Technology Tips: Exploring Hill Ciphers with Graphing Calculators

1998 ◽  
Vol 91 (3) ◽  
pp. 240-244
Author(s):  
Dennis St. John
Keyword(s):  
Relative Frequency ◽  
English Language ◽  
Matrix Multiplication ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Modular Arithmetic ◽  
Evaluation Standards ◽  
Hill Cipher ◽  
The Matrix ◽  
Coded Messages

Throughout history, coded messages have been used for various reasons. Today's students are fascinated by the secretive nature of these codes, and this fascination can lead them to explore the mathematics of cryptography. The simplest codes are called substitution ciphers. In these codes, each letter is replaced by another number or letter in the alphabet. These codes are easy to crack, or decode, because of the relative frequency of letters in messages. For example, e is the most often used letter in the English language; therefore, the substituted value for e is relatively easy to determine. One way to make substitution codes more difficult to crack is to group letters and then encode the groups of letters. A particular application of this strategy, one that combines matrix multiplication and modular arithmetic, is known as the Hill cipher (Anton and Rorres 1987). This article explains coding and decoding messages using Hill ciphers. These ciphers are an interesting example of an application of matrices called for in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 9-12. A graphing calculator will facilitate the matrix and modular arithmetic used in the coding and decoding procedures.

Applications: Using Technology to Understand the Jury Decision-making Process

1994 ◽  
Vol 87 (2) ◽  
pp. 110-114
Author(s):  
Kenneth P. Goldberg
Keyword(s):  
Teaching And Learning ◽  
Potential Effect ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Decision Making Process ◽  
Jury Decision Making ◽  
Evaluation Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Jury Decision

Two of the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) are to use technology to enhance teaching and learning mathematics and to relate school mathematics to the world in which the students Jive through developing and interpreting mathematical models. This article demonstrates how computer or graphing-calculator technology can be used to help students develop and interpret three increasingly realistic models of jwy behavior and explore the potential effect of such decisions as changing jury size. The only mathematics required is an understanding of simple binomial probabilities and the use of sigma, or summation, notation

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems

2000 ◽  
Vol 93 (3) ◽  
pp. 224-228 ◽  
Author(s):  
David C. Purdy
Keyword(s):  
High School ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Maximum Volume ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Traditional Courses

An underlying tenet of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and other movements toward reform in school mathematics is breaking down content barriers between traditional mathematical topics, with the goal of teaching mathematics as a logically interconnected body of thought. As teachers move toward integrating the various areas of mathematics into traditional courses, problems that were once reserved for higher courses, for example, precalculus and calculus, now surface earlier as interesting explorations that can be tackled with such tools as the graphing calculator. One such problem is the well-known maximum-volume-box problem. Although this problem and related optimization questions have been common in advanced algebra, precalculus, and calculus textbooks, they have only recently found their way into high school geometry textbooks, including Discovering Geometry: An Inductive Approach (Serra 1997).

scholarly journals Three-Pass Protocol Concept in Hill Cipher Encryption Technique

2017 ◽  
Author(s):  
Andysah Putera Utama Siahaan
Keyword(s):  
Matrix Multiplication ◽  
Hill Cipher ◽  
The Matrix ◽  
Square Matrix

Hill Cipher Encryption technique has a square matrix in its calculation. The ciphertext resulted is obtained from the matrix multiplication between plaintext and key. The reality is the sender must send or tell the receiver the key used to encrypt the data before the receiver can decode the ciphertext into the legible message. The listener is able to read the key that flows to the receiver. By knowing the key, the listener will absolutely break the ciphertext and turn into plaintext. Three-Pass Protocol is a way to limit the key being distributed. The sender and receiver have their own keys in hand. They do not need to share each other. This method will improve the security.

scholarly journals Enkripsi Data Citra untuk Model Warna RGB dan Treshold Menggunakan Algoritma Hill Cipher

2019 ◽  
Vol 4 (1) ◽  
pp. 175-178
Author(s):  
Ommi Alfina
Keyword(s):  
Digital Media ◽  
Threshold Model ◽  
Matrix Multiplication ◽  
Digital Data ◽  
Original Form ◽  
Diverse Range ◽  
Black And White ◽  
Hill Cipher ◽  
The Matrix ◽  
The Hill

