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Slightly Sublinear Trapdoor Hash Functions and PIR from Low-Noise LPN

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Damiano Abram
Giulio Malavolta
Lawrence Roy
Published in
Theory of Cryptography
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the construction of trapdoor hash functions (TDHs) from the low-noise Learning Parity with Noise (LPN) problem, a fundamental challenge in cryptography. The authors introduce a novel TDH construction that achieves slightly sublinear compactness, a significant improvement over previous methods. The chapter also presents the first non-trivial Private Information Retrieval (PIR) protocol from LPN, addressing a long-standing open problem in the field. The authors explore the trade-offs between compactness and correctness, providing a deeper understanding of the LPN problem's applications in cryptographic constructions. The chapter concludes with a discussion on the potential of recursive composition to improve the efficiency of TDHs and PIR protocols, offering insights into future research directions.
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This summary of the content was generated with the help of AI.

D. Abram—Work done while the author was affiliated with Bocconi University.

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previous chapter Large-Plaintext Functional Bootstrapping in FHE with Small Bootstrapping Keys
next chapter Privately Constrained PRFs from DCR: Puncturing and Bounded Waring Rank
Title
Slightly Sublinear Trapdoor Hash Functions and PIR from Low-Noise LPN
Authors
Damiano Abram
Giulio Malavolta
Lawrence Roy
Copyright Year
2026
Book
Theory of Cryptography

Print ISBN: 978-3-032-12286-5

Electronic ISBN: 978-3-032-12287-2

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-12287-2_10
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