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Paper: A Unified Method for Improving PRF Bounds for a Class of Blockcipher based MACs

Authors:
Mridul Nandi
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URL: http://eprint.iacr.org/2010/014
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Abstract: This paper provides a unified framework for {\em improving} \PRF(pseudorandom function) advantages of several popular MACs (message authentication codes) based on a blockcipher modeled as \tx{RP} (random permutation). In many known MACs, the inputs of the underlying blockcipher are defined to be some deterministic affine functions of previously computed outputs of the blockcipher. Keeping the similarity in mind, we introduce a class of \tx{ADE}s (affine domain extensions) and a wide subclass of \tx{SADE}s (secure \tx{ADE}) containing $\mathcal{C} = \{ \tx{CBC-MAC},\ \tx{GCBC}^*,\ \tx{OMAC},\ \tx{PMAC} \}$. We define a parameter $N(t,q)$ for each domain extension and show that all \tx{SADE}s have \PRF advantages $O(tq/2^n + N(t,q)/2^n)$ where $t$ is the total number of blockcipher computations needed for all $q$ queries. We prove that \PRF advantage of any \tx{SADE} is $O(t^2/2^n)$ by showing that $N(t,q)$ is always at most ${t \choose 2}$. We provide a better estimate $O(tq)$ of $N(t,q)$ for all members of $\mathcal{C}$ and hence these MACs have {\em improved advantages $O(tq / 2^n)$}. Our proposed bounds for \tx{CBC-MAC} and $\tx{GCBC}^*$ are better than previous best known bounds.
BibTeX
@misc{eprint-2010-22915,
  title={A Unified Method for Improving PRF Bounds for a Class of Blockcipher based MACs},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / affine domain extension, PRF, random permutation, CBC-MAC.},
  url={http://eprint.iacr.org/2010/014},
  note={ mridul.nandi@gmail.com 14620 received 10 Jan 2010},
  author={Mridul Nandi},
  year=2010
}