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A New Fast Modular Arithmetic Method in Public Key Cryptography
作者姓名:WANG  Bangju  ZHANG  Huanguo
作者单位:[1]School of Computer, Wuhan University, Wuhan 430072, Hubei, China [2]School of Science, Huazhong Agricultural University, Wuhan 430070, Huhei, China
摘    要:0 IntroductionPublic key cryptosystemsolvedthe secure problemof keydistributionsoundlyinsymmetric cryptosystem1],real-ized digital signature and message authentication successfullyin secureinformationsystem. However ,secure applications ofthemneed badly high-speedsoftware,hardware,andarithme-tic computation of large number .Furthermore,the secret ex-ponent cannot betoosmall2]and operands should be 1 024 bitorlarger3]whenthe securitylevel is set high.So,manylargeinteger modular multiplicatio…

关 键 词:公钥密码  模算术  模乘法  模求幂
文章编号:1007-1202(2006)06-1645-04
收稿时间:2006-03-02

A new fast modular arithmetic method in public key cryptography
WANG Bangju ZHANG Huanguo.A New Fast Modular Arithmetic Method in Public Key Cryptography[J].Wuhan University Journal of Natural Sciences,2006,11(6):1645-1648.
Authors:Wang Bangju  Zhang Huanguo
Institution:(1) School of Computer, Wuhan University, 430072 Wuhan, Hubei, China;(2) School of Science, Huazhong Agricultural University, 430070 Wuhan, Hubei, China
Abstract:Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively
Keywords:public key cryptography  modular arithmetic  modular multiplication  modular exponentiation
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