SCIENCE CHINA Information Sciences, https://doi.org/10.1007/s11432-018-9757-4

## Multi-User Security of the Tweakable Even-Mansour Cipher

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### Abstract

This paper focuses on the multi-user security of the tweakable Even-Mansour cipher. Firstly, we prove that the one-round tweakable Even-Mansour cipher (TEM-1) enjoys multi-user strong tweakable pseudorandom permutation (MU-STPRP) security in the random permutation model. Compared with the bounds of the multi-user security obtained by naive hybrid argument and point-wise proximity, the bound of the multi-user security directly derived by the expectation method is the best. Furthermore, the multi-user security of TEM-1 we derive is very close to the single-user security. Then, we consider the multi-user security of an ideal tweakable blockcipher (TBC). The ideal TBC is proven MU-STPRP secure up to close-to-optimal birthday-bound in the ideal cipher model. Furthermore, by comparison, the bound of TEM-1 we derive is close to the bound of the ideal TBC. Finally, we extend TEM-1 to the $r$-round tweakable Even-Mansour cipher, illustrate two loose bounds of the multi-user security via naive hybrid argument and point-wise proximity, and analyze the security of the $r$-round TEM cipher in various settings. The multi-user setting has wide applications in cryptography. It can be used in encryption modes, authentication modes, cryptographic protocols, and authenticated encryption modes.

### Funded by

This work was supported by National Natural Science Foundation of China (Grant Nos. 61522210 and 61632013).

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