Example of hill cipher 3x3 matrix. Patented mechanism works on 6×6 sized keys.

Example of hill cipher 3x3 matrix Wikipedia has an excellent example of how this algorithm works. Home; Coding Tool; Encrypt/Decrypt; Other Tool; Encrypt/Decrypt > Hill cipher is an alternative cipher that uses the principles of basic matrix theory. Frequency analysis would be even more complicated if we had a For a matrix to be a key for a Hill cipher, the determinant of the matrix must be 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, or 25 modulo 26. In this video of CSE concepts with Parinita Hajra Since Hill cipher is a symmetric key encryption algorithm. The key matrix must be a square matrix. Hill cipher is a polygraphic substitution cipher based on linear algebra. The key matrix should have inverse to decrypt the message. docx), PDF File (. First, we need to divide the plaintext into groups of three letters (trigraphs), since we are using a 3x3 matrix, and write them in columns (since the plaintext will not go evenly into the Get access to the latest Hill cipher - Example of 3x3 matrices - Encryption part. Once the matrix inversion has been calculated, you multiple it through each part of the cipher text in their respective 2 × 1 matrices Multiletter cipher – Hill Cipher: M – Square Matrix; M-1 – Inverse square matrix; M(M-1 ) = M-1 M = I – I is the identity matrix where only diagonal elements are 1 from upper left to lower right and all other elements are zero. A cipher starts out originally as plaintext, which is written and then is converted into a ciphertext. Hill chose an n by n encryption matrix E so that detE is not divisible by 2 or 13. Let's go through the steps of the Hill Cipher with detailed explanations and examples. Hill cipher 3*3 matrix with example in a very easy method . P is our text we want to encrypt in the form of an n×1 Matrix. The definition of Hill Cipher is given in the lecture notes. To use, hardcode in the 3x3 matrix key in the python file. General Terms Hill Cipher- Potential Cribs for 3x3 Matrix Thread starter J6204; Start date Dec 8, 2017; Tags 3x3 Hill Matrix Potential Dec 8, 2017 #1 J6204. The Hill Cipher encrypts blocks of letters simultaneously. For example: If the determinant is 0, or has common factors with the modular base, then the matrix cannot be used in the Hill cipher, and another matrix must be chosen (otherwise it will not be possible to decrypt). The size of the key matrix determines the size of the groups of letters that are encrypted together. Plaintext is broken into blocks of n characters. Quite hacky and slow but gets the job done. An alternative, less common term is encipherment. a 3×3 matrix for encryption, using the input message ‘We are safe’. This polygraphic substitution cipher For a guide on how to break Hill ciphers, see Cryptanalysis of the Hill Cipher. Encryption: The key and plaintext are converted into matrix format according to the positions like a=0 to z=25 The Hill Cipher. doc / . The key for a hill cipher is We will cover both Hill Cipher encryption and decryption procedures solving 3×3 matrices. Fortunately, matrices which satisfy the conditions to be used in the Hill cipher are fairly common. In order to decode this cipher the inverse of the key matrix A modulo 26 must be found. We will propose a new variant of hill cipher, which will find the decryption of the cipher text even when the key matrix is non invertible. To encrypt a plaintext, follow these steps: The first step is to convert the given keyword to a 3x3 matrix form. Follow edited Aug 17, 2016 at 13:32. This method makes use of matrices from mathematics. It creates functions to define the key matrix from a given key, encrypt a message with the help of the generated key matrix, and do the Hill Cipher encryption. 1. g. It is now mostly used in classical cipher teaching and learning. Input. Here the key phrase is given as ALPHABET, and we have to convert this key phrase into a matrix. Use the code matrix A and the encryption matrix M to get back the original plaintext matrix P (as in step 5). For example, if our matrix is 2x2, we can encrypt only two plain letters at a time. Encryption: To encrypt a message using the Hill cipher. Matrices are arrays of numbers arranged in rows and columns that can perform operations on vectors. h: this is the header file which binds all the files of the first example matrix modulo 13, one can use the commands A:=Matrix( [[3,10,20],[20,9,17],[9,4,17]] ); Determinant(A) mod 13. For