Abstract-In the present paper we have proposed a new variant of AES cipher with high level of security and an elegant construction called TIGRIS cipher. The TIGRIS name has been derived from one of the two famous rivers in Iraq. The proposed TIGRIS cipher is a revision for the proposed Euphrates cipher which has already been published. It has been designed with a good coherent structure that is based on solid algebraic and well mathematical opinions. The proposed cipher uses the SPN structure and what is known by the Galois Field GF (2 8 ). It is an iterated cipher that has a conservative design which is easily implemented on both hardware and software. It operates with block size of 128-bits and with three variable key lengths of 128-bits, 192-bits and 256-bits in addition to sixteen rounds or multiples of four rounds. The proposed cipher works with good invertible operations' stages and a compact duplicated ciphering key. The Tigris cipher construction strategy includes the adoption of construction a new S-box with high nonlinearity that uses the same routines of the AES-S-box stage but with different modular arithmetic of irreducible polynomial and different affine matrix in addition to the distinct constant vector. The second and the third layers of the proposed model are based on the shifting concept for the confusion and diffusion process with reversible operations. The last layer of the proposed model is the key addition layer that is responsible for the expanding and generating the ciphering key by two directions those of row and column expansion, which are associated with two constant vectors of golden ratio and base nature algorithm as a fixed word to eliminate any weak or semiweak ciphering key.

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.

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Abstract-In this paper, we have proposed a new iterated symmetric cipher, which is designed with Substitution and Permutation Network (SPN) structure and depends on strong mathematical built. It uses a compact algorithm for encryption and decryption processes, which consists of four main stages that roughly similar in its work to the Advance Encryption Standard (AES) stages. Starting by the SubByte operation, ReversibleShiftrows operation, ReversibleMixcolumns operation, and Round key addition. The proposed operations in this cipher have implemented in a straightforward manner relatively in both Encryption/Decryption by an elegant way. These four stages designed to reduce the hardware requirements and to produces high efficiency, which keeps the encryption and decryption process at the same speed in the hardware devices and eliminates the difference of execution times as well as creates a balance in forward and backward operations. The proposed cipher interested with modern design by adopted new algebraic operations and clear mathematical notations to ensure a high level of security. The proposed cipher did not build suddenly or arbitrarily but it acts as a sequence of developments and represents as a long process of design for long time, since several proposed ciphers have been published recently by us that paved the way to its new design, so the designed cipher inherited a good properties from a proven famous algorithms' features to produce high resistance against all known attacks and to submit a high performance on many platforms and in a wide range of hardware and software applications.

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