Now we must perform some matrix multiplication. According to definition in wikipedia, in classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. The final relationship between the key matrix and the inverse key matrix. So the multiplicative inverse of the determinant modulo 26 is 7. A ciphertext is a formatted text which is not understood by anyone. 2 x 2 Matrix Decryption In our case we perform the two calculations on the right. To decode the message, one would have to multiply the ciphertext with the inverse matrix of the key and apply modulo 26 to the result. Hill Cipher is a cryptographic algorithm to encrypt and decrypt an alphabetic text. Encryption – Plain text to Cipher text. Don’t stop learning now. Often the simple scheme A = 0, B = 1, …, Z = 25 is used, but this is not an essential feature of the cipher. close, link Hill cipher is a polygraphic substitution cipher based on linear algebra.Each letter is represented by a number modulo 26. So, A = 0, B = 1, C= 2, D = 3, etc. Please use ide.geeksforgeeks.org, generate link and share the link here. We then add together these three answers. Then we convert them back into letters to produce the ciphertext. Reference: https://en.wikipedia.org/wiki/Hill_cipher. The Hill cipher was the first cipher purely based on mathematics (linear algebra). We use cookies to ensure you have the best browsing experience on our website. We then follow the same process as for the 2 x 2 Matrix Example. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. and similarly for the bottom row. Calculating the adjugate matrix of the key matrix. To get the inverse key matrix, we now multiply the inverse determinant (that was 19 in our case) from step 1 by each of the elements of the adjugate matrix from step 2. For our example we get the matrix below. We get back our plaintext of "short example". Finding an inverse is somewhat more complicated (especially for a 3 x 3 matrix), and the activity below allows you to practice working these out. 3 x 3 Matrix Encryption In this cipher, each letter is represented by a number (eg. If d is the determinant, then we are looking for the inverse of d. The multiplicative inverse is the number we multiply 15 by to get 1 modulo 26. 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. Algebraic representation of matrix multiplication for a 3 x 3 matrix. Then we take each of these answers modulo 26. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. For the 2 x 2 version, looking for repeated digraphs would be the first step, and matching the most common ciphertext digraph to the most common digraph in English ("th") and then the second to the second most common in English ("he") would allow the interceptor to put together a possible key matrix acting on those four letters. The way we "combine" the six numbers to get a single number is that we multiply the first element of the key matrix row by the top element of the column vector, multiply the second element of the key matrix row by the middle element of the column vector, and multiply the third element of the key matrix row by the bottom element of the column vector. Then we move to the next column vector, where the third plaintext letter goes at the top, and the fourth at the bottom. We then right these two answers out in a column vector as shown below. We then "combine" the middle row of the key matrix with the column vector to get the middle element of the resulting column vector. To perform matrix multiplication we "combine" the top row of the key matrix with the column vector to get the top element of the resulting column vector.

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