(m, N) Threshold Multi-signature Scheme Based on ECC Over Finite Field GF(q)
Wen-Chun Tian, Chai Jin, Yi-Wu Xu · 2022
This paper expounds the invertibility of Vandermonde matrix over GF(q) field, the algorithm of matrix inversion and the time complexity, and then design a (m, N) threshold multi-signature scheme based on Ellipse Curve Cryptography (ECC, Ellipse Curve Cryptography) algorithm. In this scheme, no secret communication is required in the signature-issuing phase, verification contrast value is constant, and signature verification does not require the participation of TC(Trusted Center). Theoretical analysis shows that the scheme is safe; the test results prove the correctness of the algorithm and the analysis of computational time complexity (verification of signature and finite field matrix inversion). This multi-signature solution is especially suitable for multi-signature voting in application scenarios such as blockchain and smart contracts.