This document discusses cryptography and various encryption methods using matrices. It introduces shift ciphers, stretch ciphers, combination ciphers, and the Vigenere cipher which uses a keyword to shift between cipher alphabets. It provides examples of encoding and decoding messages with these ciphers and discusses how matrices can represent and manipulate encrypted data. It also considers the benefits and limitations of different encryption methods and how cryptography applies to fields like warfare.
The following presentation consists of information about the application of matrices. The ppt particularly focuses on the its use in cryptography i.e. encoding and decoding of messages.
Application of matrix multiplication (cryptography) with solved problemMuhammad Waqas
What is Cryptography
A cryptogram is a message written according to a secret code (the Greek word kryptos means “hidden”). This section describes a method of using matrix multiplication to encode and decode messages.
Cryptography mainly consist of encryption and decryption
Encryption
Convert the plain data into numerical by giving A to 1,B to 2,C to 3 and so on.
Place the numerical in to matrix M of order mn ≥ L.
Multiply the matrix M with a non-singular matrix A to get the encoded matrix X.
The determinate of (non singular matrix) A must be equal to ±1.
Convert the resultant, the encrypted message matrix in to a text message of length L and that will be send to the receiver
Decryption
Receiver can form a matrix with the encrypted message.
Multiply the encoded matrix X with 퐴^(−1) to get back the message matrix M.
Encryption and decryption require the use of some secret information usually referred as a key.
This first matrix , used by sender is called the encryption matrix (encoding matrix) and its inverse is called decryption matrix (decoding matrix) , which is used by the receiver.
What is matrix? Matrix in physics. Matrix in computer science. Matrix in encryption. Matrix in others sector. geology surveys,robot movement,scientific experiment.
The following presentation consists of information about the application of matrices. The ppt particularly focuses on the its use in cryptography i.e. encoding and decoding of messages.
Application of matrix multiplication (cryptography) with solved problemMuhammad Waqas
What is Cryptography
A cryptogram is a message written according to a secret code (the Greek word kryptos means “hidden”). This section describes a method of using matrix multiplication to encode and decode messages.
Cryptography mainly consist of encryption and decryption
Encryption
Convert the plain data into numerical by giving A to 1,B to 2,C to 3 and so on.
Place the numerical in to matrix M of order mn ≥ L.
Multiply the matrix M with a non-singular matrix A to get the encoded matrix X.
The determinate of (non singular matrix) A must be equal to ±1.
Convert the resultant, the encrypted message matrix in to a text message of length L and that will be send to the receiver
Decryption
Receiver can form a matrix with the encrypted message.
Multiply the encoded matrix X with 퐴^(−1) to get back the message matrix M.
Encryption and decryption require the use of some secret information usually referred as a key.
This first matrix , used by sender is called the encryption matrix (encoding matrix) and its inverse is called decryption matrix (decoding matrix) , which is used by the receiver.
What is matrix? Matrix in physics. Matrix in computer science. Matrix in encryption. Matrix in others sector. geology surveys,robot movement,scientific experiment.
matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
These Slides are very usefull interms of engineering and as well as in other fields of Study .. These are Related with linear Algebra and there Properties Methods to find out the unknowns from the equation...
Application of matrix
1. Encryption, its process and example
2. Decryption, its process and example
3. Seismic Survey
4. Computer Animation
5. Economics
6. Other uses...
Elliptic curve cryptography is additional powerful than different methodology that gains countless attention within the industry and plays vital role within the world of CRYPTOGRAPHY. This paper explains the strategy of elliptic curve cryptography victimization matrix scrambling method. during this methodology of cryptography we have a tendency to initial rework the plain text to elliptic curve so victimization matrix scrambling methodology we have a tendency to encrypt/decrypt the message. This method keeps information safe from unwanted attack to our information.
matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
These Slides are very usefull interms of engineering and as well as in other fields of Study .. These are Related with linear Algebra and there Properties Methods to find out the unknowns from the equation...