With the increasingly widespread abuse of digital media, especially in the form of images or images, it increasingly disrupts the rights and privacy of everyone. Many forms of abuse that occur in digital media through internet facilities such as plagiarism of photographer's work, recognition of the rights of the image, to upload photos of privacy to internet media. Therefore, one way to secure digital data in the form of images is to randomize (encrypt) the images that we feel are very important so that the image can no longer be interpreted by others. If we need these data, we just need to return it (decryption) so that the encryption image can return to its original form. Hill Cipher algorithm is one method to randomize a data by encoding and multiplying the matrix. For its application in the form of image data, a trial is needed by creating a software which will then analyze the results into several color models such as RGB, Grayscale (Keabuan) and Tresholding (Black and White). From the test results, it can be concluded that the greater the input matrix value of the Hill Cipher Algorithm, the more encrypted image results will be obtained or in other words the more incomprehensible the visual form by humans. Then the Hill Cipher algorithm cannot be applied to the color threshold model (black and white) because the matrix multiplication obtained does not have a diverse range of values

Reading, Writing, Arithmetic-Making Connections

1999 ◽  
Vol 6 (3) ◽  
pp. 190-197
Author(s):  
Gwen Taylor
Keyword(s):  
Language Arts ◽  
English Language Arts ◽  
English Language ◽  
School Mathematics ◽  
Evaluation Standards

As teachers review the Standards for the English Language Arts (1996) and the Curriculum and Evaluation Standards for School Mathematics (1989), they can observe many similarities. Both publications call for changes in how instruction should take place in classrooms.

Teacher to Teacher: Building A Teenage Dance Club

1998 ◽  
Vol 4 (1) ◽  
pp. 26-30
Author(s):  
Mary Ann Christina
Keyword(s):  
Teaching And Learning ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Technological Society ◽  
Conscious Decision ◽  
Paper And Pencil

As the nctm's curriculum and evaluation Standards for School Mathematics (1989) became more well known and I attended more workshops. I made a conscious decision to make algebra more closely tied to the outside world and show it importance in today's technological society. I started using the graphing calculator to eliminate some obsolete paper-and-pencil kill and started using relevant project that became an integral part of my course. I became involved in, and committed to, the philosophy of “Opening the Gate,” which is a series of activities developed in Florida to supplement the curriculum and to reform the teaching and learning of algebra. The idea is to make algebra more accessible, more dynamic, and more relevant to today's and tomorrow's society.

Publication of a scientific article in for an english-language journal. Part 2

2019 ◽  
Vol 23 (5) ◽  
pp. 116-121
Author(s):  
A. I. Nevorotin ◽  
I. V. Awsiewitsch ◽  
I. M. Sukhanov
Keyword(s):  
Detailed Analysis ◽  
English Language ◽  
Scientific Literature ◽  
Scientific Article ◽  
Scientific Journals ◽  
English Language Journal ◽  
The Matrix ◽  
Syntactic Relations

This article is the continuation of analysis and discussion from the book by Professor AI Nevorotin "Matrix phraseological collection: a manual for writing a scientific article in English". The Matrix phraseological collection is a kind of catalog of text samples. The samples were from articles selected from the leading English-language scientific journals and were systematized in such away that when writing an article in English, a Russian researchers are able easy to find examples suitable for his/her own work. Furthermore, the selected samples can be transformed accordingly saving the semantic and syntactic relations between the elements and, finally, be inserted into the text. The second part of this work is devoted to the detailed analysis of the English scientific literature and also the section "Legality of the provisions of the problem".

scholarly journals PENERAPAN METODE MULTI ATTRIBUTE UTILITY THEORY (MAUT) DALAM PEMETAAN TINGKAT DAMPAK BENCANA BANJIR DI KABUPATEN BANTUL

Telematika ◽  
2020 ◽  
Vol 17 (1) ◽  
pp. 26
Author(s):  
Afif Irfan Abdurrahman ◽  
Bambang Yuwono ◽  
Yuli Fauziah
Keyword(s):  
Utility Theory ◽  
Matrix Multiplication ◽  
Flood Disaster ◽  
Accuracy Rate ◽  
Affected Area ◽  
A Value ◽  
Multi Attribute Utility Theory ◽  
The Matrix ◽  
The Difference ◽  
The Impact

Flood disaster is a dangerous disaster, an event that occurs due to overflow of water resulting in submerged land is called a flood disaster. Almost every year Bantul Regency is affected by floods due to high rainfall. The flood disaster that struck in Bantul Regency made the Bantul District Disaster Management Agency (BPBD) difficult to handle so that it needed a mapping of the level of the impact of the flood disaster to minimize the occurrence of floods and provide information to the public.This study will create a system to map the level of impact of floods in Bantul Regency with a decision support method namely Multi Attribute Utility Theory (MAUT). The MAUT method stage in determining the level of impact of flood disasters through the process of normalization and matrix multiplication. The method helps in determining the areas affected by floods, by managing the Indonesian Disaster Information Data (DIBI). The data managed is data on criteria for the death toll, lost victims, damage to houses, damage to public facilities, and damage to roads. Each criteria data has a value that can be used to determine the level of impact of a flood disaster. The stages for determining the level of impact of a disaster require a weighting calculation process. The results of the weighting process display the scoring value which has a value of 1 = low, 2 = moderate, 3 = high. To assist in determining the affected areas using the matrix normalization and multiplication process the process is the application of the Multi Attribute Utility Theory (MAUT) method.This study resulted in a mapping of the level of impact displayed on google maps. The map view shows the affected area points and the level of impact of the flood disaster in Bantul Regency. The mapping produced from the DIBI data in 2017 produced the highest affected area in the Imogiri sub-district. The results of testing the data can be concluded that the results of this study have an accuracy rate of 95% when compared with the results of the mapping previously carried out by BPBD Bantul Regency. The difference in the level of accuracy is because the criteria data used are not the same as the criteria data used by BPBD in Bantul Regency so that the accuracy rate is 95%.

