Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing...Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.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
文摘Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.
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.
