Paper 2024/1686

Circular Insecure Encryption: from Long Cycles to Short Cycles

Abstract

A length $n$ encryption cycle consists of a sequence of $n$ keys, each encrypting the next, forming a cycle, and an encryption scheme is $n$-circular secure if a length $n$ encryption cycle is computationally indistinguishable from encryptions of zeros. An interesting problem is whether CPA security implies circular security. This is shown to be not true. Using standard cryptographic assumptions and LWE, it was shown that within the class of CPA secure encryption schemes, for any $n$, there exists an $n$-circular insecure encryption scheme. Furthermore, there exists a particular encryption scheme that is $\ell$-circular insecure for all $\ell$. Following these results, it is natural to ask whether a circular insecurity of a particular length implies circular insecurity of different lengths and of multiple lengths. We answer this problem with an affirmative in this paper. We constructively prove that a CPA secure encryption scheme that is insecure in the presence of encryption cycles of length $(n+1)$ implies the existence of such a scheme for encryption cycles of any length less than $(n+1)$. The constructed $(\le n)$-circular insecure construction may have the same message space as the $(n+1)$-circular insecure encryption scheme, and our results apply to both public key and symmetric key settings.