The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers
Joint Authors
Shah, Tariq
Shaukat Jamal, Sajjad
Shah, Dawood
Deajim, Abdulaziz
Source
Security and Communication Networks
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-24
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Information Technology and Computer Science
Abstract EN
Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem.
In block ciphers, the S-boxes create confusion and add valuable strength.
The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field.
For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256.
Conventionally, construction of affine power affine S-box is based on Galois field of order 256, depending on a single degree 8 primitive irreducible polynomial over ℤ2.
In this manuscript, we study affine power affine S-boxes for all the 16 distinct degree 8 primitive irreducible polynomials over ℤ2 to propose 16 different 8×8 substitution boxes.
To perform this idea, we introduce 16 affine power affine transformations and, for fixed parameters, we obtained 16 distinct S-boxes.
Here, we thoroughly study S-boxes with all possible primitive irreducible polynomials and their algebraic properties.
All of these boxes are evaluated with the help of nonlinearity test, strict avalanche criterion, bit independent criterion, and linear and differential approximation probability analyses to measure the algebraic and statistical strength of the proposed substitution boxes.
Majority logic criterion results indicate that the proposed substitution boxes are well suited for the techniques of secure communication.
American Psychological Association (APA)
Shaukat Jamal, Sajjad& Shah, Dawood& Deajim, Abdulaziz& Shah, Tariq. 2020. The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers. Security and Communication Networks،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1208862
Modern Language Association (MLA)
Shaukat Jamal, Sajjad…[et al.]. The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers. Security and Communication Networks No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1208862
American Medical Association (AMA)
Shaukat Jamal, Sajjad& Shah, Dawood& Deajim, Abdulaziz& Shah, Tariq. The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers. Security and Communication Networks. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1208862
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1208862