## Cryptology ePrint Archive: Report 2017/220

Cryptanalysis of PMACx, PMAC2x, and SIVx

Kazuhiko Minematsu and Tetsu Iwata

Abstract: At CT-RSA 2017, List and Nandi proposed PMACx and PMAC2x which are variable input length pseudorandom functions (VO-PRFs) that use a tweakable block cipher (TBC) as the underlying primitive. These schemes are provably secure up to the query complexity of $2^n$, where $n$ denotes the block length of the TBC. In this paper, we falsify the provable security claims by presenting concrete attacks. We show that with the query complexity of $O(2^{n/2})$, i.e., with the birthday complexity, PMACx and PMAC2x are both insecure. Furthermore, we consider a deterministic authenticated encryption scheme called SIVx. This scheme is built on PMAC2x, and is provably secure up to the query complexity of $2^n$. However, we show a birthday complexity attack against it.

Category / Keywords: secret-key cryptography / Cryptanalysis, PMACx, PMAC2x, SIVx, provable security