A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field
Cryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encry...
Main Authors: | , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
IEEE
2020-01-01
|
Series: | IEEE Access |
Subjects: | |
Online Access: | https://ieeexplore.ieee.org/document/9243939/ |
id |
doaj-3697f8d2594946ddb7e7b0663fcb7ce2 |
---|---|
record_format |
Article |
spelling |
doaj-3697f8d2594946ddb7e7b0663fcb7ce22021-03-30T04:16:49ZengIEEEIEEE Access2169-35362020-01-01819763019764310.1109/ACCESS.2020.30348329243939A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois FieldNasir Siddiqui0https://orcid.org/0000-0002-0612-4835Hira Khalid1Fiza Murtaza2Muhammad Ehatisham-Ul-Haq3https://orcid.org/0000-0001-9949-6664Muhammad Awais Azam4https://orcid.org/0000-0003-0488-4598Department of Basic Sciences, University of Engineering and Technology, Taxila, PakistanDepartment of Basic Sciences, University of Engineering and Technology, Taxila, PakistanPak Center for Artificial Intelligence, Pak-Austria Fachhochschule: Institute of Applied Sciences and Technology, Haripur, PakistanDepartment of Computer Engineering, University of Engineering and Technology, Taxila, PakistanWhitecliffe Technology, Wellington, New ZealandCryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encryption Standard (AES) is the most effective encryption algorithm proposed till now. Substitution-box (S-box) is the most crucial and only nonlinear component in AES (or any cryptographic algorithm), which provides data confusion. A highly nonlinear S-box offers high confidentiality and security against cryptanalysis attacks; hence, the design of S-box is very crucial in any encryption algorithm. To address this challenge, we propose the action of matrices (conforming to the basis of P<sub>7</sub> [Z<sub>2</sub>]) on the Galois field GF (2<sup>8</sup>). Consequently, a novel algebraic technique for S-box construction to generate highly nonlinear 8 × 8 S-boxes based on by our proposed algorithm, we obtain 1.324×10<sup>14</sup> different S-boxes. Standard S-box tests analyze the cryptographic strength of our proposed S-boxes. The examined results show that the proposed S-boxes possess state-of-the-art cryptographic properties. Moreover, we also demonstrate the effectiveness of the proposed S-boxes in image encryption applications using the majority logic criterion.https://ieeexplore.ieee.org/document/9243939/Advanced encryption standardconfusioncryptographyGalois fieldimage encryptionsubstitution-box |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nasir Siddiqui Hira Khalid Fiza Murtaza Muhammad Ehatisham-Ul-Haq Muhammad Awais Azam |
spellingShingle |
Nasir Siddiqui Hira Khalid Fiza Murtaza Muhammad Ehatisham-Ul-Haq Muhammad Awais Azam A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field IEEE Access Advanced encryption standard confusion cryptography Galois field image encryption substitution-box |
author_facet |
Nasir Siddiqui Hira Khalid Fiza Murtaza Muhammad Ehatisham-Ul-Haq Muhammad Awais Azam |
author_sort |
Nasir Siddiqui |
title |
A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field |
title_short |
A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field |
title_full |
A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field |
title_fullStr |
A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field |
title_full_unstemmed |
A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field |
title_sort |
novel algebraic technique for design of computational substitution-boxes using action of matrices on galois field |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2020-01-01 |
description |
Cryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encryption Standard (AES) is the most effective encryption algorithm proposed till now. Substitution-box (S-box) is the most crucial and only nonlinear component in AES (or any cryptographic algorithm), which provides data confusion. A highly nonlinear S-box offers high confidentiality and security against cryptanalysis attacks; hence, the design of S-box is very crucial in any encryption algorithm. To address this challenge, we propose the action of matrices (conforming to the basis of P<sub>7</sub> [Z<sub>2</sub>]) on the Galois field GF (2<sup>8</sup>). Consequently, a novel algebraic technique for S-box construction to generate highly nonlinear 8 × 8 S-boxes based on by our proposed algorithm, we obtain 1.324×10<sup>14</sup> different S-boxes. Standard S-box tests analyze the cryptographic strength of our proposed S-boxes. The examined results show that the proposed S-boxes possess state-of-the-art cryptographic properties. Moreover, we also demonstrate the effectiveness of the proposed S-boxes in image encryption applications using the majority logic criterion. |
topic |
Advanced encryption standard confusion cryptography Galois field image encryption substitution-box |
url |
https://ieeexplore.ieee.org/document/9243939/ |
work_keys_str_mv |
AT nasirsiddiqui anovelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT hirakhalid anovelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT fizamurtaza anovelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT muhammadehatishamulhaq anovelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT muhammadawaisazam anovelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT nasirsiddiqui novelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT hirakhalid novelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT fizamurtaza novelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT muhammadehatishamulhaq novelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield AT muhammadawaisazam novelalgebraictechniquefordesignofcomputationalsubstitutionboxesusingactionofmatricesongaloisfield |
_version_ |
1724182066969444352 |