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Groups Complexity Cryptology

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The Latin squares and the secret sharing schemes

Chi Sing Chum / Xiaowen Zhang
  • Computer Science Department, College of Staten Island, CUNY, 2800 Victory Blvd, Staten Island, NY 10314, USA. E-mail:
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Published Online: 2010-09-09 | DOI: https://doi.org/10.1515/gcc.2010.011


The Latin square is a good candidate in a secret sharing scheme to represent a secret, because of the huge number of the Latin squares for a reasonably large order. This makes outsiders difficult to discover the secret due to tremendous possibilities. We can improve the efficiency by distributing the shares of the critical set, instead of the full Latin square, to the participants. By different critical sets of the same Latin square, different secret sharing schemes can be implemented. However, finding a critical set of a large order Latin square is very difficult. This makes the implementation of Latin square based secret sharing scheme hard. We explore these limitations, then we propose to apply herding hash technique to overcome them.

Keywords.: Secret sharing scheme; Latin square; partial Latin square; critical set; hash functions; herding and Nostradamus attack

About the article

Received: 2010-06-22

Published Online: 2010-09-09

Published in Print: 2010-12-01

Citation Information: Groups – Complexity – Cryptology, Volume 2, Issue 2, Pages 175–202, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc.2010.011.

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Rebecca J. Stones, Ming Su, Xiaoguang Liu, Gang Wang, and Sheng Lin
Designs, Codes and Cryptography, 2016, Volume 80, Number 3, Page 635
Chi Sing Chum and Xiaowen Zhang
Security and Communication Networks, 2013, Volume 6, Number 5, Page 584

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