Publication:
Secret Sharing Schemes and Advanced Encryption Standard

Loading...
Thumbnail Image
Authors
Lim, Bin Yong
Subjects
secret sharing
secret reconstruction
monic polynomials
Advanced Encryption Standard
Advisors
Stanica, Pantelimon
Date of Issue
2015-09
Date
Sep-15
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
The major objective of this study is to identify a simplified methodology to reconstruct a secret that is distributed using Shamir’s Secret Sharing Scheme, and to use the derived results to investigate implications on Advanced Encryption Standard. This thesis begins by using existing mathematical conjectures to simplify a monic polynomial generated by the dealer in a threshold secret sharing scheme. The second part of the thesis then identifies the variable bounds that an individual (eavesdropper or outsider) can use to reconstruct the secret by gathering just two shares out of multiple public shares. In conclusion, the findings from the first two parts of the simplified secret sharing scheme can be effectively used to identify weaknesses of side-channel attacks, and subsequently applied to improve on the mechanics of Advanced Encryption Standard. Future work could include generalizing the methodology to include non-monic polynomials, or exploring the use of prime coefficients in the dealer-generated polynomial.
Type
Thesis
Description
Department
Applied Mathematics
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
Copyright is reserved by the copyright owner.
Collections