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
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
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
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.
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.
