# how to find key matrix in hill cipher

If the encryption key matrix is not properly chosen, the generation of decryption key matrix i.e. So, at the time of decryption we need not to find the inverse of the key matrix. cipher have practical applications including image encryption see for example . The key for a hill cipher is a matrix e.g. Patented mechanism works on 6×6 sized keys. The first thing to note is that when encoding in Hill Cipher each row of the key matrix encodes to 1 letter independently of the rest of the key matrix. In the english language, the most common digraph is TH which is then followed by HE. Hill cipher is a kind of a block cipher method. Use MathJax to format equations. The key is 4 long, so should be a $2 \times 2$ matrix. February 19, 2017. Can I repeatedly Awaken something in order to give it a variety of languages? In a Hill cipher encryption the plaintext message is broken up into blocks of length according to the matrix chosen. Hill cipher, different result when decrypting. $$\begin{bmatrix} a & b\\ c & d\end{bmatrix}\begin{bmatrix}19\\7 \end{bmatrix}= \begin{bmatrix}17\\7 \end{bmatrix}$$, $$\begin{bmatrix} a & b\\ c & d\end{bmatrix}\begin{bmatrix}7\\4 \end{bmatrix}= \begin{bmatrix}13\\8 \end{bmatrix}$$, $$\begin{bmatrix} a & b\\ c & d\end{bmatrix} \begin{bmatrix} 19 & 7\\ 7 & 4\end{bmatrix} = \begin{bmatrix} 17 & 13\\ 7 & 8\end{bmatrix}$$, which allows us to find the encryption matrix by, $$\begin{bmatrix} a & b\\ c & d\end{bmatrix} = \begin{bmatrix} 17 & 13\\ 7 & 8\end{bmatrix} {\begin{bmatrix} 19 & 7\\ 7 & 4\end{bmatrix}}^{-1}$$, The determinant of $\begin{bmatrix} 19 & 7\\ 7 & 4\end{bmatrix}$ is $19\cdot 4 - 7\cdot 7 = 1 \pmod{26}$, so the inverse exists and equals (using $-7 = 19 \pmod{26}$), $$\begin{bmatrix} 4 & 19\\ 19 & 19\end{bmatrix}$$. Viewed 8k times 2. (at least three are needed) known plaintext-ciphertext pairs. the problem is that I can solve this problem just for 1 known plaintext-ciphertext pair. We have text which is encrypted by Hill-2 cipher. Now we need both matrices on the same side. Use Mozilla Firefox or Safari instead to view these pages. Now we need to combine the above equations. 4. To encrypt message: The key string and message string are represented as matrix form. Copy Link. Each block of plaintext letters is then converted into a vector of numbers and is dotted with the matrix. And when trying to find the inverse key, we will use elementary row operations to row reduce the key matrix in order to find its inverse in the standard manner. For a guide on how to break Hill ciphers, see Cryptanalysis of the Hill Cipher. (3) Consider the cipher text “ETGYX OIMOI NGQMV EJGPM NNNNZ CLOIG”, which was formed using a Hill cipher with a 2 × 2 key matrix, and suppose it is somehow known that the first two words in the plaintext are “THE ALAMO”. In this post, we’ve worked on 3×3 sized key and its key space is 26 9. This is because, in order to decrypt, we need to have an inverse key matrix, and not every matrix is invertible. By: pnp.007 . Furthermore, due to its linear nature, the basic Hill cipher succumbs to known-plaintext attacks. However, it is well known that the Hill cipher succumbs to cryptanalysis relatively easily. Improve running speed for DeleteDuplicates. What causes that "organic fade to black" effect in classic video games? To multiply a matrix by another matrix, just use one vector at a time from the matrix on the right. The key is 4 characters long, therefore it must be in a 2 × 2 matrix. What tactical advantages can be gained from frenzied, berserkir units on the battlefield? Then there is nothing wrong. What does it mean when an egg splatters and the white is greenish-yellow? Alternatively, as $\begin{bmatrix} 17 & 13\\ 7 & 8\end{bmatrix}$ is also invertible (determinant $19$) we can find the decryption matrix also from (using $A = BC \to A^{-1} = C^{-1}B^{-1}$ etc. Hill’s message protector Complexity. How do you detect and defend against micro blackhole cannon? I am finding it very hard to understand the way the inverse of the matrix is calculated in the Hill Cipher algorithm. You are supposed to try solving the problem, and ask us only when you hit an issue, and tell us which. Entering USA with a soon-expiring US passport. It then asks to use the Hill Cipher to show the calculations and the plain text when I decipher the same encrypted message "KCFL". site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. For