Evolving Homomorphic Secret Sharing for Hierarchical Access Structures

Kittiphop Phalakarn; Vorapong Suppakitpaisarn; Nuttapong Attrapadung; Kanta Matsuura

Paper 2023/1168

Evolving Homomorphic Secret Sharing for Hierarchical Access Structures

Kittiphop Phalakarn, The University of Tokyo, Tokyo, Japan

Vorapong Suppakitpaisarn, The University of Tokyo, Tokyo, Japan

Nuttapong Attrapadung, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

Kanta Matsuura, The University of Tokyo, Tokyo, Japan

Abstract

Secret sharing is a cryptographic primitive that divides a secret into several shares, and allows only some combinations of shares to recover the secret. As it can also be used in secure multi-party computation protocol with outsourcing servers, several variations of secret sharing are devised for this purpose. Most of the existing protocols require the number of computing servers to be determined in advance. However, in some situations we may want the system to be "evolving". We may want to increase the number of servers and strengthen the security guarantee later in order to improve availability and security of the system. Although evolving secret sharing schemes are available, they do not support computing on shares. On the other hand, "homomorphic" secret sharing allows computing on shares with small communication, but they are not evolving. As the contribution of our work, we give the definition of "evolving homomorphic" secret sharing supporting both properties. We propose two schemes, one with hierarchical access structure supporting multiplication, and the other with partially hierarchical access structure supporting computation of low degree polynomials. Comparing to the work with similar functionality of Choudhuri et al. (IACR ePrint 2020), our schemes have smaller communication costs.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. IWSEC 2021
DOI: 10.1007/978-3-030-85987-9_5
Keywords: Secure multi-party computation Evolving secret sharing Homomorphic secret sharing Hierarchical secret sharing
Contact author(s): kittiphop phalakarn @ gmail com
History: 2023-08-03: revised; 2023-07-29: received; See all versions
Short URL: https://ia.cr/2023/1168
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1168,
      author = {Kittiphop Phalakarn and Vorapong Suppakitpaisarn and Nuttapong Attrapadung and Kanta Matsuura},
      title = {Evolving Homomorphic Secret Sharing for Hierarchical Access Structures},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1168},
      year = {2023},
      doi = {10.1007/978-3-030-85987-9_5},
      note = {\url{https://eprint.iacr.org/2023/1168}},
      url = {https://eprint.iacr.org/2023/1168}
}