New digital signature scheme based on MDLP and multinacci matrices

Abstract

A new digital signature scheme based on Matrices Discrete Logarithm Problem (MDLP) and generalized Fibonacci or Multinacci matrices is proposed. The security of the scheme is based on the difficulty of solving the Discrete Logarithm Problem (DLP) in matrices. MDLP is a new one-way function based on matrices that provides the same security as the DLP. The use of matrices increases the complexity of the scheme, as it involves matrix exponentiation rather than integers. In the proposed scheme, the signer uses a Multinacci matrix Fkn to generate the signature and an inverse Multinacci matrix Fn-k to verify it. The computational complexity and security of the scheme are also discussed.