Paper 2017/718

Conditionally Secure Secrecy Computation using Secret Sharing Scheme for n<2k-1 (full paper)

Ahmad Akmal Aminuddin Mohd Kamal and Keiichi Iwamura

Abstract

Typically, when secrecy multiplication is performed in multiparty computation using Shamir’s (k,n) threshold secret sharing scheme, the result is a polynomial with degree of 2k-2 instead of k-1. This causes a problem where, in order to reconstruct a multiplication result, the number of polynomials needed will increase from k to 2k-1. Shingu et al. proposed a method to solve the problem that the degree of polynomial increases when secrecy multiplication is performed by using the (scalar value×polynomial) approach instead of the typical (polynomial×polynomial). However, this method is not secure when a combination operation, such as a product-sum operation, is performed. In this paper, we propose a multiparty computation that uses a secret sharing scheme that is secure against a product-sum operation but does not increase the degree of polynomial of the output. We prove that all combinations of the basic operations (addition, subtraction, multiplication, and division) can be performed securely using this scheme. We also propose three preconditions and finally show that our proposed method is information-theoretic secure against a passive adversary.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Published elsewhere. Major revision. IEEE Xplore
Keywords
conditionally securesecret sharingsecrecy computationproduct-sum operationn<2k-1
Contact author(s)
ahmad @ sec ee kagu tus ac jp
History
2017-07-27: received
Short URL
https://ia.cr/2017/718
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/718,
      author = {Ahmad Akmal Aminuddin Mohd Kamal and Keiichi Iwamura},
      title = {Conditionally Secure Secrecy Computation using Secret Sharing Scheme for n<2k-1 (full paper)},
      howpublished = {Cryptology ePrint Archive, Paper 2017/718},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/718}},
      url = {https://eprint.iacr.org/2017/718}
}
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