Polynomial expressions of p-ary auction functions

Shizuo Kaji, Toshiaki Maeno, Koji Nuida, Yasuhide Numata

Research output: Contribution to journalArticle

Abstract

One of the common ways to design secure multi-party computation is twofold: To realize secure fundamental operations and to decompose a target function to be securely computed into them. In the setting of fully homomorphic encryption, as well as some kinds of secret sharing, the fundamental operations are additions and multiplications in the base field such as the field F2 with two elements. Then the second decomposition part, which we study in this paper, is (in theory) equivalent to expressing the target function as a polynomial. It is known that any function over the finite prime field Fp has a unique polynomial expression of degree at most p-1 with respect to each input variable; however, there has been little study done concerning such minimal-degree polynomial expressions for practical functions. This paper aims at triggering intensive studies on this subject, by focusing on polynomial expressions of some auction-related functions such as the maximum/minimum and the index of the maximum/minimum value among input values.

Original languageEnglish
Pages (from-to)69-80
Number of pages12
JournalJournal of Mathematical Cryptology
Volume13
Issue number2
DOIs
Publication statusPublished - Jun 1 2019

Fingerprint

Auctions
Polynomials
Polynomial
Secure multi-party Computation
Homomorphic Encryption
Decompose
Target
Secret Sharing
Cryptography
Multiplication
Decomposition

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

Polynomial expressions of p-ary auction functions. / Kaji, Shizuo; Maeno, Toshiaki; Nuida, Koji; Numata, Yasuhide.

In: Journal of Mathematical Cryptology, Vol. 13, No. 2, 01.06.2019, p. 69-80.

Research output: Contribution to journalArticle

Kaji, Shizuo ; Maeno, Toshiaki ; Nuida, Koji ; Numata, Yasuhide. / Polynomial expressions of p-ary auction functions. In: Journal of Mathematical Cryptology. 2019 ; Vol. 13, No. 2. pp. 69-80.
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