example: Diagraph: "nt" Encrypted Text: rq Encryption: n -> r t -> q. This is very large even for today computation power. Here is source code of the C Program to Implement the Hill Cypher. The document describes the Hill cipher encryption algorithm. These numbers will form the key (top row, bottom row). As we can see, there are only 8 letters, and we need at least 9 letters for a 3×3 matrix. في فيديو سابق شرحنا التشفير بطريقة هيل باستخدام مصفوفة قياس 2x2 وبالتفصيل وفي هذا الفيديو نشرح استخدام نفس Network Security: Hill Cipher (Decryption)Topics discussed:1) Classical encryption techniques: Substitution and Transposition techniques. Each pair of Cipher text multiply with inverse key matrix. Using the modulo operator allows you to map every possible output of the matrix multiplication (encryption) to a letter in the alphabet (834 = 2 (mod 26) which is C), which lets you store the encrypted message in the form of a string of letters. 37 Hill Cipher. Now we will take an example for. Suppose Naval Intelligence intercepts the following coded message and believes it was encrypted using a Hill code. The Hill cipher is a polygraphic substitution cipher based on linear algebra that operates on blocks of 2 or 3 letters at a time (depending on the word), each letter represented by a number in modulo 26, and using a key matrix with nxn dimension (there's a 2x2 default key matrix in the code). Although this ciphering method has lost its practicality in this technological era and easily succumb to plain text 2. Hill cipher is a polygraphic substitution cipher. cpp: this file contains the basic operations implemented on the matrix hillcipher. Solution. The determinant of K must be relatively prime with 26. Key. txt) or read online for free. Next, convert the keyword matrix into a key matrix by replacing the letters with corresponding numeric values. In order to decode this cipher the inverse of the key matrix A modulo 26 must be For example: Diagraph: "st" Encrypted Text: tl Encryption: s -> t t -> l. It uses one matrix key to encrypt plaintext and another matrix key to decrypt cipher text [8]. Invented by Lester S. C Program to Implement the Hill Cypher - Based on linear algebra Hill cipher is a polygraphic substitution cipher in cryptography. To understand how the Hill Cipher works, we will encrypt the text, 'FLY'. That is, the secret key is a 3×3 matrix over Z26. To encrypt the letter block "NU", we apply an invertible linear transformation$\pmod{26}$ to the corresponding vector, and then interpret the result as another letter block. You signed in with another tab or window. FLY. 2) Multiply Inverse matrix with ciphertext The Hill cipher The Playfair cipher is a polygraphic cipher; it enciphers more than one letter is a simple example of a block cipher, since it takes two-letter blocks and encrypts them to two-letter blocks. Takes at most a 3x3 (9 character) matrix key. Note: This implementation supports 4 numbers only. M JavaScript Example of the Hill Cipher § This is a JavaScript implementation of the Hill Cipher. Hill Cipher Solved Example 3x3 Key Matrix Hill Cipher Encryption and Decryption Cryptography and Network Security by Mahesh Huddar1. With this we have a matrix operator on the plaintext: which is used to encode, and then the decoder is the inverse of this: This is a C Program to implement Hill Cipher. Module 3: substitution techniques – Hill cipher Multiletter cipher – Hill Cipher: M – Square Matrix M-1 – Inverse square matrix M(M-1) = M-1 M = I – I is the identity matrix where only diagonal elements are 1 from upper left to lower right and all other elements are zero. Then we choose a matrix of n x n size, which will be the cipher's key. As an example of the Hill Cipher technique, let’s encrypt the text, ‘ACT’, and, later, decrypt the resulting ciphertext. This means that when we apply Hill's cipher machine, from figure 4 of the patent. The loop will run till the entire ciphertext is decrypted and congrats! You have successfully decrypted a hill cipher. Write a function to generate the 3X3 matrix for the key string, which is 'CODINGANU'. For Example, Plain Text = SUNDAY If key matrix is 2 x 2, Plain text divided in into group of 2 alphabets: SU ND AY If key matrix is 3 x 3, Plain text divided in into group of 3 alphabets: SUN Lester S. It includes functions for encrypting and decrypting text Introduction to Hill Cipher In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on at once. Here’s the best way to solve it. With this