As a fundamental of number theory, Chinese Re1 minder Theorem (CRT) is widely used to construct cryptographic 2 primitive. This paper studies security of a compression and 3 encryption scheme based on CRT, called CECRT. Based on 4 some properties of CRT, the equivalent secret key of CECRT 5 can be reconstructed efficiently: the pair number of required 6 of chosen plaintext and the corresponding...

This report is an incomplete survey of Chinese Remaindering Codes. We study the work of Goldreich, Ron and Sudan [GRS00] and Boneh [B02] which give unique and list-decoding algorithms for an error correcting code based on the Chinese Remaindering Theorem. More specifically, we will look at a decoding algorithm from [GSM00] which uniquely decodes upto (n − k) log p1 log p1+log pn errors. We will...

In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundament...

The aim of this paper is to find more Karatsuba-like formulae for a fixed set of moduli polynomials in GF (2)[x]. To this end, a theoretical framework is established. We first generalize the division algorithm, and then present a generalized definition of the remainder of integer division. Finally, a previously generalized Chinese remainder theorem is used to achieve our initial goal. As a by-p...