Generalized Method for Constructing Magic Cube by Folded Magic Squares

Abstract

In the present paper we have developed a new method for constructing magic cube by using the folded magic square technique. The proposed method considers a new step towards the magic cube construction that applied a good insight and provides an easy generalized technique. This method generalized the design of magic cube with N order regardless the type of magic square whether odd order, singly even order or doubly even order. The proposed method is fairly easy, since it have depended mainly on the magic square construction methods, and all what the designer need is just how to builds six magic square sequentially or with constant difference value between each pair of the numbers in the square matrix, whereby each one of this magic square will represents the surface or dimension for magic cube configuration. The next step for the designer will be how to arrange each square in the proper order to constitute the regular cube in order to maintain the properties of magic cube, where the sum of rows, columns and the diagonals from all directions are the same.

A New Block Cipher Algorithm Using Magic Square of Order Five and Galois Field Arithmetic with Dynamic Size Block

“…As for the third proposed algorithm for GF(P), the result of the second algorithm will be multiplied by the key matrix used, which is equal to the size of MS5 and the prime number = P, see (6), and for GF (2 8 ) will also the result for algorithm #2 proposed multiplied by the matrix Key and multiplied by the number of irreducible polynomials allowed used for GF(2 8 ), as shown in (7). B7 = (P) length of message × 3 × (P) 25 (6) B8 = (256) length of message × 3 × (256) 25 × 30 (7)…”

“…Also, a group of researchers developed an algorithm using the magic square, in which two specific magic squares were used and created, then they have used it in cryptography [6]. In 2016, Dawood et al developed a new method by building the magic cube by folding the magic square, and this method was generalized regardless of the type of magic square used [7]. In 2017, Umar proposed a method based mainly on the 32nd magic square, whereby the duplication of characters was eliminated and the encryption efficiency was improved [8].…”

An Enhancement of LSB Audio Steganography Using Magic Cube

“…Magic Cubes are widely used in cryptography, steganography, watermarking, computer games, and error correcting codes, statistics and mathematical field [10].…”

“…A magic cube is a cube matrix drawn as a checkerboard filled with numbers or letters in particular arrangements. It consists (N 3 ) boxes, called cells, filled with integers that are all different [10]. Such an array of numbers is called a magic cube if the sums of the numbers in the horizontal rows, vertical columns, and main diagonals are all equal.…”

“…The magic cube is based on the folding six of series magic squares with sequential or with period numbers of ndimensions that represent the faces or dimensions of the magic.Omar A.Dawood et.al. (2016) [10] presented a new method for constructing magic cube by using the folded magic square technique. This method generalizes the design of magic cube with N order regardless the type of magic square whether odd order, singly even order or doubly even order, since it has depended mainly on the magic square construction methods, and all what the designer need is just how to builds six magic square sequentially or with constant difference value between each pair of the numbers in the square matrix…”