Paper 2025/2111

SoK: Secure Computation over Secret Shares

Arthur Zamarin, The Open University of Israel

Abstract

Secure multiparty computation (MPC) enables mutually distrustful parties to jointly compute functions over private data without revealing their inputs. A central paradigm in MPC is the secret-sharing-based model, where secret sharing underpins the efficient realization of arithmetic, comparison, numerical, and Boolean operations on shares of private inputs. In this paper, we systematize protocols for these operations, with particular attention to two foundational contributions \cite{ChidaGHIKLN18,NO07} that devised secure multiplication and comparison. Our survey provides a unified, self-contained exposition that highlights the composability, performance trade-offs, and implementation choices of these protocols. We further demonstrate how they support practical privacy-preserving systems, including recommender systems, distributed optimization platforms, and e-voting infrastructures. By clarifying the protocol landscape and connecting it to deployed and emerging applications, we identify concrete avenues for improving efficiency, scalability, and integration into real-world MPC frameworks. Our goal is to bridge theory and practice, equipping both researchers and practitioners with a deeper understanding of secret-sharing-based MPC as a foundation for privacy technologies.

Note: Improved the protocols for secure division and secure extraction of roots so that they do not depend on the bit decomposition of the operand u.

@misc{cryptoeprint:2025/2111,
      author = {Tamir Tassa and Arthur Zamarin},
      title = {{SoK}: Secure Computation over Secret Shares},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/2111},
      year = {2025},
      url = {https://eprint.iacr.org/2025/2111}
}