A Model on Dynamic Threshold Multi-Secret Sharing Scheme using Pell's Equation with Jacobi Symbol

Abstract

We propose a dynamic threshold and verifiable multi-secret sharing scheme using Pell's equation with Jacobi symbol. Some secrets are protected by distributing them among many participants, whereby only an authorized group of participants can reconstruct the secrets. In out scheme, the secret will change periodically and the dealer will periodically publish some of the information, in addition, the participants can verify the information which they have received. Each participant holds only one permanent, private secret, and some of them use it during different time periods to reconstruct the corresponding shared secrets without revealing their own private information. Because some public information is renewed in our scheme, the old information has nothing to do with the next secret. Dynamic multi-secrete sharing scheme developed is a public key cryptosystem and it is based on Pell's equation. This paper demonstrates algorithms for key generation, encryption and decryption based on Pell's equation with Jacobi symbol.