Critical sets of Latin squares based on autoparatopisms
Cryptographers use Latin-square autoparatopisms to design critical sets that improve secret sharing.
The paper studies critical sets of Latin squares, structures used in cryptographic secret-sharing schemes. It addresses share holders who appear in multiple critical sets and become indispensable for recovering the secret. Using orbits from a square's autoparatopism group, the authors compute critical sets that depend only on the autoparatopism conjugacy class and the square's main class. They determine the smallest and largest such sets for squares of order up to six and apply the method to a new secret-sharing scheme.
- Critical sets of Latin squares underpin some secret-sharing designs.
- Autoparatopism orbits avoid holders who become indispensable.
- Smallest and largest set sizes are computed through order six.
- The method is applied to a new secret-sharing scheme.
From the original article
1 min read at arxiv.orgIn cryptography, critical sets of Latin squares have particularly been implemented to design secret sharing schemes. A main problem in these cryptographic protocols arises from absent holders of pieces of information that are common to different critical sets, because they become indispensable to recover the secret.
By Manuel González-Regadera · arxiv.org
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