Mathematical Method to Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field GF(pq)

2017 ◽  
Vol 2 (11) ◽  
pp. 17-22
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Mathematical Method ◽  
Execution Time ◽  
Galois Field ◽  
Polynomial Multiplication ◽  
Irreducible Polynomials ◽  
Multiplicative Inverse ◽  
Advance Encryption Standard ◽  
Cipher Text ◽  
Substitution Boxes ◽  
Encryption And Decryption

Substitution boxes or S-boxes play a significant role in encryption and decryption of bit level plaintext and cipher-text respectively. Irreducible Polynomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard the 8-bit the elements S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where α GF(pq) and assume values from 2 to (p-1) to monic IPs.

scholarly journals Modified Advanced Encryption Standard Algorithm for Information Security

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1484 ◽  
Author(s):  
Oluwakemi Christiana Abikoye ◽  
Ahmad Dokoro Haruna ◽  
Abdullahi Abubakar ◽  
Noah Oluwatobi Akande ◽  
Emmanuel Oluwatobi Asani
Keyword(s):  
Execution Time ◽  
Advanced Encryption Standard ◽  
Avalanche Effect ◽  
Plain Text ◽  
Aes Algorithm ◽  
Cipher Text ◽  
Encryption And Decryption ◽  
To Come ◽  
Cryptographic Techniques ◽  
Modified Aes

The wide acceptability of Advanced Encryption Standard (AES) as the most efficient of all of the symmetric cryptographic techniques has further opened it up to more attacks. Efforts that were aimed at securing information while using AES is still being undermined by the activities of attackers This has further necessitated the need for researchers to come up with ways of enhancing the strength of AES. This article presents an enhanced AES algorithm that was achieved by modifying its SubBytes and ShiftRows transformations. The SubBytes transformation is modified to be round key dependent, while the ShiftRows transformation is randomized. The rationale behind the modification is to make the two transformations round key dependent, so that a single bit change in the key will produce a significant change in the cipher text. The conventional and modified AES algorithms are both implemented and evaluated in terms avalanche effect and execution time. The modified AES algorithm achieved an avalanche effect of 57.81% as compared to 50.78 recorded with the conventional AES. However, with 16, 32, 64, and 128 plain text bytes, the modified AES recorded an execution time of 0.18, 0.31, 0.46, and 0.59 ms, respectively. This is slightly higher than the results obtained with the conventional AES. Though a slightly higher execution time in milliseconds was recorded with the modified AES, the improved encryption and decryption strength via the avalanche effects measured is a desirable feat.

scholarly journals 4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(pq)

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Functions ◽  
Galois Field ◽  
Data Encryption ◽  
First Century ◽  
Additive Constant ◽  
Substitution Box ◽  
Data Encryption Standard ◽  
Substitution Boxes ◽  
Early Twenty ◽  
Encryption And Decryption

Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.

scholarly journals 4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(pq)

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Functions ◽  
Galois Field ◽  
Data Encryption ◽  
First Century ◽  
Additive Constant ◽  
Substitution Box ◽  
Data Encryption Standard ◽  
Substitution Boxes ◽  
Early Twenty ◽  
Encryption And Decryption

Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.

Application of Linear and Non Linear Modified 3D Cellular Automata Rules in Cryptography for Improved Security of Transmitted Data

2014 ◽  
Vol 573 ◽  
pp. 600-604
Author(s):  
K. Latha ◽  
S. Amirthalingam
Keyword(s):  
Cellular Automata ◽  
Data Encryption ◽  
Internet Security ◽  
Data Encryption Standard ◽  
Advance Encryption Standard ◽  
Cipher Text ◽  
Keywords Internet ◽  
Encryption And Decryption ◽  
Using Data ◽  
Made In

Internet is the prime vehicle to disseminate information from one place to another. Providing security to data is a major issue in transmitting data. One way of providing security to the data is encryption and decryption. Normal encryption is the way of changing the plaintext into cipher text using encryption and decryption algorithm and key. Literature reported different methods for encryption. An attempt is made in this paper to propose a modified encryption and decryption process performed with modified cellular automata rules. Cellular automata is idealized parallel processing machine which depends upon the cell value which is updated based on updating rule, which involves the cell and other cell values in a particular neighbourhood .Discrete references were made in the literature on the application of cellular automata rules. However lot more work remains to be done in this area. An attempt is made in this paper to provide encryption and decryption with cellular automata rules, using Data Encryption Standard (DES) and Advance Encryption Standard (AES) algorithms. They are operated at various stages, with the number of stages involved in sequential and cellular automata operating parallel. The major contribution of present work is, to develop methodology for identifying and application of 1D and 2D cellular automata rules and to fix the issues and challenges there in. A modified cellular automata set of rules are considered to develop 3D cellular automata rules for improved safety. Further a comparison is provided between existing 1, 2D automata rules versus the modified 3D cellular automata rules with respect to certain parameters. Keywords : Internet, Security, Cipher text, Plaintext, Cell value.

scholarly journals Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q).

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Efficient Algorithm ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Galois Field ◽  
Division Algorithm ◽  
Irreducible Polynomials ◽  
New Approach ◽  
Multiplication Algorithm ◽  
Research Article ◽  
Substitution Boxes

Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.

scholarly journals Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q).