scholarly journals Variability in Global Prevalence of Interstitial Lung Disease

2021 ◽  
Vol 8 ◽  
Author(s):  
Bhavika Kaul ◽  
Vincent Cottin ◽  
Harold R. Collard ◽  
Claudia Valenzuela
Keyword(s):  
Interstitial Lung Disease ◽  
North America ◽  
Lung Disease ◽  
Relative Frequency ◽  
English Language ◽  
Population Based ◽  
Epidemiologic Studies ◽  
Disease Classification ◽  
Global Burden ◽  
Community Based

There are limited epidemiologic studies describing the global burden and geographic heterogeneity of interstitial lung disease (ILD) subtypes. We found that among seventeen methodologically heterogenous studies that examined the incidence, prevalence and relative frequencies of ILDs, the incidence of ILD ranged from 1 to 31.5 per 100,000 person-years and prevalence ranged from 6.3 to 71 per 100,000 people. In North America and Europe, idiopathic pulmonary fibrosis and sarcoidosis were the most prevalent ILDs while the relative frequency of hypersensitivity pneumonitis was higher in Asia, particularly in India (10.7–47.3%) and Pakistan (12.6%). The relative frequency of connective tissue disease ILD demonstrated the greatest geographic variability, ranging from 7.5% of cases in Belgium to 33.3% of cases in Canada and 34.8% of cases in Saudi Arabia. These differences may represent true differences based on underlying characteristics of the source populations or methodological differences in disease classification and patient recruitment (registry vs. population-based cohorts). There are three areas where we feel addition work is needed to better understand the global burden of ILD. First, a standard ontology with diagnostic confidence thresholds for comparative epidemiology studies of ILD is needed. Second, more globally representative data should be published in English language journals as current literature has largely focused on Europe and North America with little data from South America, Africa and Asia. Third, the inclusion of community-based cohorts that leverage the strength of large databases can help better estimate population burden of disease. These large, community-based longitudinal cohorts would also allow for tracking of global trends and be a valuable resource for collective study. We believe the ILD research community should organize to define a shared ontology for disease classification and commit to conducting global claims and electronic health record based epidemiologic studies in a standardized fashion. Aggregating and sharing this type of data would provide a unique opportunity for international collaboration as our understanding of ILD continues to grow and evolve. Better understanding the geographic and temporal patterns of disease prevalence and identifying clusters of ILD subtypes will facilitate improved understanding of emerging risk factors and help identify targets for future intervention.

scholarly journals HILL CIPHER ON SHAMIR’S THREE PASS PROTOCOL

2017 ◽  
Author(s):  
hasdiana
Keyword(s):  
Matrix Element ◽  
Execution Time ◽  
Invertible Matrix ◽  
Multidisciplinary Research ◽  
The Third ◽  
Xor Operation ◽  
Hill Cipher ◽  
The Matrix ◽  
Level Of Difficulty ◽  
Time Required

This preprint has been presented in the 3rd International Conference on Multidisciplinary Research, Medan, october 16 – 18, 2014---In this study the authors use the scheme of Shamir's Three Pass Protocol for Hill Cipher operation. Scheme of Shamir's Three Pass Protocol is an attractive scheme that allows senders and receivers to communicate without the key exchange. Hill Cipher is chosen because of the key-shaped matrix, which is expected to complicate the various techniques of cryptanalyst. The results of this study indicate that the weakness of the scheme of Shamir's Three Pass Protocol for XOR operation is not fully valid if it is used for Hill Cipher operations. Cryptanalyst can utilize only the third ciphertext that invertible. Matrix transpose techniques in the ciphertext aims to difficulties in solving this algorithm. The original ciphertext generated in each process is different from the transmitted ciphertext. The level of difficulty increases due to the use of larger key matrix. The amount of time required for the execution of the program depends on the length of the plaintext and the value of the matrix element. Plaintext has the same length produce different execution time depending on the value of the key elements of the matrix used.

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