Public Key Cryptosystem Based on Singular Matrix

Abstract

The algorithms such as RSA, ElGamal and ECC work on integers. Commutative operations on integer multiplication leave these algorithms vulnerable to attack by eavesdroppers. For this reason, experts develop the concept of non-commutative algebra in the public key cryptosystem by adding non-commutative properties to groups, semirings, semiring division, matrices and matrix decomposition. However, the key generating process in some public key cryptosystems is quite complicated to carry out. Therefore, in previous research, Liu used nonsingular matrices to form a simpler public key cryptosystem. However, eavesdroppers use the inverse of nonsingular matrices to construct the private key. As a result, this public key cryptosystem is still vulnerable to attacks. Therefore, we use a singular matrix to modify and build the proposed public key cryptosystem in this study. This study indicates that the singular matrix can be used to modify the public key cryptosystem. The results also show that the key generating algorithm only uses ordinary matrix multiplication (without using matrix power operations), so it is not too complicated. Furthermore, the proposed public key cryptosystem works on a matrix over integers so that the possible brute force attack trials are endless. The proposed public key cryptosystem also cannot be attacked by matrix inversion because it uses a singular matrix.