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.
 HIGHLIGHTS
 
 Public key cryptosystems that use commutative operations are vulnerable to eavesdropping attacks
 This study uses a singular matrix to modify and build a public key cryptosystem
 The proposed public key cryptosystem works on ordinary matrix multiplication operations and cannot be attacked by matrix inversion

Suatu Modifikasi Sistem Kriptografi Kunci Publik Berbasis Komposisi Fungsi Atas Matriks Untuk Meningkatkan Keamanan Pengiriman Data

“…Pada faktanya, semua sistem kriptografi kunci publik berbasis grup komutatif rentan terhadap quantum algorithms attack. Untuk itu para pakar mengembangkan sistem kriptografi kunci publik berbasis grup non-komutatif yaitu konsep matriks atas ring dan lapangan [1][2][3][4][5][6][7][8], matriks khusus [9][10][11], dan dekomposisi matriks [12][13].…”

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

“…The lineage of matrix-based cryptosystems, stretching back to foundational works such as [1], has been marked by continual advancements. Diverse matrix forms were incorporated, ranging from singular [2,3] and non-singular matrices [4] to matrices over bit strings [5]; Tribonacci matrices [6]; Hadamar matrices [7]; non-negative [8] and lattice matrices [9]. Tropical matrices are also of interest ( [10][11][12][13][14][15]).…”