On the Security of Key-Based Interval Splitting Arithmetic Coding With Respect to Message Indistinguishability

Key-based interval splitting arithmetic coding (KSAC) has been proposed to improve the security of traditional arithmetic coding (AC). Chosen-plaintext attacks have been proposed for KSAC when the same key is used to encrypt different messages. In this paper, we consider a stronger version of KSAC, where different keys are used to encrypt different messages. We then use message indistinguishability to prove that this version of KSAC is insecure under ciphertext-only attacks, a weaker form of attack than chosen-plaintext attacks. Indistinguishability in the presence of an eavesdropper is a security definition equivalent to semantic security. We prove the insecurity over the alphabet {A,B} with p B =(1/2(1+2 s )) and p A =1- p B where p A and p B are the probabilities of the source generating A and B, respectively, and s is the number of bits in each splitting key.