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**2024/725**

**Title:**

Multi User Security of LightMAC and LightMAC_Plus

**Authors:**
Nilanjan Datta, Shreya Dey, Avijit Dutta, Devdutto Kanungo

**Abstract:**

In FSE’16, Luykx et al. have proposed \textsf{LightMAC} that provably achieves a query length independent PRF security bound. To be precise, the construction achieves security roughly in the order of O(q^2/2^n), when instantiated with two independently keyed n-bit block ciphers and q is the total number of queries made by the adversary. Subsequently, in ASIACRYPT’17, Naito proposed a beyond-birthday-bound variant of the \textsf{LightMAC} construction, dubbed as \textsf{LightMAC_Plus}, that is built on three independently keyed n-bit block ciphers and achieves 2n/3-bits PRF security. Security analyses of these two constructions have been conducted in the single-user setting, where we assume that the adversary has the access to a single instance of the construction. In this paper, we investigate, for the first time, the security of the \textsf{LightMAC} and the \textsf{LightMAC_Plus} construction in the context of multi-user setting, where we assume that the adversary has access to more than one instances of the construction. In particular, we have shown that \textsf{LightMAC} remains secure roughly up to 2^{n/2} construction queries and 2^k ideal-cipher queries in the ideal-cipher model and \textsf{LightMAC_Plus} maintains security up to approximately 2^{2n/3} construction queries and 2^{2k/3} ideal-cipher queries in the ideal-cipher model, where n denotes the block size and k denotes the key size of the block cipher.

**ePrint:**
https://eprint.iacr.org/2024/725

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