we have a matrix operator on the plaintext: For example we take the matrix: \[\begin{equation}A=\begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix} \end{equation}\] Then the reverse will be: \[\begin{equation}A=\begin{bmatrix} 5 & -3 \\ -3 & 2 \end{bmatrix} \end{equation}\] We thus use The Hill cipher The Playfair cipher is a polygraphic cipher; it enciphers more than one letter is a simple example of a block cipher, since it takes two-letter blocks and encrypts them to two-letter blocks. Once it has been determined that a matrix A is invertible modulo 26, it may be used as a key matrix for a Hill substitution cipher. Exercise 5. The [15 4 7] came from The Hill cipher is an example of an asymmetric cipher [4]. $\;$ Again, write down what known plaintext The key is 4 characters long, therefore it must be in a 2 × 2 matrix. Get link; Facebook; X; Ø In this Hill cipher technique, the KEY and PLAINTEXT must be in the form of square matrix. Show suggested Question Text Note that the matrix in your text uses the transpose (as it left multiplies by $1 \times 2$ matrices instead, so all equations transpose) and the one from the online calculator is not an inverse at all (which becomes obvious if we do the full matrix multiplication; only the first row looks OK). Reload to refresh your session. Encryption process. 56 2. – GATE Exam Lester S. 3×3 Hill Ciphers are extremely useful when hiding a single-letter or two-letter frequency information. Hill Cipher Encryption Example. Mod[n,p] calculates n mod p. Plaintext Grouping and Ciphertext Generation. The determinant of . To perform decryption, the hill cipher requires the inverse of the key matrix. It details the encryption process for each segment of the plaintext, calculating the resulting ciphertext Example. when plaintext in 2x2 then key value also in 2x2 matrix and 3x3 use then 3x3 matrix key. cpp: this is to write the algorithm of decrypting text using hill cipher linearalgebra. This calculator uses Hill cipher to encrypt/decrypt a block of text. Converts a matrix along its diagonal to transpose Hill cipher encryption and decryption example is explained fully explained here with step by step solution. Note that this Thanks for contributing an answer to Stack Overflow! Please be sure to answer the question. The case here is restricted to 2x2 case of the hill cipher for now, it may be expanded to 3x3 later. \end{equation*} For Hill Cipher Example. Tool to decrypt/encrypt with Hill cipher, a ciphering system similar to affine cipher but using a coefficient matrix instead of 2 affine coefficients (gradient). In this post, we’ve worked on 3×3 sized key and its key space is 26 9. The inverse matrix E−1 ≡D(mod 26) will be the decryption matrix that decodes the message. Example § This example will rely on some linear algebra and some number theory. Hill cipher part 1. To encipher a message, first the plaintext is broken into blocks of n letters which are converted to numbers, where A=0, B=1, C=2 Discussed in this video. for val in encrypted_block) return ciphertext # Example usage plaintext HILL CIPHER. Hill Cipher Encryption 3×3 matrix Hello everyone my name is SHYJU RAJU. However, it is possible to use Hill Cipher for higher matrices (4×4, 5×5, or 6×6) with The cipher is basically based on matrix multiplication for both encryption and decryption. Then the number detE has an inverse mod 26 and so does the matrix E. 3 4 19 11. pdf), Text File (. For example, in a key matrix of size 2, a 2×2 matrix of integers is created and used to transform pairs of letters into ciphered values. I've currently created a 3x3 matrix in python using numpy (initializing every value to 0). be/wyTfvkDSmwMIf this video is helpful Cipher). Hill created the Hill cipher, which uses matrix manipulation. Plaintext SKY SUN HAT Ciphertext BAA ABA AAB . Hill’s message protector Complexity. Plain Text. Your help is greatly appreciated! python; numpy; matrix; brute-force; Share. Every time inverse of the matrix does not exist. , 2x2, 3x3). Essentially I'm trying to brute for the Crypto Hill Cipher. If neither of the above rules is true: Form a rectangle with the two letters and take the letters on the horizontal opposite corner of the rectangle. Use Mathematica to find 201 mod 29. (E. 26 is the length of your dictionary, which happens to be the length of the English alphabet (A to Z). To begin encryption, a key matrix of a certain size is chosen. Each letter is represented by a number modulo 26. Welcome to my YouTube channel SR COMPUTER EDUCATIONThis video will explain in detail vector in turn by the key matrix; for example, the first message vector becomes Once it has been determined that a matrix Ais invertible modulo 26, it may be used as a key matrix for a Hill substitution cipher. The matrix used in the Hill cipher encryption key must be invertible. The following discussion assumes an elementary knowledge of matrices. Hill Cipher Solved Ex Hill cipher: why can the cipher key matrix’s determinant not share common factors with the modulus? 