Application of matrix
1. Encryption, its process and example
2. Decryption, its process and example
3. Seismic Survey
4. Computer Animation
5. Economics
6. Other uses...
Elliptic curve cryptography is additional powerful than different methodology that gains countless attention within the industry and plays vital role within the world of CRYPTOGRAPHY. This paper explains the strategy of elliptic curve cryptography victimization matrix scrambling method. during this methodology of cryptography we have a tendency to initial rework the plain text to elliptic curve so victimization matrix scrambling methodology we have a tendency to encrypt/decrypt the message. This method keeps information safe from unwanted attack to our information.
Instructions · Take this test during the week (with late submiss.docxnormanibarber20063
Instructions
· Take this test during the week (with late submission Monday; a maximum of 10% penalty) Work alone. You may not confer with other class members, or anyone else, directly or by e-mail or otherwise, regarding the questions, issues or your answers. You may use your notes, OER, textbooks, and other published materials.
· It is scored based on 100 points for the test.
· When composing your answers, be thorough. Do not simply examine one alternative if two or more alternatives exist. However, choose only one as your answer giving reasons for your choice. The more complete your answer, the higher your score will be. Be sure to identify any assumptions you are making in developing your answers and describe how your answer would change if the assumptions were different. For multiple choice questions if you think there are two correct answers choose the best one and justify your answers. Please write justification in your own words, avoid cut and paste or merely copying the sentences from references. If you are describing methodology, please describe it in sufficient details so that by following it, anybody can reach the same result without additional help from you.
· While composing your answers, be VERY careful to cite your sources. Use only reputable sources. Personal blogs or the websites that are set up to sell are not reputable sources. Remember, failure to cite sources constitutes an academic integrity violation.
· For Parts I and II, when you are providing justification as I mentioned above reference is required. If you are giving reference of a book, I will need page number(s). I cannot go through the complete book to verify your reference. The page number gives me some indication that you have.
· Your answers should be contained in a Microsoft Word (or compatible format that can be opened by MSWord) document, uploaded to your assignments folder. If you use some other word processor, please make sure that the numbering does not change. I will return files (ungraded) in any other format if I cannot open them in one try. I may also check your part III answers with Turnitin.
______________________________________________________________________________
Part I (Each 4 Pts. Total 40.) Choose the best one. Please provide reason of your choice in a few sentences or reasons not choosing the other choices. Reason must be in your own words. Use guidelines for reference as given in the instructions.
1. To protect information, one must protect against possible virus threats True/False justify your answer
2. Which are the weaknesses of a shift cipher?
A. Natural language letter frequency makes them easy to decode.
B. The number of letters in the alphabet makes them easy to decode.
C. Once the shift is determined the message is decoded.
D. Once you have the code book you can decode the message instantly
E. A&B
F. A, B & C
G. A, B, C and D
H. A & C
No reason required
3. What is the basis of the modern cryptography? _________________
.
Numeral Structure Base Cryptography Design to Secure Distribution of Internet...AM Publications
The Internet is a collection of shared resources. The present internet architecture has limited support for both securing
and identifying shared Internet resources. As a result, resource exhaustion does occur due to inefficiently scaling systems, selfish
resource consumption and malicious attack. In this context, cryptography can be used to provide confidentiality using encryption
methods and can also provide data integrity, authentication and non-repudiation. The purpose of this paper is to deploy number
systems based cryptography schemes for secure sharing of internet and intranet resources without global protocol redeployment
or architectural support. Quaternionic Farey fractions are used to achieve rotations/orientations in three dimensions. The use of
Quaternionic Farey fractions is preferred in this work, since; they have the proven advantage that combining many quaternion
transformations is more numerically stable than combining many matrix transformations
Symmetric Key Generation Algorithm in Linear Block Cipher Over LU Decompositi...ijtsrd
In symmetric key algorithm in linear block cipher to encrypt and decrypt the messages using matrix and inverse matrix. In this proposed technique generate lower and upper triangular matrices from the square matrix using decomposition. In encryption process, the key is a lower triangular matrix and decryption process, the key is upper triangular matrix under modulation of the prime number. We illustrate the proposed technique with help of examples. P.Sundarayya | M.G.Vara Prasad"Symmetric Key Generation Algorithm in Linear Block Cipher Over LU Decomposition Method " Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-4 , June 2017, URL: http://www.ijtsrd.com/papers/ijtsrd90.pdf http://www.ijtsrd.com/computer-science/computer-security/90/symmetric-key-generation-algorithm-in--linear-block-cipher-over-lu-decomposition-method--/psundarayya-
When composing your answers, be thorough. Do not simply exam.docxmansonagnus
When composing your answers,
be thorough
. Do not simply examine one alternative if two or more alternatives exist. However,
choose only one
as your answer giving reasons for your choice. The more complete your answer, the higher your score will be. Be sure to identify any assumptions you are making in developing your answers and describe how your answer would change if the assumptions were different. For multiple choice questions if you think there are two correct answers
choose the best one
and justify your answers. Please write justification in
your own words
, avoid cut and paste or merely copying the sentences from references. If you are describing methodology, please describe it in
sufficient details
so that by following it, anybody can reach the same result without
additional
help from you
.
