Secrecy Computation without Changing Polynomial Degree in Shamir's (K, N) Secret Sharing Scheme

Abstract

In This Paper, We Propose a New Secrecy Multiplication Scheme without Changing the Degree in Shamir’s (K, N) Secret Sharing Scheme. This Scheme Generates a Scalar Value Called Concealed Secret, Which Multiplies a Secret by a Random Number, and Distributes the Concealed Secret by using a Secret Sharing Scheme. When Secrecy Multiplying, We Temporarily Reconstruct the Concealed Secret, and Multiply It with a Share. Therefore, We Can Perform Secrecy Multiplication without Changing the Degree of Polynomials by Multiplying a Polynomial and Scalar Value. Our Scheme Can Extend to Secrecy Division by Dividing a Share with the Concealed Secret. in Addition, We Propose Secrecy Addition and Subtraction Schemes. We Evaluate the Security of Our Schemes, and Show a Possible Application That Cannot Realized using the Conventional Scheme.