Cryptography Software System using Galois Field arithmetic

Cryptography Software System (CSS) is a set of tools to simulate and analyze a number of cryptography algorithms. It is written using Microsoft C# programming language and has a user friendly GUI. Arithmetic operations for encryption and decryption are in GF(2(8)) and the analysis provides the user with the basic statistics of data before and after the application of the selected cryptography algorithm. Along with the implementation of five cryptography algorithms (Affine, Vigenere, Linear-Feedback-Shift-Register, One-Time-Pad, and Weighted Sum), CSS is built modularly and the ability to add more algorithms is a definite advantage. Cryptography algorithms use integer mathematics, in particular number theory to perform invertible operations such as addition, multiplication, exponentiation, etc. over a finite set of integers. Computer information with different formats such as Microsoft Word, Microsoft Excel, digital image, himl,.... etc. are coded using the ASCII standard for the printable and non-printable bytes as the integers [0, 1, 2...... 255]. However, there are a very limited number of invertible operations using modulo 256 arithmetic. Galois Field GF (2(8)) offers a large number of such operations. For example, Advanced Encryption Standard (AES) uses the multiplicative inverse in GF (2(8)) [1]. CSS was written initially to implement and test a new stream cipher; Weighted Sum Cryptography (WSC) using Galois Field GF(2(8)). Four historical stream ciphers (Affine, Vigenere, Linear-Feedback-Shift-Register, and One-Time-Pad) were added for the purpose of the evaluation of WSC. GF (2(8)) defines the basic arithmetic operations over the finite set of bytes. For example addition as well as subtraction is the simple bitwise XOR and multiplication is modulo irreducible polynomial of power 8 with coefficients in GF (2) [1]. Table 1 shows the corresponding integers of irreducible polynomials of power 8. For example, the integer 283 refers to the irreducible polynomial m(a) = a(8) + a(4) + a(3) + a + 1, where m(2) = 283 or 100011011 in binary. CSS has three selections in the opening menu: (1) Irreducible polynomial, (2) Cryptography Algorithm, and (3) Statistics (Yes/No).