Secret Sharing Schemes and Advanced Encryption Standard

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.