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Efficient Algorithm ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Galois Field ◽  
Division Algorithm ◽  
Irreducible Polynomials ◽  
New Approach ◽  
Multiplication Algorithm ◽  
Research Article ◽  
Substitution Boxes

Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.

scholarly journals The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Sajjad Shaukat Jamal ◽  
Dawood Shah ◽  
Abdulaziz Deajim ◽  
Tariq Shah
Keyword(s):  
Secure Communication ◽  
Irreducible Polynomial ◽  
Galois Field ◽  
Block Ciphers ◽  
Affine Transformations ◽  
Differential Approximation ◽  
Irreducible Polynomials ◽  
Substitution Boxes ◽  
Nonlinearity Test ◽  
Galois Field Extensions

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.

scholarly journals ANALISIS PERBANDINGAN ALGORITMA SIMETRIS RIVEST CODE 5 DENGAN ALGORITMA SIMETRIS RIVEST CODE 6) (Studi Kasus : SMK Negeri Seluma)

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Rozali Toyib ◽  
Ardi Wijaya
Keyword(s):  
Execution Time ◽  
Hash Function ◽  
Storage Media ◽  
Encryption And Decryption ◽  
Secure Data ◽  
Computer Based ◽  
Message Digest ◽  
Set Up

Abstack: Data stored in storage media is often lost or opened by certain parties who are not responsible, so that it is very detrimental to the owner of the data, it is necessary to secure data so that the data can be locked so that it cannot be opened by irresponsible parties. The RC5 and RC6 algorithms are digestive massage algorithms or sometimes also known as the hash function which is an algorithm whose input is a message whose length is not certain, and produces an output message digest from its input message with exactly 128 bits in length. RC6 password is a protection for the user in securing data on a PC or computer. Based on the results of the conclusions taken: For the experiments carried out on the RC5 algorithm the execution time for the generation of keys (set-up key) is very fast, which is about 9-10 ns, a trial carried out on the RC6 algorithm execution time for the key generator (set up key ) faster than 10-11 ns. In the encryption and decryption process, the execution time depends on the size or size of the plaintext file. The larger the size of the plaintext file, the longer the execution time.Abstrak : Data yang tersimpan dalam media penyimpanan sering hilang atau dibuka oleh pihak-pihak tertentu yang tidak bertanggung jawab, sehinga merugikan sekali bagi pemilik data tersebut, untuk itu diperlukan suatu pengamanan data agar data tersebut dapat terkunci sehingga tidak dapat dibuka oleh pihak yang tidak bertanggung jawab.. Algoritma RC5 dan RC6 merupakan algoritma massage digest atau kadang juga dikenal dengan hash function yaitu suatu algoritma yang inputnya berupa sebuah pesan yang panjangnya tidak tertentu, dan menghasilkan keluaran sebuah message digest dari pesan inputnya dengan panjang tepat 128 bit. Password RC6 merupakan salah satu perlindungan kepada user dalam pengamanan data yang berada dalam sebuah Pc atau computer. Berdasarkan hasil pengujian diambil kesimpulan : Untuk uji coba yang dilakukan pada algoritma RC5 waktu eksekusi untuk pembangkitan kunci  (set up key) sangat cepat sekali yaitu sekitar  9-10 ns, uji coba yang dilakukan pada algoritma RC6 waktu eksekusi untuk pembangkit kunci (set up key) lebih cepat sekali yaitu 10-11 ns, Pada proses enkripsi dan dekripsi, waktu eksekusi tergantung dari besar atau kecilnya ukuran file plaintext.s emakin besar ukuran file plaintext maka semakin lama waktu eksekusinya.

scholarly journals Komparasi Waktu Algoritma RSA dengan RSA-CRT Base On Computer

2020 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Nur Cayo Hendro Wibowo ◽  
Khotibul Umam ◽  
Albadru Muh Izul Khaq ◽  
Favian Agung Rizki
Keyword(s):  
Data Analysis ◽  
Product Development ◽  
Research And Development ◽  
Everyday Life ◽  
Execution Time ◽  
Rsa Algorithm ◽  
Encryption And Decryption ◽  
Long Time ◽  
Computer Based ◽  
Manual Calculation

<p align="center"><em>Cryptography is a branch of mathematics. Asymmetric algorithms such as RSA, including the type of cryptography that is more widely used to be implemented in everyday life because it has an algorithm that is not easy to be misused by others. However, the encryption and decryption process of RSA requires quite a long time. For this reason, RSA - CRT emerged. In this study a time comparison between the RSA algorithm and the RSA-CRT Base On Computer is done. The purpose of this study was to determine the execution time of the RSA-CRT algorithm using PHP.</em></p><p><em>This research uses the Research and Development or R&amp;D method, with the R&amp;D method created by the product development RSA-CRT algorithm application from UIN Walisongo Semarang based on computer. Based on the data analysis, the conclusion is that although the manual calculation of the RSA-CRT algorithm takes longer than the others in this case RSA. But have a faster time when using PHP.</em></p><p align="center"> </p>

Sign in / Sign up

Export Citation Format

Share Document