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Cryptography. Encode the message "WINGARDIUMLEVIOSA" using matrix
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- Show that B=1132 is the inverse of A=2131.arrow_forward9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m - 20 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.arrow_forwardStart with the following matrix: -10 3-8-2 0 10 0 9 6 6 -4-2 Perform the following 3 elementary row operations, one after the other, and give the resulting matrix at each step: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. a) Add -1 times row 3 to row 1 000 000 000 b) Multiply row 3 by 2 000 000 000 c) Interchange rows 1 and 3 000 000 000arrow_forward
- 12. Maria has four-digit PIN(Personal Identification Number). She needs to send the PIN to her mother by email. Maria decides to encode the PIN and uses the process: Maria forms a 2 X 2 Matrix A from the digit of her PIN where: A = |1* digit |3d digit 2nd digit 4h digit She chooses then matrix B 20 6 and calculates AB. 3 6 She performs the encoded message by writing down the four elements of AB and following them with the number of digits of each element. 57|, the encoded message would be 125732942222. She then emailed the 32 94 encoded PIN to her mother. For example: if AB = 12 Find: b. Maria's PIN if the encoded message is 4148189722232 ? NOTE: Use Inverse Matrix Solution to solve this problem.arrow_forwardProblem 3. The generator matrix for a linear error correcting code with message length k and block length n has size nxk.arrow_forward(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the…arrow_forward
- 1. use A-1 to decode the cryptograph A in the picture below. 2. Encode the message "TUESDAY" using the Matrix A in the picture below.arrow_forwardI need help decoding this matrix message using cryptography. (I know Matrix C is not invertible but is their a way to solve it and reveal the message from Matrix D) Matrix C: 5x4[[1,-2,-3,2],[2,-2,0,0],[-2,-1,-9,-6],[-3,1,-6,-4],[1,0,3,2]]Matrix D (Decoded): 5x2[[-21,-62],[18,-16],[-168,-470],[-127,-300],[59,154]]arrow_forwardStart with the following matrix: 8-78 -9-10 9 -8 -3 -7 Perform the following 3 elementary row operations, one after the other, and give the resulting matrix at each step: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. a) Add-2 times row 1 to row 2 000 000 000 b) Multiply row 3 by 5 000 000 000 1 c) Interchange rows 1 and 2 000 000 000arrow_forward
- 1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m × nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 × 3 matrix M by using the cipher and then grouping the numbers into 2 × 1 columns, thus 16 1 5 M = 5 3 27 If we now take a 2 × 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if 4 E = 3 1 the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 26 34 42 The following message was encrypted using the matrix C where: 1 2 3 C = 2 5 3 1 0 8 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this…arrow_forwardCompute the following matrix. -2 -1 -3 -1 -1 -4 -3 -3 3 -1 + 1 2 3 4 5 6 =arrow_forward
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