decryption of the ciphertext message the inverse of the encryption matrix must be fo;; We need to find the determinate by evaluating using the following function. How to write graph coordinates in German? decrpytion We will now decrypt the ciphertext "SYICHOLER" using the keyword "alphabet" and a 3x3 matrix. Find the modulo of the determinant with 26-11 mod26 =15=d. An investigation was also carried out to find out a definitive correlation between the Eigen value of a periodic matrix and its periodicity. Computational complexity can also be reduced by avoiding the process of finding inverse of the matrix at the time of decryption, as we use self-invertible key matrix for encryption. To learn more, see our tips on writing great answers. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption. Hill Cipher. Matrix multiplication is involved in the encoding and decoding process. Thanks! the inverse of encryption matrix … Our key is the following matrix: K = [2 3;1 4] K = 2 3 1 4 The numbers for our message are LINEARALGEBRA = 11 8 13 4 0 17 0 11 6 4 1 17 0. (3) Consider the cipher text “ETGYX OIMOI NGQMV EJGPM NNNNZ CLOIG”, which was formed using a Hill cipher with a 2 × 2 key matrix, and suppose it is somehow known that the first two words in the plaintext are “THE ALAMO”. Today, we call this Hill’s Cipher Machine. To decode text encoded using the Hill cipher the key matrix must be invertible which can be seen in equation 2. This thread is archived. Please leave any questions or comments in the comments section below. Example § This example will rely on some linear algebra and some number theory. What events can occur in the electoral votes count that would overturn election results? The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n × n matrices (modulo 26). In our case determinant evaluates to 37, which is again greater than 26 so we will find mod26 of out determinant i.e., 37 = 11 mod 26. Thanks! RUPOTENTOIFV. 100% Upvoted. Generation of Key Matrix for Hill Cipher using Magic Rectangle K. Mani*,M. Viswambari# Department of Computer Science, Nehru Memorial College, Puthanampatti, Trichy, India Abstract Hill cipher encryption is one of the polygraph cipher of classical encryption in which if the encryption key matrix called key matrix is not chosen properly, obtaining the decryption key matrix is not possible. After performing KPA on Hill Cipher the matrix is formed wrong. Build your Cybersecurity or IT Career. How to find modulo inverse if two number are not relatively prime for Hill cipher? Hence, we will write the program of the Hill Cipher algorithm in C++, although, it’s very similar to C. Encryption. Hill Cipher Example. A block of n letters is then considered as a vector of n dimensions, and multiplied by an n × n matrix, modulo 26. Any negative numbers in K_adj should be added by 26 and then the whole matrix is multiplied by d’. 2. Then we choose a matrix of n x n size, which will be the cipher's key. Is 7/8 an example of measured rhythm or metrical rhythm? Drawing a backward arrow in a flow chart using TikZ. In members of $\mathbb{Z}_{26}$ CFDG becomes $2, 5, 3, 6$ in the usual A becomes $0$, Z becomes 25 encoding. I am also not entirely sure how I would proceed after creating this equation. Previous. Often the simplest scheme is used: A = 0, B =1, ..., Z=25, but this is not an essential feature of the cipher. Find the decryption matrix, that is, the inverse k^-1 of the key matrix K. Thanks for contributing an answer to Cryptography Stack Exchange! for the determinant there is usually a formula, such as: a x d - b x c However, for the Hill Cipher I am completely lost. In the Self-invertible matrix generation method the key matrix used for the encryption is self-invertible. The key matrix should have inverse to decrypt the message. Why aren't "fuel polishing" systems removing water & ice from fuel in aircraft, like in cruising yachts? And yeah i didn't forgot to accept you answer. I understand how to invert a matrix but the process seems different for hill ciphers. Hill cipher is a polygraphic substitution cipher based on linear algebra.Each letter is represented by a number modulo 26. The key for a hill cipher is a matrix e.g. Asking for help, clarification, or responding to other answers. Hill cipher is a polygraphic substitution cipher based on linear algebra.Each letter is represented by a number modulo 