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

摘要

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