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Learning Burnside Homomorphisms with Rounding and Pseudorandom Function

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Innovative Security Solutions for Information Technology and Communications (SecITC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14534))

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Abstract

The use of pseudorandom function (PRF) and weak PRF as foundational primitives is common in a variety of cryptographic applications, including encryption, authentication, and identification. In this paper, we present a new PRF construction derived from a weak PRF family. Specifically, we propose a derandomization technique from a post-quantum hardness assumption known as learning Burnside homomorphisms with noise (\(B_n\)-LHN). Through the derandomization, a new hardness assumption arises, which we refer to as learning Burnside homomorphisms with rounding (\(B_n\)-LHR). We establish the security of the derandomization by demonstrating that the \(B_n\)-LHR problem is at least as hard as the \(B_n\)-LHN problem.

In the work by Naor and Reingold (NR), a PRF construction is introduced based on a weak PRF family, utilizing a novel cryptographic primitive called a pseudorandom synthesizer (PRS). However, this approach necessitates an excessively large key size to design a PRF family. To overcome this issue and produce a more efficient PRF construction, we design a length-doubling pseudorandom generator (PRG) from a weak PRF. Here, the PRG is defined using the secret-key components of a PRF. Notably, in our PRF construction, the length-doubling PRG exhibits efficiency primarily when employed as an intermediate function. We also provide insight into the \(B_n\)-LHR problem by discussing the details of the concatenation operation and error distribution in the Burnside group.

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Acknowledgements

We sincerely thank the reviewers for their valuable and insightful feedback on the initial draft of this paper.

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Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Dhiraj K. Pandey & Antonio R. Nicolosi

Authors
  1. Dhiraj K. Pandey
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  2. Antonio R. Nicolosi
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Correspondence to Dhiraj K. Pandey .

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Editors and Affiliations

  1. Universität der Bundeswehr München, Munich, Germany

    Mark Manulis

  2. Technology Innovation Institute, Abu Dhabi, United Arab Emirates

    Diana Maimuţ

  3. Advanced Technologies Institute, Bucharest, Romania

    George Teşeleanu

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Pandey, D.K., Nicolosi, A.R. (2024). Learning Burnside Homomorphisms with Rounding and Pseudorandom Function. In: Manulis, M., Maimuţ, D., Teşeleanu, G. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2023. Lecture Notes in Computer Science, vol 14534. Springer, Cham. https://doi.org/10.1007/978-3-031-52947-4_13

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  • DOI: https://doi.org/10.1007/978-3-031-52947-4_13

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  • Print ISBN: 978-3-031-52946-7

  • Online ISBN: 978-3-031-52947-4

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