Hill Cipher Cryptosystem over Complex Numbers

Maxrizal, Maxrizal

doi:10.31002/ijome.v2i1.1217

Cited by 3 publications

(1 citation statement)

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“…Furthermore, we also examine a symmetric cryptographic system that works on nonsingular matrices, namely Hill Cipher. This system has also undergone many developments and modifications [15][16][17]. In the original Hill Cipher, the message sender encrypts mod C KP p = , with C a ciphertext matrix, P any plaintext matrix, and K a nonsingular matrix (private key).…”

Section: Introductionmentioning

confidence: 99%

Public Key Cryptosystem Based on Singular Matrix

Maxrizal¹

2022

Trends Sci

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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

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Section: Introductionmentioning

confidence: 99%

Public Key Cryptosystem Based on Singular Matrix

Maxrizal¹

2022

Trends Sci

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RC4 Algorithm and Steganography to Double Secure Messages in Digital Image

Sulaiman¹,

Kirana²,

Sugihartono³

et al. 2020

2020 8th International Conference on Cyber and IT Service Management (CITSM)

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Determinants and Permanents of Hessenberg Matrices with Perrin’s Bivariate Complex Polynomials and Its Application

Kantalo

2023

Wseas Transactions on Mathematics

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In this paper, we define some n x n Hessenberg matrices and then we obtain determinants and permanents of their matrices that give the odd and even terms of bivariate complex Perrin polynomials. Moreover, we use our results to apply the application cryptology area. We discuss the Affine-Hill method over complex numbers by improving our matrix as the key matrix and present an experimental example to show that our method can work for cryptography.

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Hill Cipher Cryptosystem over Complex Numbers

Cited by 3 publications

References 5 publications

Public Key Cryptosystem Based on Singular Matrix

Public Key Cryptosystem Based on Singular Matrix

RC4 Algorithm and Steganography to Double Secure Messages in Digital Image

Determinants and Permanents of Hessenberg Matrices with Perrin’s Bivariate Complex Polynomials and Its Application

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