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**2007/292**

**Title:**

Improved security analysis of OMAC

**Authors:**
Mridul Nandi

**Abstract:**

We present an improved security analysis of OMAC, the construction is widely used as a candidate of MAC or Pseudo Random Function (or PRF). In this direction, the first result was given in Crypto-05 where an improved security analysis of CBC (for fixed length or for arbitrary length prefix-free messages) had provided. Followed by this work, improved bounds for XCBC, TMAC and PMAC were found. The improved bounds are of the form \mathrm{O}(\frac{Lq^2}{2^n}) where the original bounds are \mathrm{O}(\frac{\sigma^2}{2^n}) which is roughly \mathrm{O}(\frac{L^2q^2}{2^n}). Here, a distinguisher can make at most q queries having at most \sigma many blocks with L as the maximum block size. The original bound for OMAC was roughly \frac{5L^2q^2}{2^n} shown in FSE-03 and the next improved bound was \frac{4\sigma^2}{2^n} shown in Indocrypt-03. In this paper we have provided an improved bound (a similar form as provided for others) for OMAC and the bound we show is roughly \frac{4q\sigma}{2^n} = \mathrm{O}(\frac{Lq^2}{2^n}).

**ePrint:**
https://eprint.iacr.org/2007/292

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