0 How to find modulo inverse if two number are not relatively prime for Hill cipher? Implementation of Encryption and Decryption using Hill Cipher in C++. Using To design a Hill cipher, we first assign a number to each letter of the alphabet, then add three punctuation marks so that we have a prime number (29) of coded letters. Hill Cipher Key Matrix Property. 2) Introduction to t The Hill cipher is a polygraphic substitution cipher based on linear algebra. 2 of the text (pages 115-116) Hill cipher. Text is divided into blocks of size n, and each block forms a vector of size n. The key ‘K’ is the n x n matrix used for encryption and decryption. 2x2, 3x3, 4x4 and so on). We also turn the plaintext into digraphs (or trigraphs) and each Cryptography - Hill Cipher - In the context of classical cryptography, the Hill Cipher uses a polygraphic substitution cipher, which means homogeneous substitution over many levels of blocks. Hill in 1929. On the other hand, hill cipher could be adapted into the Hill Cipher 3×3 example. The C program is successfully compiled and run In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. Steps: To turn the keyword into a matrix, if the keyword was longer than the 4 letters Progressive Matrix with 3x3 grids that have dark blue and light blue cells Story identification - alcoholic android Why do two electrons having the same spin and position not violate Pauli's principle unless they are in orthogonal orbitals? Get access to the latest Hill cipher - Example of 3x3 matrices - Decryption part. This is the major shortcoming of Hill cipher since every key matrix is not invertible. https://youtu. Do you have any idea of phrases that may have been enciphered in that example? A restriction to only letters, say modulo 26, would mean that 2. The implementation is done purely in Python, without relying on external libraries for matrix Implementation of the hill cipher in python using numpy and sympy. At this point, the adjoined identity matrix has become the inverse of the original matrix. M(M-1) = I: [1] Cryptography and Network Security By William 👉 In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester Hill in 1929, this cipher uses matrices and matrix multiplication to mix up the plaintext. 2) Introduction to t Steps to Encrypt with Hill Cipher Key Matrix Generation. The document provides a step-by-step example of encrypting the phrase 'pay more money' using the Hill cipher with a specified 3x3 key matrix. For example, 25 mod 29 = 25, 30 mod 29=1, 183 mod 29 = 9 and -1 mod 29 = 28. It also covers topics such as matrix addition, subtraction, multiplication, scalar multiplication, transposes, determinants, and calculating determinants for mainhillcipher. Here the key phrase is given as Hill Cipher is easily solvable when dealing with 2×2 matrices. Explanation: The Hill Cipher uses a 3×3 key matrix to encrypt a 3-letter message. ⇒ Generate a vector of 2x1 matrices with numeric codes of plain text characters. Suppose Key ‘K’ is a 2 x 2 matrix then For example, 3 7 8 18 59 68 5 12 5 2 100 114 Therefore, a matrix can be a key for a Hill cipher, only if the determinant of the matrix is one of 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, or 25 modulo 26. Each letter is converted to a numerical value (A=0, B=1, , Z=25), and the matrix multiplication of the key matrix and message vector generates the The general formula for Encrypting text using the Hill Cipher Algorithm is K × P mod 26. Increasing the size of key matrix makes the cipher much For example, encrypting when the phrase another type the digraphs are an ot he rt yp e_, and the common digraph th is split between blocks. cpp: this is to write the algorithm of encrypting text using hill cipher decrypt. When it asks for the code, give it the entire ciphertext. Decryption Of course, we Hill Cipher: Uses a matrix key, size depending on the block size (e. Playfair Cipher: Employs a keyword to construct a 5x5 matrix for