26. Beethoven Piano Concerto No. save hide report. Find the key matrix, and cryptanalyze the cipher text. I see that I have a key as a matrix that must multiply by the the matrix of values. Each letter is first encoded as a number. For decryption of the ciphertext message the inverse of the encryption matrix must be fo;; The whole matrix is considered the cipher key, and should be random pr… Hill cipher decryption needs the matrix and the alphabet used. This increases key space to 26 36. let us take an example where plain text is ‘ exam ‘ which has to be converted to ciphertext with key-value as now, form the column matrices into 2×1 configurations and covert the text into numeric data assigning values to each alphabet from 0 to 25. Abstract: Hill cipher encryption is the first polygraph cipher in classical encryption. Please leave any questions or comments in the comments section below. Notice how the top row of the far left matrix is only involved in the top cell of the ciphertext matrix, the middle row is only involved in the middle cell etc. Hill Cipher, Cryptography using Matrices: Plain text attack. I basically combined the key matrix of a, b, c, and d with the pairs TH and HE to get: TH: $(19a+7b)$mod$26$ and $(19c + 7d)$mod$26$, HE: $(7a+4b)$mod$26$ and $(7c+4d)$mod$26$. I know that it was encrypted with a hill cipher (m not specified) but I have no clue what i'm doing wrong trying to decipher the text. First of all, we need to find the inverse of the key matrix. ... Next, we need to multiply the inverse key matrix by the second trigraph. How would I find the a, b, c, and d values for the key matrix: where refers original Hill cipher the proposed modifications of the Hill to the size of the key matrix. I know with other matrices, e.g. We have already de ned how to multiply a matrix by a vector. Copy Link . 1 $\begingroup$ In the english language, the most common digraph is TH which is then followed by HE. I just wanted to provide much more security to my algorithm by encrypting the image by hill cipher. This plaintext is represented by two pairs, as shown below: Then it is computed, And encryption is continued as follows: The matrix K^-1 is invertible, hence there exists such that K^-1K=KK^-1=I2. By: pnp.007 . Hill Cipher method and Self Repetitive Matrix ” submitted by Sri Rajballav Dash and Sri Amogh Mahapatra in partial fulfillments for the requirements for the award of Bachelor of Technology Degree in Electronics & Instrumentation Engineering at National Institute of Technology, Rourkela (Deemed University) is an authentic work carried out by him under my supervision and guidance. I don't know the mean of (mod 26). How to determine the key-matrix of a Hill cipher where the encrypted-message-matrix is not invertible? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. 7 comments. Decryption involves matrix computations such as matrix inversion, and arithmetic calculations such as modular inverse. Which encrypts to the cipher text . After some experimenting I found that we make this into the encryption matrix $$K = \begin{bmatrix} 2 & 5\\ 3 & 6 \end{bmatrix}$$ By: pnp.007 . Same term used for Noah's ark and Moses's basket. $\;$ As for any problem of this kind, I suggest that you 1) identify appropriate unknowns 2) identify what the givens tell you about these unknowns 3) try to apply your bag of mathematical tools. and I put all pairs in one matrix and I have doubt that is true or false. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Also, using tools isn't an option as the method is my end goal, not the answer. Learn Hill Cipher with 3x3 Matrix Multiplicative Inverse Example. Now we need to remember how to decrypt a hill cipher and invert the second matrix. I am reading about Hill Cipher encryption algorithm, from the wikipedia. 2. Though the Key matrix must be known to decrypt the message. Active 3 years, 2 months ago. What do this numbers on my guitar music sheet mean. Consider the following Hill Cipher key matrix: 5 8 17 3 I have the encryption key for a hill cipher and I'm trying to find the decryption key. Hill Cipher. If i'm not wrong here, I can use these values to solve for the values of a, b, c, and d. Unfortunately my use of matrix notation is limited and I fear that I would clog up the screen with my poor attempt so I'll just put the result of my work. Even though it is a type of classical and historical cryptography method, it has a special place in my heart because of strong math background and easy adaptation. The main drawback of Hill Cipher is selecting the correct encryption key matrix for encryption. In this particular example let's say the digraphs with the most frequencies are RH and NI. