Newton Interpolation Theory Based On Finite Field Three New Secret Sharing Scheme

In 1979, Shamir and Blakley first proposed the( t ,n ) threshold schemes based on Lagrange interpolation theory and projective geometry theory respectively, This scheme could assure that at least t participants could calculate the master key, less than t participants couldn't do so. Later scholars puted forward lots of secret sharing scheme, The existing secret sharing schemes mostly based on the Lagrange interpolation theory in finite field, These schemes were excellent only in the static secret sharing session. But in the dynamic updating, the reconstruction of secret was costly ect. In this paper, explored and studied the Lagrange interpolation theory and Newton interpolation theory in real number field ; explored and studied the Lagrange interpolation theory and Newton interpolation theory in finite field. three new secret sharing scheme were successfully designed based on Newton interpolation theory in the finite field: multi-secret sharing scheme , verifiable secret sharing scheme and verifiable multi-secret sharing scheme. The main achievements were as follows:⑴A changeable threshold multi-secret sharing scheme was successfully designed based on the ( t ,n ) threshold scheme and Newton interpolation theory in the finite field . Multiple secrets can be shared in one sharing session; This scheme by adjusting the quantity of ( )N d r to adjust the threshold values t . And the numerical example were given, numerical examples could verify the correctness.⑵A verifiable secret sharing scheme was successfully designed based on Newton interpolation theory in the finite field, The scheme had the following advantages: It could not only prevent external deception but also prevent the internal deception; articipant's key shadow was chose and protected by himself, articipant's key shadow could use several sharing sessions. For using of RSA cryptosystem, The scheme had no secure channel, and prevented the participants from cheating , each one could verify whether the participant was cheating ect. And the numerical example were given, numerical examples could verify the correctness.(3) Combined with the design idea of Feldman verified secret share, a verifiable multi-secret sharing scheme was successfully designed based on Newton interpolation theory in finite field. This scheme could not only prevent participants cheating and could prevent secret sharing organizers not distributing key shadows or false key shadows to participants, compensating for the organizer coludn't verify the information which announced on bulletin board. And the numerical example were given, numerical examples could verify the correctness.