Paper 2024/1394

SLAMP-FSS: Two-Party Multi-Point Function Secret Sharing from Simple Linear Algebra

Toomas Krips, University of Tartu

Hendrik Eerikson, Cybernetica AS, University of Tartu

Darya Pisetskaya, University of Tartu

Pille Pullonen-Raudvere, Cybernetica AS

Abstract

Multi-point function secret sharing (FSS) is a building block for pseudo-random correlation generators used in the novel silent correlation generation methods for various secure multi-party computation applications. However, the main construction used so far is the naive approach to combining several point functions. In this paper, we propose an efficient and natural generalisation of the point function FSS scheme of Boyle et al. 2016 using a tree structure, a pseudorandom generator and systems of linear equations. We propose a new notion of distributed random multi-point function. Our construction splits the distributed multi-point function scheme into a random multi-point function scheme and an algorithm to transform a random output into the desired output value. The resulting scheme, which we call SLAMP-FSS, improves upon the state of the art in terms of calls to a pseudorandom generator (PRG).

Note: Inlined the appendices, fixed some details, added more analysis of performance

@misc{cryptoeprint:2024/1394,
      author = {Erki Külaots and Toomas Krips and Hendrik Eerikson and Darya Pisetskaya and Pille Pullonen-Raudvere},
      title = {{SLAMP}-{FSS}: Two-Party Multi-Point Function Secret Sharing from Simple Linear Algebra},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1394},
      year = {2024},
      doi = {10.62056/avommpxqi},
      url = {https://eprint.iacr.org/2024/1394}
}