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Elementary symmetric polynomials in Shamir's scheme

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
130
Issue
7
Identifiers
DOI: 10.1016/j.jnt.2010.02.009
Keywords
  • Multisecret Sharing
  • Shamir'S Scheme
  • Threshold Cryptography
  • Elementary Symmetric Polynomials

Abstract

Abstract The concept of k-admissible tracks in Shamir's secret sharing scheme over a finite field was introduced by Schinzel et al. (2009) [10]. Using some estimates for the elementary symmetric polynomials, we show that the track ( 1 , … , n ) over F p is practically always k-admissible; i.e., the scheme allows to place the secret as an arbitrary coefficient of its generic polynomial even for relatively small p. Here k is the threshold and n the number of shareholders.

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