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Homomorphic secret sharing (HSS) is a distributed analogue of fully homomorphic encryption (FHE) where clients secret-share their inputs among two (or more) servers, who then non-interactively compute additive shares of the function output. Unlike FHE, HSS enables a distributed form of homomorphic computation from a broader set of cryptographic assumptions. All known multi-client HSS schemes require a correlated setup that is used by the clients to share their inputs. In contrast, multi-client delegation of computation using only a CRS has been known from assumptions that imply FHE since the introduction of multi-key FHE (Lopez-Alt et al., STOC 2012). We close this gap by providing the first construction of client-server HSS in the CRS only model from DDH, DCR, and more. Our constructions subsume all existing variants of group-based HSS schemes, including public-key HSS (Boyle et al., Crypto 2016), succinct HSS (Abram et al., Eurocrypt 2024), and multi-key HSS (Couteau et al., Eurocrypt 2025), and their applications.

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Client-Server Homomorphic Secret Sharing in the CRS Model

  • 会议论文

  • 发表日期：

    2026年

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  • Damiano Abram,
  • Geoffroy Couteau,
  • Lalita Devadas,
  • Aditya Hegde,
  • Abhishek Jain,
  • Lawrence Roy,
  • Sacha Servan-Schreiber

摘要

Homomorphic secret sharing (HSS) is a distributed analogue of fully homomorphic encryption (FHE) where clients secret-share their inputs among two (or more) servers, who then non-interactively compute additive shares of the function output. Unlike FHE, HSS enables a distributed form of homomorphic computation from a broader set of cryptographic assumptions. All known multi-client HSS schemes require a correlated setup that is used by the clients to share their inputs. In contrast, multi-client delegation of computation using only a CRS has been known from assumptions that imply FHE since the introduction of multi-key FHE (Lopez-Alt et al., STOC 2012). We close this gap by providing the first construction of client-server HSS in the CRS only model from DDH, DCR, and more. Our constructions subsume all existing variants of group-based HSS schemes, including public-key HSS (Boyle et al., Crypto 2016), succinct HSS (Abram et al., Eurocrypt 2024), and multi-key HSS (Couteau et al., Eurocrypt 2025), and their applications.