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Multiparty Homomorphic Secret Sharing and More from LPN and MQ

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Geoffroy Couteau
Naman Kumar
Xiaxi Ye
Published in
Theory of Cryptography
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the realm of multiparty homomorphic secret sharing (HSS), a cryptographic primitive that allows multiple parties to perform distributed computations on private inputs while maintaining the confidentiality of the inputs. The text explores the evolution of HSS from its initial introduction to recent advancements that support more than two parties. Key topics include the construction of an N-party HSS scheme from the Learning Parity with Noise (LPN) and Multivariate Quadratic (MQ) assumptions, the development of an N-party distributed point function scheme, and the generation of pseudorandom correlations for constant-degree polynomials. The chapter also discusses applications of these techniques in sublinear secure computation, private information retrieval (PIR), and silent preprocessing for secure computation. The text concludes with a detailed analysis of the efficiency and security of these constructions, providing insights into their practical implications and potential future developments.
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previous chapter Pseudorandom Correlation Functions for Garbled Circuits
Title
Multiparty Homomorphic Secret Sharing and More from LPN and MQ
Authors
Geoffroy Couteau
Naman Kumar
Xiaxi Ye
Copyright Year
2026
Book
Theory of Cryptography

Print ISBN: 978-3-032-12292-6

Electronic ISBN: 978-3-032-12293-3

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-12293-3_16
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