA cryptographic using Residue number system (RNS). We choose four modulo similar in the form for every computational unit. The reduction unit supports these four modulo is smaller and shorter than the required reduction unit corresponding to the conventional method selection. According to our proposed method
we select seven groups of modulo with a width of 74
and design a RNS Montgomery multiplier based on Cox-Rower architecture to implement RSA cryptography. In the SMIC 0.13 m standard cell library
clock frequency reaches up to 278 MHz. At this frequency
1 024
2 048-bit RSA decryption in Chinese Remainder Theorem (CRT) mode and 1 024-bit RSA decryption require 710 s
99 s
350 s
respectively
faster than the published related designs.
关键词
Keywords
references
Shieh M D, Chen J H, Wu H H, et al. A new modular exponentiation architecture for efficient design of RSA cryptosystem[J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2008, 16(9): 1151-1161. DOI: 1151
Kawamura S, Koike M, Sano F, et al. Cox-rower architecture for fast parallel montgomery multiplication[C]// Advances in Cryptology - EUROCRYPT 2000, International Conference on the Theory and Application of Cryptographic Techniques. Bruges, Belgium, 2000: 523-538.
Montgomery P L. Modular multiplication without trial division[J]. Mathematics of Computation, 1985, 44(17): 519-521. DOI: 519
Néto J C, Tenca A F, Ruggiero W V. CRT RSA decryption: modular exponentiation based solely on montgomery multiplication[C]//Signals, Systems and Computers, 2015 49th Asilomar Conference on. Pacific Grove, CA, USA, IEEE, 2015: 431-436.
Nozaki H, Motoyama M, Shimbo A, et al. Implementation of RSA algorithm based on RNS montgomery multiplication[C]//International Workshop on Cryptographic Hardware and Embedded Systems. Springer, Berlin, Heidelberg, 2001: 364-376.
Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems[J]. Communications of the ACM, 1978, 21(2): 120-126. DOI: 120
Gandino F, Lamberti F, Paravati G, et al. An algorithmic and architectural study on Montgomery exponentiation in RNS[J]. IEEE Transactions on Computers, 2012, 61(8): 1071-1083. DOI: 1071
Tao W U, Shuguo L I, Liu L T. Fast RSA decryption through high-radix scalable montgomery modular multipliers[J]. Science China Information Sciences, 2015, 58(6): 1-16. DOI: 1