Part I (Each 4 Pts. Total 40.) Choose the best one. Please provide reason of your choice in a few sentences or reasons not choosing the other choices. Reason must be in
your own words
. Use guidelines for reference as given in the instructions.
1. To protect information, one must protect against possible virus threats True/False justify your answer
2. Which are the weaknesses of a shift cipher?
A. Natural language letter frequency makes them easy to decode.
B. The number of letters in the alphabet makes them easy to decode.
C. Once the shift is determined the message is decoded.
D. Once you have the code book you can decode the message instantly
E. A&B
F. A, B & C
G. A, B, C and D
H. A & C
No reason required
3. What is the basis of the modern cryptography? _________________
A. the laws of mathematics
B. manipulation of data
C. creating disguises for information
D. none of the above
Reason:
4.
Historically
, the primary and compelling reason for advances in cryptography has been _____________.
a. protecting business assets
b. the need for individual privacy
c. wars
d. keeping diplomatic conversations secret
Reason: _
5. A _______________ requires that the cipher alphabet changes throughout the encryption process.
a. monoalphabetic substitution cipher
b. polyalphabetic substitution cipher
c. quantum cipher
d. alphanumeric shift cipher
Reason: _
6. one of the Network threats is
A. buffer overflow
B. slowing the computer
C. denial of service
D. computer lock up
how it happens: _
7. Risk is __.
A. a weakness in the system
B. a circumstance that may cause loss or is possible danger
C. is a vulnerability that can be exploited
D. Nothing to worry about
Reason: _
8. The trustworthiness of a system is diminished because of.
a. demand for keys
b. confidence decrease
c. exposure to risks
d. bad weather
Reason: _
9. The _______ controls the action of the algorithm.
a. The receiver
b. the length of the plain text
c. cipher text
d. key
Reason: _
10. What has become a major web problem with respect to security?
a. mapping attacks
b. on-line surveys
c. user ignorance
d. ...
Improved Caesar Cipher with Random Number Generation Technique and Multistage...ijcisjournal
Secured Communication involves Encryption process at the sending end and Decryption process at the receiving end of the communication system. Many Ciphers have been developed to provide data security . The efficiency of the Ciphers that are being used depends mainly on their throughput and memory requirement. Using of large key spaces with huge number of rounds with multiple complex operations may provide security but at the same time affects speed of operation. Hence in this paper we have proposed a method to improve Caesar cipher with random number generation technique for key generation operations. The Caesar cipher has been expanded so as to include alphabets, numbers and symbols. The original Caesar cipher was restricted only for alphabets. The key used for Caesar Substitution has been derived using a key Matrix Trace value restricted to Modulo 94. The Matrix elements are generated using recursive random number generation equation, the output of which solely depends on the value of seed selected . In this paper, we made an effort to incorporate modern cipher properties to classical cipher. The second stage of encryption has been performed using columnar transposition with arbitrary random order column selection. Thus the proposed Scheme is a hybrid version of classical and modern cipher properties. The proposed method provides appreciable Security with high throughput and occupies minimum memory space. The Method is resistant against brute-force attack with 93! Combinations of keys, for Caesar encryption.
