The Chinese Remainder Theorem, The Use Of Cryptographic Techniques

In this paper, we introduce the application of Chinese remainder theorem in Cryptography. On the basis of this, we solve the following problems:First of all, we show that a group signature scheme based on Chinese Remainder Theorem is insecure through the security analysis, and improve it. The improved scheme is more secure while keeping the benefits based on CRT.Secondly, we propose a (t,n) threshold shared signature scheme, using improved Miyaji signature scheme and threshold shared scheme based on CRT (Asmuth-Bloom scheme).Meanwhile, we introduce a high-efficiency algorithm for RSA modular multiplication, especially the application, and the insecurity of digital signature schemes with message recovery. Both of them are based on CRT.