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How to Build Optimally Secure PRFs Using Block Ciphers

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conference contribution
posted on 2023-11-29, 18:13 authored by Benoît-Michel Cogliati, Ashwin Jha, Mridul Nandi
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.

History

Preferred Citation

Benoît-Michel Cogliati, Ashwin Jha and Mridul Nandi. How to Build Optimally Secure PRFs Using Block Ciphers. In: International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT). 2020.

Primary Research Area

  • Algorithmic Foundations and Cryptography

Name of Conference

International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT)

Legacy Posted Date

2020-10-08

Open Access Type

  • Unknown

BibTeX

@inproceedings{cispa_all_3190, title = "How to Build Optimally Secure PRFs Using Block Ciphers", author = "Cogliati, Benoît-Michel and Jha, Ashwin and Nandi, Mridul", booktitle="{International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT)}", year="2020", }

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