Improved Caesar Cipher with Random Number Generation Technique and Multistage...ijcisjournal
Secured Communication involves Encryption process at the sending end and Decryption process at the receiving end of the communication system. Many Ciphers have been developed to provide data security . The efficiency of the Ciphers that are being used depends mainly on their throughput and memory requirement. Using of large key spaces with huge number of rounds with multiple complex operations may provide security but at the same time affects speed of operation. Hence in this paper we have proposed a method to improve Caesar cipher with random number generation technique for key generation operations. The Caesar cipher has been expanded so as to include alphabets, numbers and symbols. The original Caesar cipher was restricted only for alphabets. The key used for Caesar Substitution has been derived using a key Matrix Trace value restricted to Modulo 94. The Matrix elements are generated using recursive random number generation equation, the output of which solely depends on the value of seed selected . In this paper, we made an effort to incorporate modern cipher properties to classical cipher. The second stage of encryption has been performed using columnar transposition with arbitrary random order column selection. Thus the proposed Scheme is a hybrid version of classical and modern cipher properties. The proposed method provides appreciable Security with high throughput and occupies minimum memory space. The Method is resistant against brute-force attack with 93! Combinations of keys, for Caesar encryption.
This presentation is about how global terminology can evolve without a centralized organisation. The simple idea is, that everybody has to disclose the identity of at least two identifiers for the same think. These local semantic handshakes will have the effect of global terminological alignment.
ENCRYPTION USING LESTER HILL CIPHER ALGORITHMAM Publications
The Hill cipher algorithm is one of the symmetrickey algorithms that have several advantages in data
encryption as well as decryptions. But, the inverse of the key matrix used for encrypting the plaintext does not always
exist. Then if the key matrix is not invertible, then encrypted text cannot be decrypted. In the Involuntary matrix
generation method the key matrix used for the encryption is itself invertible. So, at the time of decryption we need not to
find the inverse of the key matrix. The objective of this paper is to encrypt an text using a technique different from the
conventional Hill Cipher
Introduction to Mathematics is an exploration into the fascinating world of numbers and patterns. It serves as a fundamental stepping stone for understanding the language of the universe. This topic delves into the origins of mathematics, its fundamental concepts, problem-solving strategies, and practical applications in various fields. From arithmetic operations to algebra, geometry to trigonometry, mathematics provides the tools to solve complex problems and make informed decisions. With its blend of logic and creativity,
5 Lessons Learned from Designing Neural Models for Information RetrievalBhaskar Mitra
Slides from my keynote talk at the Recherche d'Information SEmantique (RISE) workshop at CORIA-TALN 2018 conference in Rennes, France.
(Abstract)
Neural Information Retrieval (or neural IR) is the application of shallow or deep neural networks to IR tasks. Unlike classical IR models, these machine learning (ML) based approaches are data-hungry, requiring large scale training data before they can be deployed. Traditional learning to rank models employ supervised ML techniques—including neural networks—over hand-crafted IR features. By contrast, more recently proposed neural models learn representations of language from raw text that can bridge the gap between the query and the document vocabulary.
Neural IR is an emerging field and research publications in the area has been increasing in recent years. While the community explores new architectures and training regimes, a new set of challenges, opportunities, and design principles are emerging in the context of these new IR models. In this talk, I will share five lessons learned from my personal research in the area of neural IR. I will present a framework for discussing different unsupervised approaches to learning latent representations of text. I will cover several challenges to learning effective text representations for IR and discuss how latent space models should be combined with observed feature spaces for better retrieval performance. Finally, I will conclude with a few case studies that demonstrates the application of neural approaches to IR that go beyond text matching.
In light of the most recent Winter Olympic Games, mathematical modeling problems involving algebra, geometry, trigonometry & calculus are presented via dynamic geometry software in the context of pairs figure skating. An aesthetically pleasing & athletically demanding pairs figure skating element, the death spiral, is discussed. Activities related to the pairs death spiral which are suitable for middle & high school students are provided in this workshop. Teachers’ work on these problems are analyzed & discussed.
Maa word math making letters into numbers ppt 12 24 2014dianasc04
We show how a seemingly simple word sum problem, “FOUR + ONE = FIVE,” in which letters are substituted with digits, can be used in the classroom at multiple levels across the curriculum from elementary through high school and beyond. We describe instructional activities related to this problem in light of the Common Core State Standards for Mathematics. Three methods of finding the total number of solutions to this word sum are discussed.
2. HSN.VM.C
Perform operations on matrices & use matrices in applications.
6 Use matrices to represent & manipulate data, e.g., to represent
payoffs or incidence relationships in a network.