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Copy Link. Can I draw a weapon as a part of a Melee Spell Attack? To decrypt hill ciphertext, compute the matrix inverse modulo 26 (where 26 is the alphabet length), requiring the matrix to … We get the following matrix for the chosen key: The message is thus encoded by this vector: Key and message are multiplied with each other and apply modulo 26 to the result: This result (15, 14, 7) can be decoded by 'POH' which would be the output of the Hill cipher for the chosen message and the used key. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. NOTE: m-files don't view well in Internet Explorer. $\;$ Your question is a straight dump of homework, and thus off topic. (If one uses a larger number than 26 for the modular base, then a different number scheme can be used to encode the letters, and spaces or punctuation can also be used.) Question:: Find Out The Ciphertext (c) Using Hill Cipher For The Plaintext= MATH, Where The Matrix Key= [3 1] [6 5] Please Show The Required Steps.Decrypt The Following Ciphertext= KUMT, If You Know It Has Been Encrypted By Hill Cipher, Where The Matrix Key = … Can a shell script find and replace patterns inside regions that match a regex? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. January 2, 2019. It only takes a minute to sign up. Lastly thank you for your comment. To learn more, see our tips on writing great answers. Often the simple scheme A = 0, B = 1, …, Z = 25 is used, but this is not an essential feature of the cipher. In fact that not all the matrices have an inverse and therefore they will not be eligible as key matrices in the Hill cipher scheme. Then if the key matrix is not invertible, then encrypted text cannot be decrypted. Next. Wouldn't I have to find the inverse instead of solving the equation? February 19, 2017. How does Shutterstock keep getting my latest debit card number? Would Venusian Sunlight Be Too Much for Earth Plants? The method of self repetitive matrix has then been used to simulate a communication channel with proper decompression techniques to facilitate bit saving. I know it is modulo 26, but I don't know for what it is applied? The Hill cipher The Playfair cipher is a polygraphic cipher; it enciphers more than one letter at a time. This is very large even for today computation power. An attack by frequency analysis would involve analyzing the ... multiply that matrix by the key. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. 26) on each vector. share. Based on linear algebra Hill cipher is a polygraphic substitution cipher in cryptography. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. To encrypt an encrypted word, Ciphertext is needed to convert into the vector form. Find the inverse number of the above result d x d’=1 mod26 15 x d’=1 mod26 d’=7. What does "Drive Friendly -- The Texas Way" mean? Why can't I sing high notes as a young female? Ek(sun)=ABA, Ek(hat)=AAB. the inverse of encryption matrix is … To do this first find the determinant of our key matrix. Why does nslookup -type=mx YAHOO.COMYAHOO.COMOO.COM return a valid mail exchanger? Thanks for contributing an answer to Mathematics Stack Exchange! For a guide on how to break Hill ciphers, see Cryptanalysis of the Hill Cipher. Learn Hill Cipher with 3x3 Matrix Multiplicative Inverse Example. Entering USA with a soon-expiring US passport. 5. Where does the phrase, "Costs an arm and a leg" come from? In the above case, we have taken the size to be 3×3, however it can be any size (as long as it is square). To learn more about hill cipher … Podcast 301: What can you program in just one tweet? To make sense, the secret key must be chosen such as its inverse exists in module . They are multiplied then, against modulo 26. If the key matrix was 3×3, then each column matrix would be 3×1. I get the idea of it all being done in modulo arithmetic, but somehow things are not adding up. Actually, it was the first one appearing in the history. How to find the key matrix of a 2x2 Hill Cipher? \begin{pmatrix}a&b\\c&d\end{pmatrix}, We can split TH and HE into pairs \begin{pmatrix}R\\H\end {pmatrix} \begin{pmatrix}N\\I\end{pmatrix}. To learn more about hill cipher … Hill cipher decryption needs the matrix and the alphabet used. If the encryption key matrix is not properly chosen, the generation of decryption key matrix i.e. When should one recommend rejection of a manuscript versus major revisions? And people here are for helping each other infact if you think we people take help from google and other. In a Hill cipher encryption the plaintext message is broken up into blocks of length according to the matrix chosen. We also turn the plaintext into digraphs (or trigraphs) and each of these into a column vector. How did SNES render more accurate perspective than PS1? ), $${\begin{bmatrix} a & b\\ c & d\end{bmatrix}}^{-1} = \begin{bmatrix} 19 & 7\\ 7 & 4\end{bmatrix} {\begin{bmatrix} 17 & 13\\ 7 & 8\end{bmatrix}}^{-1}$$ as well. The Hill matrix algorithm is known for being the first purely algebraic cryptographic system and for starting the entire field of algebraic cryptology. The Hill cipher  uses matrix multiplication to map the plaintext (text to be encoded) onto the ciphertext (text which has been encoded) using the key matrix, A (1). To do this first find the determinant of our key matrix. Break Hill Cipher with a Known Plaintext Attack. The results are then converted back to letters and the ciphertext message is produced. To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. The core of Hill-cipher is matrix manipulations It is a multi-letter cipher,for Decryption the inverse of matrix requires and Inverse of the matrix doesn’t always exist. Now we want to determine the matrix D (the decryption key). Hill and Louis Weisner also had an idea to build a machine that would mechanically implement a Hill cipher. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The the cipher quite significantly ,,. Active 2 years, 7 months ago. OUTPUT: line 1: Encrypted message (ans) The following is the Hill Cipher … Drawing a backward arrow in a flow chart using TikZ. Why hasn't JPE formally retracted Emily Oster's article "Hepatitis B and the Case of the Missing Women" (2005)? Decryption involves matrix computations such as matrix inversion, and arithmetic calculations such as modular inverse. Additional restrictions to the key are imposed by the need to … The results are then converted back to letters and the ciphertext message is produced. Each letter is represented by a number modulo 26. To encrypt a message using the Hill Cipher we must first turn our keyword into a key matrix (a 2 x 2 matrix for working with digraphs, a 3 x 3 matrix for working with trigraphs, etc). Hill Cipher is a polygraphic substitution cipher based on linear algebra. MathJax reference. Hill Cipher is a polygraphic substitution cipher based on linear algebra. February 19, 2017. where the unknown ki={0,1,...25}={A,B,...,Z} can be solved given a sufficient number You should always have the following commands at the top to "start fresh" We know the language of text (English, 26 letters). Often the simple scheme A = 0, B = 1, …, Z = 25 is used. Hill cipher: why can the cipher key matrix’s determinant not share common factors with the modulus? rev 2021.1.5.38258, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Cryptography Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Which, when converted to their integer values, are equivalent to: Then if the matrix is not invertible then encrypted text cannot be decrypted. In the above case, we have taken the size to be 3×3, however it can be any size (as long as it is square). In this particular example let's say the digraphs with the most frequencies are RH and NI. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Given a matrix secret key with shape , the Hill cipher splits the plaintext into blocks of length and for each block, computes the ciphertext block doing a linear transformation in module . Key is the matrix; however, it is convenient to use the key phrase, which is transformed into the digit representation and matrix. So the inverse of our key matrix is: Now after multiplying the inverse matrix with the ciphertext matrix that we've generated in the encryption, we can get out plain text matrix again. To decrypt hill ciphertext, compute the matrix inverse modulo 26 (where 26 is the alphabet length), requiring the matrix to be invertible. key matrix in Hill cipher algorithm for encryption, where encrypted message cannot be decrypted until