Cryptanalyzing a class of image encryption schemes based on Chinese Remainder Theorem

As a fundamental theorem in number theory, the Chinese Reminder Theorem (CRT) is widely used to construct cryptographic primitives. This paper investigates the security of a class of image encryption schemes based on CRT, referred to as CECRT. Making use of some properties of CRT, the equivalent secret key of CECRT can be recovered efficiently. The required number of pairs of chosen plaintext and the corresponding ciphertext is only $(1+\lceil (\log_2L)/l \rceil)$. The attack complexity is only $O(L)$, where $L$ is the plaintext length and $l$ is the number of bits representing a plaintext symbol. In addition, other defects of CECRT such as invalid compression function and low sensitivity to plaintext, are reported. The work in this paper will help clarify positive role of CRT in cryptology.