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Paper: How to Build Optimally Secure PRFs Using Block Ciphers

Authors:
Benoît Cogliati
Ashwin Jha
Mridul Nandi
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DOI: 10.1007/978-3-030-64837-4_25
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Abstract: In EUROCRYPT '96, Aiello and Venkatesan proposed two candidates for $ 2n $-bit to $ 2n $-bit pseudorandom functions (PRFs), called Benes and modified Benes (or mBenes), based on $ n $-bit to $ n $-bit PRFs. While Benes is known to be secure up to $ 2^n $ queries (Patarin, AFRICACRYPT '08), the security of mBenes has only been proved up to $ 2^{n(1-\epsilon)} $ queries for all $ \epsilon > 0 $ by Patarin and Montreuil in ICISC '05. In this work, we show that the composition of a $ 2n $-bit hash function with mBenes is a secure variable input length (VIL) PRF up to $ 2^{n-2} $ queries (given appropriate hash function bounds). We extend our analysis with block ciphers as the underlying primitive and obtain two optimally secure VIL PRFs using block ciphers. The first of these candidates requires $ 6 $ calls to the block cipher. The second candidate requires just $ 4 $ calls to the block cipher, but here the proof is based on Patarin's mirror theory. Further, we instantiate the hash function with a PMAC+/LightMAC+ like hash, to get six candidates for deterministic message authentication codes with optimal security.
Video from ASIACRYPT 2020
BibTeX
@article{asiacrypt-2020-30706,
  title={How to Build Optimally Secure PRFs Using Block Ciphers},
  booktitle={Advances in Cryptology - ASIACRYPT 2020},
  publisher={Springer},
  doi={10.1007/978-3-030-64837-4_25},
  author={Benoît Cogliati and Ashwin Jha and Mridul Nandi},
  year=2020
}