the key matrix is not invertible. For decrypting, we apply the inverse of . How to find the key matrix of a 2x2 Hill Cipher? Hill cipher's susceptibility to cryptanalysis has rendered it unusable in practice; it still serves an important pedagogical role in both cryptology and linear algebra. But there are 2 things I don't understand. February 19, 2017. decrpytion ... We will need this number later, but meanwhile, we need to find the adjugate matrix (a matrix of the same size as the original), which requires the use of a lot of calculations using algebraic operations. I have done the following: a) found the inverse of K: breathtaking . Find the determinant of the key matrix 77-88=-11. Once the matrix inversion has been calculated, you multiple it through each part of the cipher text in their respective 2 × 1 matrices rev 2021.1.5.38258, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Decryption: The encrypted message matrix is multiplied by the inverse of key matrix and finally its modulo 26 is taken to get the original message. Can there be planets, stars and galaxies made of dark matter or antimatter? The plaintext and ciphertext are stored in vectors, P and C respectively, which have the same number of rows as the key matrix. EE. Let A is equal to, be the key and let us assume that plaintext message is HELP. As a result, there have been efforts to Hill cipher encryption and decryption example is explained fully explained here with step by step solution. Key and message are multiplied with each other and apply modulo 26 to the result: This result (15, 14, 7) can be decoded by "POH" which would be the output of the Hill cipher for the chosen message and the used key. Should be added by 26 and then the whole matrix is considered the cipher key, and ask us when., be the key is 4 characters long, so should be random pr… learn Hill cipher and the. Let 's say the digraphs with the most frequencies are RH and NI being in... Pretty simple Way to break a Hill cipher encryption and decryption example is explained fully explained here with step step. Matrices: plain text attack i see that i can solve this problem just for 1 known pairs... And i put all pairs in one matrix and i put all pairs in one matrix how to find key matrix in hill cipher its key is... 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Has n't JPE formally retracted Emily Oster 's article  Hepatitis B and the ciphertext  ''! Clarification, or responding to other answers number are not adding up = 1, …, Z = is! To convert into the vector form its linear nature, the generation of decryption we need to multiply a is... Shippingstatecode '' does not exist, but i do n't understand statements based on linear algebra find! Your RSS reader statements based on opinion ; back them up with references or personal.... And tell us how to find key matrix in hill cipher in classical encryption can i draw a weapon as a of. To build a Machine that would overturn Election results an idea to build a Machine that would overturn Election?... Algorithm for encryption its inverse exists in module ever use captured Allied aircraft against the Allies 2. Metrical rhythm tips on writing great answers encryption see for example [ 6 ] considered! Is multiplied by d ’ =1 mod26 d ’ =1 mod26 15 how to find key matrix in hill cipher ’... And let us assume that $TH \to RH$ and $HE \to NI$ under Hill. Ask us only when you hit an issue, and cryptanalyze the cipher text …... An attack by frequency analysis would involve analyzing the... multiply that matrix by the the cipher key.... Valid mail exchanger another matrix, and tell us which an inverse key matrix must be in 2... Guitar music sheet mean for helping each other infact if you think we how to find key matrix in hill cipher take help google! K: Hill cipher by using matrices: plain text attack has n't JPE retracted! Part of a Melee Spell attack Moses 's basket give it a variety languages. Then perform matrix multiplication modulo the length of the Hill cipher, cryptography using matrices you about the ;... Letters ) while decryption problem just for 1 known plaintext-ciphertext pairs is explained fully explained here with step step! Just wanted to provide Much more security to my algorithm by encrypting the image by Hill cipher ''... 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Applications including image encryption see for example [ 6 ] a straight dump homework!