Some Structural and Security Properties of the Modular Secret Sharing

We mainly study the modular secret sharing over the ring of univariate polynomials over the Galois field. The proposed modular schemes over these rings achieve improvements both in security and applicability compared to classical schemes over the ring of integers. Our threshold schemes are perfect i...

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Published in:Symbolic and Numeric Algorithms for Scientific Computing, Proceedings pp. 197 - 200
Main Authors: Galibus, T., Matveev, G., Shenets, N.
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2008
Subjects:
Cryptography
Data analysis
Data security
Galois fields
Information security
Information theory
Mathematical model
Mathematics
Polynomials
Scientific computing
ISBN:0769535232, 9780769535234
Online Access:Get full text
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Abstract We mainly study the modular secret sharing over the ring of univariate polynomials over the Galois field. The proposed modular schemes over these rings achieve improvements both in security and applicability compared to classical schemes over the ring of integers. Our threshold schemes are perfect i.e. secure in the sense of information theory and ideal i.e. efficient in the terms of memory storage (the size of the secret is equal to the size of the shares). Then we consider the modular secret sharing schemes with pairwise co-prime moduli over the ring of polynomials and the ring of integers. We give a complete description of the access structures that can be realized by such modular schemes.
AbstractList We mainly study the modular secret sharing over the ring of univariate polynomials over the Galois field. The proposed modular schemes over these rings achieve improvements both in security and applicability compared to classical schemes over the ring of integers. Our threshold schemes are perfect i.e. secure in the sense of information theory and ideal i.e. efficient in the terms of memory storage (the size of the secret is equal to the size of the shares). Then we consider the modular secret sharing schemes with pairwise co-prime moduli over the ring of polynomials and the ring of integers. We give a complete description of the access structures that can be realized by such modular schemes.
Author Galibus, T.
Matveev, G.
Shenets, N.
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  surname: Shenets
  fullname: Shenets, N.
  organization: Dept. of Math. Modelling & Data Anal., Belorussian State Univ., Minsk, Belarus
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Snippet We mainly study the modular secret sharing over the ring of univariate polynomials over the Galois field. The proposed modular schemes over these rings achieve...
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StartPage 197
SubjectTerms Cryptography
Data analysis
Data security
Galois fields
Information security
Information theory
Mathematical model
Mathematics
Polynomials
Scientific computing
Title Some Structural and Security Properties of the Modular Secret Sharing
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