Recently, the residue number system (RNS) has been intensively studied. The Chinese remainder theorem (CRT) is a solution to the conversion problem of a number to RNS with a general moduli set. This paper introduces the generalized CRT (GCRT) with parallel algorithms used for the conversion. The GCRT differs from the CRT because it has the advantage of having more applications than does the CRT...

With the rapid development of MANET, secure and practical authentication is becoming increasingly important. The existing works perform the research from two aspects, i.e., (a)secure key division and distributed storage, (b)secure distributed authentication. But there still exist several unsolved problems. Specifically, it may suffer from cheating problems and fault authentication attack, which...

In this paper we analyze the cheating detection and cheater identification problems for the secret sharing schemes based on the Chinese remainder theorem (CRT ), more exactly for Mignotte [1] and Asmuth-Bloom [2] schemes. We prove that the majority of the solutions for Shamir’s scheme [3] can be translated to these schemes and, moreover, there are some interesting specific solutions.

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure from an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop...

In this paper, new context of Chinese Remainder Theorem (CRT) based analysis of combinatorial sequence generators has been presented. CRT is exploited to establish fixed patterns in LFSR sequences and underlying cyclic structures of finite fields. New methodology of direct computations of DFT spectral points in higher finite fields from known DFT spectra points of smaller constituent fields is ...

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure by an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop a...

Based on the Chinese Remainder Theorem (CRT), Quisquater and Couvreur proposed an RSA variant, RSA-CRT, to speedup RSA decryption. According to RSA-CRT, Wiener suggested another RSA variant, Rebalanced RSA-CRT, to further speedup RSA-CRT decryption by shifting decryption cost to encryption cost. However, such an approach will make RSA encryption very time-consuming because the public exponent e...

Homomorphic encryption technology is the holy grail of cryptography and has a wide range applications in practice. This paper proposes homomorphic scheme over fraction based on Chinese remainder theorem (CRT) Dayan qiuyi rule. performs decryption operations by forming congruence groups homomorphism. The solution this first combines traditional CRT algorithm with rule to obtain CRTF that can be ...