Digital signature scheme with matrix-based approach

Abstract

The use of digital signatures in various electronic services such as e-transactions, e-commerce, and e-learning is necessary for today's humans. All types of these services are highly dependent on the privacy, integrity, and authenticity between the sender and recipient of the data. Mathematically, many digital signature schemes such as Rivest Shamir Adleman (RSA), Elgamal, and Elliptic Curve Cryptography (ECC) are made using the concept of integer multiplication. Previous research introduced the RSA signature with a square matrix that changes data as a matrix instead of integers. The security of the scheme depends on the matrix with order . The larger  the digit chosen, the better the level of protection. This modification makes this digital signature system more secure than systems using integers because the randomization process is more random and complicated. However, the operating system involves matrix exponentiation, requiring a lot of computing time and space. In this study, researchers changed the matrix exponentiation to ordinary matrix multiplication. The advantage is that the proposed algorithm has a faster computing speed because it only involves ordinary matrix multiplication. In the first step, the researcher forms several rectangular matrices as random variables for the key generation algorithm. Next, the researcher models the signing and signature verification algorithms. After that, the researcher codes in Mathematica and simulates the proposed signature scheme. In the final stage, the researcher performs a mathematical attack test analysis on the algorithm. The results show that the proposed scheme can generate keys and sign and verify signatures well. In addition, the proposed scheme system has also been tested for possible mathematical attacks.