scholarly journals A Study of Authenticated Communication Based on Magic Square and Goldbach’s Conjecture

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Group Learning ◽  
Prime Numbers ◽  
Learning Problems ◽  
Student Group ◽  
Magic Square ◽  
Innovative Method ◽  
Encryption Decryption ◽  
Novel Applications ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

Although the magic square is a historical and universal study, its progress has been limited, to numeric games, which is closer to digital games or word games, and lacks the connection with mainstream mathematics. Recently, its study has extended from exciting mathematical games to various novel applications, such as image encryption, decryption processing, watermarking solutions, and student group learning problems, or different engineering applications. In terms of employment in information security, it is the blue ocean that requires more innovative research to enrich its content. In this study, we engage the magic square and Goldbach’s Conjecture to develop an innovative method to search prime numbers

scholarly journals On the Universal Encoding Optimality of Primes

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3155
Author(s):  
Ioannis N. M. Papadakis
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
Prime Numbers ◽  
Prime Factors ◽  
Universal Quantum ◽  
Optimality Properties ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows from Goldbach’s conjecture, and is viewed as an upper efficiency limit for encoding any integer with the fewest possible additions. A consequence of the above is that primes optimally encode—multiplicatively and additively—all integers. Thus, the set P of primes is the unique, irreducible subset of ℤ—in cardinality and values—that optimally encodes all numbers in ℤ, in a factorial and summative sense. Based on these dual irreducibility/optimality properties of P, we conclude that primes are characterized by a universal “quantum type” encoding optimality that also extends to non-integers.

scholarly journals Exploring Goldbach’s conjecture, the Pebonacci sequence and its five-dimensional vortex structure based on the logarithm of the circle

2020 ◽  
Vol 7 (8) ◽  
pp. 398-408
Author(s):  
Yiping Wang
Keyword(s):  
Mathematical Model ◽  
Closed Interval ◽  
Three Dimensional ◽  
Prime Numbers ◽  
Quadratic Equation ◽  
Space Structure ◽  
Number Sequence ◽  
Number Series ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

A method based on circle logarithm to prove Goldbach’s conjecture and Pebonacci sequence is proposed. Its essence is to deal with the real infinite series, each of the finite three elements (prime numbers, number series) has asymmetry problems, forming a basic even function one-variable quadratic equation and odd function one-variable three-dimensional number sequence; it is converted to "The irrelevant mathematical model expands latently in a closed interval of 0 to 1," forming a five-dimensional vortex space structure.

scholarly journals Proof of the Goldbach's Conjecture

2021 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Prime Numbers ◽  
Goldbach’S Conjecture ◽  
Mathematics Problem ◽  
Goldbach's Conjecture

Goldbach’s Conjecture states that every even number greater than 3, can be written as a summation of two prime numbers. This conjecture is roughly 300 years old and a very famous unsolved mathematics problem. To prove the Goldbach’s Conjecture, I use the contradiction method in mathematics as below.

7. Conjectures and theorems

2020 ◽  
pp. 112-129
Author(s):  
Robin Wilson
Keyword(s):  
Prime Numbers ◽  
Unique Factorization ◽  
The 1950S ◽  
Positive Integers ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

‘Conjectures and theorems’ investigates a number of topics, such as the distribution of prime numbers, and two unsolved problems, Goldbach’s conjecture and the twin prime conjecture. The factorization of positive integers into primes is unique, but this does not hold for certain other systems of numbers. A more in-depth look at unique factorization gives deeper results, including a proposed result of Gauss. Mathematicians in the 1950s and 1960s confirmed that he was correct, as shown in the so-called ‘Baker-Heegner-Stark theorem’.

scholarly journals Study A Public Key in RSA Algorithm

2020 ◽  
Vol 5 (4) ◽  
pp. 395-398
Author(s):  
Taleb Samad Obaid
Keyword(s):  
Private Information ◽  
Original Data ◽  
Prime Numbers ◽  
Public Key ◽  
The Internet ◽  
Sensitive Information ◽  
Rsa Algorithm ◽  
Encryption And Decryption ◽  
Main Disadvantage ◽  
Encryption Decryption

To transmit sensitive information over the unsafe communication network like the internet network, the security is precarious tasks to protect this information. Always, we have much doubt that there are more chances to uncover the information that is being sent through network terminals or the internet by professional/amateur parasitical persons. To protect our information we may need a secure way to safeguard our transferred information. So, encryption/decryption, stenographic and vital cryptography may be adapted to care for the required important information. In system cryptography, the information transferred between both sides sender/receiver in the network must be scrambled using the encryption algorithm. The second side (receiver) should be outlook the original data using the decryption algorithms. Some encryption techniques applied the only one key in the cooperation of encryption and decryption algorithms. When the similar key used in both proceeds is called symmetric algorithm. Other techniques may use two different keys in encryption/decryption in transferring information which is known as the asymmetric key.  In general, the algorithms that implicated asymmetric keys are much more secure than others using one key.   RSA algorithm used asymmetric keys; one of them for encryption the message, and is known as a public key and another used to decrypt the encrypted message and is called a private key. The main disadvantage of the RSA algorithm is that extra time is taken to perform the encryption process. In this study, the MATLAB library functions are implemented to achieve the work. The software helps us to hold very big prime numbers to generate the required keys which enhanced the security of transmitted information and we expected to be difficult for a hacker to interfere with the private information. The algorithms are implemented successfully on different sizes of messages files.

Magic squares of squares over a finite field

2021 ◽  
pp. 111-122
Author(s):  
Stewart Hengeveld ◽  
Giancarlo Labruna ◽  
Aihua Li
Keyword(s):  
Finite Field ◽  
Prime Numbers ◽  
Similar Question ◽  
Magic Squares ◽  
Content Type ◽  
Magic Square ◽  
Twin Primes ◽  
Quadratic Residues ◽  
Perfect Squares ◽  
Open Question

A magic square M M over an integral domain D D is a 3 × 3 3\times 3 matrix with entries from D D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M M are perfect squares in D D , we call M M a magic square of squares over D D . In 1984, Martin LaBar raised an open question: “Is there a magic square of squares over the ring Z \mathbb {Z} of the integers which has all the nine entries distinct?” We approach to answering a similar question when D D is a finite field. We claim that for any odd prime p p , a magic square over Z p \mathbb Z_p can only hold an odd number of distinct entries. Corresponding to LaBar’s question, we show that there are infinitely many prime numbers p p such that, over Z p \mathbb Z_p , magic squares of squares with nine distinct elements exist. In addition, if p ≡ 1 ( mod 120 ) p\equiv 1\pmod {120} , there exist magic squares of squares over Z p \mathbb Z_p that have exactly 3, 5, 7, or 9 distinct entries respectively. We construct magic squares of squares using triples of consecutive quadratic residues derived from twin primes.

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