encryption and decryption processes. Voila! Science Olympiad Code Busters - Hill Cipher (4/6)Encoding with a 3x3 matrix The document discusses the Hill cipher encryption technique for encrypting plaintext using a 2x2 matrix key. The first step is to create a matrix using the keyword (since the keyword is shorter than 9 letters, just start the alphabet HILL CIPHER EXAMPLE - Free download as Word Doc (. To get cipher text, the matrix key is multiplied by the matrix formed The key of a Hill Cipher is a 3x3 matrix K. In Hill cipher, a Network Security: Hill Cipher (Encryption)Topics discussed:1) Classical encryption techniques: Substitution and Transposition techniques. You switched accounts on another tab or window. docx - Free download as Word Doc (. Make up a new 3x3 encryption matrix M. To decrypt message: Th Basic Hill Cipher decryptor I wrote for Ghost in the Shellcode 2015. For example, the pair "NU" would be associated with the vector $\begin{pmatrix}13\\20\end{pmatrix}$. Where K is our n ×n Matrix that serves as the Key. This technique encrypt plaintext in matrix form of 2x2 or 3x3. Improve this question. The standard solution is to use Padding or some other agreed-upon mechanism to encode variable-length messages as a multiple of the blocksize. decrpytion We will now decrypt the ciphertext "SYICHOLER" using the keyword "alphabet" and a 3x3 matrix. When the ciphertext is received, it is unreadable without the Just look up 'Gauss Jordan Matrix Inverse' - but to summarise, you simply adjoin a copy of the identity matrix to the right of the matrix to be inverted, then use row operations to reduce your matrix to be solved until it itself is an identity matrix. In the data file a8. Steps ===== ⇒ Generate a cipher key 2x2 matrix by replacing characters with numerical values. Luckily, we can handle this with python and numpy easily for today. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption. 4 Decrypting Hill's Cipher Objectives. Decryption Of course, we Key features of Hill Cipher: The key matrix used in Hill Cipher must be invertible, meaning it has a non-zero determinant and its inverse exists. Hill Cipher 3×3 example. For example: This is a standard problem in modern cryptography (eg for CBC-mode). In order to perform encryption using Hill Cipher, one should have an idea about certain mathematical concepts, precisely from Linear Algebra. The numbers in this matrix must be the inverse of the encryption key matrix, and there are various methods to work this out (see this link). Exercise 1. prepared with GATE - Iconic Pro course curated by Ansha P on Unacademy to prepare for the toughest competitive exam. The hill_cipher function accepts a message and a key as input, creates the key matrix, also encrypts the message with the key matrix, and prints the output as ciphertext. Encryption with the Hill Cipher The original cipher used the letters A to Z with p = 26. Patented mechanism works on 6×6 sized keys. 37 5 12 Relying heavily on linear algebra, Hill Cipher depend on a key matrix and involve basic and fundamental principles in order to encrypt messages. Today, we call this Hill’s Cipher Machine. For this example we will use a 3x3 matrix. $\begingroup$ No you can't solve this problem with a single known plaintext-ciphertext pair (where plaintext and ciphertext are 3 characters): that's $3\cdot\log_2(26)$ bits worth of information, when the matrix holds nearly $9\cdot\log_2(26)$ bits of information (not quite, because it is known invertible; but close). You signed out in another tab or window. They are multiplied then, against modulo 26. A Hill key is a matrix of order n x n. The matrix used for encryption is the cipher key, and it should be chosen 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). In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Hill cipher has the advantage of high diffusion and Hill Cipher || With 3x3 Matrix Multiplicative Inverse Example in Mod 26 This is My First Video Lecture, (*Sorry for Audio Quality & Little Disturbance) Note: Watch this video in 1. Review some matrix material; Ciphertext only attack on Hill's Cipher; Known plaintext attack on Hill's Cipher; Recall that when we encipher a message using Hill's Cipher we use either the equation: \begin{equation*} \mathtt{Cipher}\equiv m\cdot Message\ \text{or}\ \mathtt{Cipher}\equiv m\cdot Message+s. Show transcribed image text. Often the simple scheme A = 0, B = 1, , Z = 25 is used, but this is not an essential feature of The Question Text doesn't indicate that the text should be encoded. The same algorithm as presented in Section 2. It explains how to convert plaintext letters to numbers, arrange them in a matrix based on the key size, and use matrix multiplication to encrypt the plaintext matrix with the key matrix modulo 26 to get the ciphertext matrix. