The substitution table (S-Box) of Advanced Encryption Standard (AES) and its properties are key elements in cryptanalysis ciphering. We aim here to propose a straightforward method for the non-linear transformation of...The substitution table (S-Box) of Advanced Encryption Standard (AES) and its properties are key elements in cryptanalysis ciphering. We aim here to propose a straightforward method for the non-linear transformation of AES S-Box construction. The method reduces the steps needed to compute the multiplicative inverse, and computes the matrices multiplication used in this transformation, without a need to use the characteristic matrix, and the result is a modern method constructing the S-Box.展开更多
As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to...As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to derive suitable formulas from these methods. In this paper, we present a novel way to compute the powers of an octonion number using formulas derived from the binomial expansion.展开更多
The first step in converting a plaintext to ciphertext by the famous Advanced Encryption Standard (AES), which is called Rijndael ByteSub Transformation, involves some operations: computing a multiplicative inverse, m...The first step in converting a plaintext to ciphertext by the famous Advanced Encryption Standard (AES), which is called Rijndael ByteSub Transformation, involves some operations: computing a multiplicative inverse, multiplying this multiplicative inverse by a specific matrix, and adding the result to a specific vector. The purpose of this research is to simplify these operations. This paper gives elegant techniques and presents the matrices multiplication as simple XOR operations, and the result is a simple, straightforward way finding the transformation.展开更多
In this work, we create a new mathematical formula that computes the power of a quaternion number raised to a positive integer by reducing the real matrix of order 4 × 4 that we take to represent this quaternion ...In this work, we create a new mathematical formula that computes the power of a quaternion number raised to a positive integer by reducing the real matrix of order 4 × 4 that we take to represent this quaternion number to a matrix that makes the process of multiplying this quaternion number by itself simpler. We also present a new method for computing the power of a real matrix of order 2 × 2 as an application of this formula.展开更多
文摘The substitution table (S-Box) of Advanced Encryption Standard (AES) and its properties are key elements in cryptanalysis ciphering. We aim here to propose a straightforward method for the non-linear transformation of AES S-Box construction. The method reduces the steps needed to compute the multiplicative inverse, and computes the matrices multiplication used in this transformation, without a need to use the characteristic matrix, and the result is a modern method constructing the S-Box.
文摘As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to derive suitable formulas from these methods. In this paper, we present a novel way to compute the powers of an octonion number using formulas derived from the binomial expansion.
文摘The first step in converting a plaintext to ciphertext by the famous Advanced Encryption Standard (AES), which is called Rijndael ByteSub Transformation, involves some operations: computing a multiplicative inverse, multiplying this multiplicative inverse by a specific matrix, and adding the result to a specific vector. The purpose of this research is to simplify these operations. This paper gives elegant techniques and presents the matrices multiplication as simple XOR operations, and the result is a simple, straightforward way finding the transformation.
文摘In this work, we create a new mathematical formula that computes the power of a quaternion number raised to a positive integer by reducing the real matrix of order 4 × 4 that we take to represent this quaternion number to a matrix that makes the process of multiplying this quaternion number by itself simpler. We also present a new method for computing the power of a real matrix of order 2 × 2 as an application of this formula.
