Applications Of Chinese Remainder Theorem In Cryptography

The ancient Chinese people and mathematicians put forward the ChineseRemainder Theorem,which has made a tremendous contribution to the worldmathematics. The CRT not only deeply influenced modern mathematics but also hada great many applications in cryptology and daily life. On this case, this paper dosome research as followed:Firstly, this paper deeply discusses the applications of Chinese Remainder Theorem indigital signature. Based on the nature of this theorem, it has many good properties ingroup signature schemes.Some new mumber’s join-in or his/her leaving whoseauthority has been revoked will not affect other members’ private key. The twoprocesses above of course will be implemented rapidly. While properly designed, thecommon mode attacks will be avoided and all these schemes can meet almost all therequirements of security in digital signatures, say basic anonymity, unforgeability,resistance against joint-attack. We can also do some further improvement in details tomeet other specific properties, say unlinkability and so on.Secondly, in the perspective of computational complexity, this paper proves andanalyses the role of the CRT in improving the operational efficiency. With the help ofthe CRT, the large integer mode has been decomposited into smaller modulus so thatthe calculation in modular exponentiation has been remarkbly speed up, which is themain core of the cryptology schemes.finally, this paper introduces the CRT to other crytographic protocols and do somereserch in key distribution, key recovery, channel coding, traitor tracing, digitalsecurity. The author achieve the goal of optimizing many crytographic protocols invarious aspects.