7 Multiply matrices by scalars to produce new matrices, e.g., as
when all of the payoffs in a game are doubled.
8 Add, subtract, & multiply matrices of appropriate dimensions.
9 Understand that, unlike multiplication of numbers, matrix
multiplication for square matrices is not a commutative operation,
but still satisfies the associative & distributive properties.
10 Understand that the zero & identity matrices play a role in
matrix addition & multiplication similar to the role of 0 & 1 in the
real numbers. The determinant of a square matrix is nonzero if &
only if the matrix has a multiplicative inverse.
11 Multiply a vector (regarded as a matrix with one column) by a
matrix of suitable dimensions to produce another vector. Work with
matrices as transformations of vectors.
3. The goal of cryptography…
Is to hide a message’s meaning, & not
necessarily hide the existence of a
message.
If a first message is hidden inside a second
message, the second message can be
made public, yet a person seeing the
second message may not be able to
understand the meaning of the first
message.
4. Try to crack this cipher:
Try to crack this cipher:
7 0 21 4 0 13 8 2 4 3 0 24
7. Julius Caesar’s cipher
Used for military purposes & its use is
documented in his Gallic Wars.
For the first letter in the plaintext, the first letter
in the ciphertext is the letter a fixed number n
letters higher in the alphabet; repeat this
process for each letter of the plaintext.
E.g., plaintext ABCD could be shifted three
(n=3) letters, to become ciphertext, CDEF.
8. Shift Cipher:
Matrix Addition by a constant
How many keys would
you need to try, if you
knew that a message
was encoded using our
coding scheme and the
shift cipher?
11. Polyalphabetic cipher…
Was developed since the monoalphabetic
substitution ciphers were not sufficiently
keeping messages hidden anymore.
Blaise de Vigenère, (French diplomat born in
1523) created the idea of switching between
cipher alphabets. Within 1 message, multiple
cipher alphabets are used.
Vigenère’s cipher is equivalent to the Caesar
shifts of 1 through 26 (Hamilton & Yankosky,
2004; Singh, 1999).
15. Practice using Vigenere
Cipher
Discussion Question: Using the Vigenere cipher, in how many ways could
you encrypt the word “THE” using keyword “SUPER”?
16. Matrix multiplication
“Operations with Matrices”
How would the students who produced
the work on question 1 respond to
question 2? How can you help them with
matrix multiplication?
From:
Tobey, C. & Arline, C. (2014). Uncovering Student Thinking
about Mathematics in the Common Core: High School.
Corwin: Thousand Oaks, CA.
17. Matrix Multiplication (non-scalar)
Activity Adapted from “Produce Intrigue
with Crypto!” article
[A] x [B] = [C]
To solve for [B], what do you need to
know?
Encode two plaintext messages & decode
two plaintext messages!
18. Discussion Questions
What are the benefits and shortcomings
of each of these methods of encryption?
What is the role of the choice of the
coding scheme?
How can we improve our encryption
methods?
19. SmP?
Make sense of problems & persevere in
solving them
Reason abstractly and quantitatively
Construct viable arguments and critique
the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in
repeated reasoning
20. References
• Avila, C. & Ortiz, E. (2012). Produce intrigue with Crypto!
Mathematics Teaching in the Middle School, 18(4), 212-220.
• Chua, B. (2008). Harry Potter and the coding of secrets.
Mathematics Teaching in the Middle School, 14(2), 114-121.
• FBI website –
• http://www.fbi.gov/news/stories/2009/december/code_122409
• Garfunkel, S., Gobold, L., & Pollak, H. (1998). Mathematics:
Modeling our world, Course 1 (Annotated Teacher's Edition ed.).
Lexington, MA: Consortium for Mathematics and Its Applications.
• Hamilton, M., & Yankosky, B. (2004). The Vigenere cipher with the
TI-83. Mathematics and Computer Education, 38(1), 19-31.
• NCTM (2006). Rock Around the Clock. Navigating through Number
and Operations in Grades 9-12. Reston, VA.
• Nykamp, D. Introduction to matrices. From Math Insight.
• http://mathinsight.org/matrix_introduction
• Singh, S. (1999). The code book. New York: First Anchor Books.