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. . Asking for help, clarification, or responding to other answers. o Depending on how big our key is, we can encrypt that much of data using the Hill Cipher. It was invented by Lester S. mat posted on Canvas you will find five plaintexts x1,x2,x3,x4,x5 as well as five ciphertexts y1,y2,y3,y4,y5. For example, a 2×2 key matrix will encrypt and decrypt pairs of letters. Ø For example: PLAINTEXT message: ATTACK, KEY:CDDG. Provide details and share your research! But avoid . They think the first three words of the Step-2: Find the inverse of given key matrix (2x2 or 3x3), Step-3: Make a group of Cipher text as per given key matrix size. Example: The matrix $ M $ is a 2x2 matrix, DCODE, split in 2-grams, becomes DC,OD,EZ (Z letter has been added to complete the last bigram) Substitute the letters of the plain message by a value: their rank in the alphabet Compute the code matrix A and translate to the coded message. It defines what a matrix is and provides examples of different types of matrices including symmetric, diagonal, upper triangular, lower triangular, zero, and identity matrices. Encryption First, we need to turn the keyword into a matrix. Write a C/JAVA program to perform encryption and decryption using Hill Cipher. The 'key' should be input as 4 numbers, e. A change of one Encryption is like using a multiplicative cipher except that multiplying by a matrix allows us to encipher more than one letter at a time. ⇒ Multiply the key mtx. If it's supposed to be nonsingular, none of the examples appear to be valid. We must first turn our keyword into a key matrix ( a $ \ 2 \times 2$ matrix for working with digraphs, a $ 3 \times 3$ matrix for working with trigraphs, etc) Plain text = “short example” Keyword = “hill” and a $2 \times 2$ matrix. For example, if a 3x3 matrix is normally used, but there is only one or two characters left, a 2x2 or 1x1 matrix could be used to handle the remaining The Hill Cipher is a polygraphic substitution cipher that uses linear algebra, particularly matrix multiplication, to encrypt and decrypt messages. To encrypt message: The key string and message string are represented as matrix form. for example, the alphabet in the above calculator includes space, comma, and dot symbols) are encoded with digits, for example, symbol's order number in the set. , or cipher. Plaintext The document discusses matrix and Hill cipher. Homework Statement I've created code to crack a Hill Cipher (n=3). Hill Cipher encrypts a group of letters called a polygraph. Inverse Consider Hill Cipher with block length b=3. DECRYPTION: Steps: 1) Find inverse of random chosen key matrix. with each 2x1 matrix in plain text matrix vector & mod the Online Hill password encryption and decryption tool, providing 2x2 matrix Hill password conversion verification. 2 Modulus For this example, we are modding the matrix by 26 since we will be using the The Hill cipher was the first cipher purely based on mathematics (linear algebra). In the Hill password, each letter is treated as a 26 The Hill cipher utilizes a numerical substitution where each character (A-Z) is assigned a numerical value from 0-25. Encrypting 'pay' using the Hill cipher with the given key matrix results in 'HUX'. cpp: this file contains 'main' function encrypt. Exercise 6. 5x if Hill Cipher. To encipher or In the context of the Hill Cipher, a matrix represents the encryption key, and each letter of the plaintext is represented as a vector. The most common padding is PKCS#7 padding: If one byte is left, append 0x01, if two are left append 0x02 0x02 and so on. An example of this can be the code itself written in ciphertext. - nBoyd-98/HillCipher Hill Cipher is a polygraphic substitution cipher based on linear algebra invented by Lester S. Any size matrix can be used, as long as it results in a box (for example, 2x2 or 3x3). It then provides examples of encrypting and decrypting Section 6. This increases key space to 26 36. (all operations are mod 26) Given the following plaintext-ciphertext pairs, compute the key matrix K. maqsfu lletkz uypsj ddmpk aqjf lngc hmwq hrpda codk cmpghl ehwdw aymm nftyk rtzesip yxxf