Behavior of powers of odd ordered special circulant magic squares

Rani, Narbda; Mishra, Vinod

doi:10.1080/0020739x.2021.1890846

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…Another advantage of the magic squares is when switching a row or column that is far from the center by N with another row or another column that is equally far from the center. It remains a magic square, in addition to preserving its properties [9].…”

Section: Previouly Existing Technologies That Have Been Relied Uponmentioning

confidence: 99%

A Comparative Study of Researches Based on Magic Square in Encryption with Proposing a New Technology

2021

IJCCCE

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This paper aims to develop a new cryptographic algorithm that is based on the magic square method of order five with multi message lengths to be more complex in order to increase the complexity; in addition to comparing the cipher with the use of the magic square of order five, four and three (all single message length. The proposed work has been done by using two extra rounds and depending on round statuse ( even or odd) , messages are detected to be used. The key is placed in agreed positions, then the remaining positions are filled with the message, and then certain sums are calculated to represent the encrypted text. Speed, complexity, histogram calculations for images, and NIST calculations for texts were calculated, and the results were compared, where the complexity of the algorithms was as follows ((P)15 × (256)10)2 × (P)11 × (256)14 and ((256)15 × (256)10)2 × (256)11 × (256)14 for GF(P) and GF(28) respectively , From that, it has been discovered that the proposed algorithm (Magic Square of order five with multi message length) is better than the rest of the algorithms as it has excellent complexity and a slight difference in the speed. Index Terms— Cryptography, GF(28), linear equation system, Magic Square.

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Section: Previouly Existing Technologies That Have Been Relied Uponmentioning

confidence: 99%

A Comparative Study of Researches Based on Magic Square in Encryption with Proposing a New Technology

2021

IJCCCE

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“…Usually, we call an MS(n, 2) a bimagic square and an MS(n, 3) a trimagic square. Many researchers have done a lot of work on the existence and construction of normal multimagic squares [23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row-Square Magic Rectangles

Hu,

Pan

2024

Preprint

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As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem for trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known for the existence of trimagic squares with other even orders except for the only three examples and three families. We construct normal trimagic squares by using product constructions, row-square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We give a new product construction: For positive integers p, q, and r having the same parity other than 1, 2, 3, 6, if normal p × q and r × q row-square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we construct normal trimagic squares of orders 8q^3 and 8pqr for all odd integers q not less than 7 and p,r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

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Section: Introductionmentioning

confidence: 99%

New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row–Square Magic Rectangles

Hu,

Pan

2024

Mathematics

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As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem of trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known about the existence of trimagic squares with other even orders, except for only three examples and three families. We constructed normal trimagic squares by using product constructions, row–square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We gave a new product construction: for positive integers p, q, and r having the same parity, other than 1, 2, 3, or 6, if normal p × q and r × q row–square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we constructed normal trimagic squares of orders 8q3 and 8pqr for all odd integers q not less than 7 and p, r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

show abstract

Behavior of powers of odd ordered special circulant magic squares

Cited by 6 publications

References 5 publications

A Comparative Study of Researches Based on Magic Square in Encryption with Proposing a New Technology

A Comparative Study of Researches Based on Magic Square in Encryption with Proposing a New Technology

New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row-Square Magic Rectangles

New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row–Square Magic Rectangles

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