Revisiting structure graphs: Applications to CBC-MAC and EMAC

@article{Jha2016RevisitingSG,
  title={Revisiting structure graphs: Applications to CBC-MAC and EMAC},
  author={Ashwin Jha and Mridul Nandi},
  journal={Journal of Mathematical Cryptology},
  year={2016},
  volume={10},
  pages={157 - 180}
}
Abstract In [2], Bellare, Pietrzak and Rogaway proved an O ⁢ ( ℓ ⁢ q 2 / 2 n ) ${O(\ell q^{2}/2^{n})}$ bound for the PRF (pseudorandom function) security of the CBC-MAC based on an n-bit random permutation Π, provided ℓ < 2 n / 3 ${\ell<2^{n/3}}$ . Here an adversary can make at most q prefix-free queries each having at most ℓ ${\ell}$ many “blocks” (elements of { 0 , 1 } n ${\{0,1\}^{n}}$ ). In the same paper an O ⁢ ( ℓ o ⁢ ( 1 ) ⁢ q 2 / 2 n ) ${O(\ell^{o(1)}q^{2}/2^{n})}$ bound for EMAC (or… 
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