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Compute A² and hence determine A-¹. Demonstrate this cryptography scheme using the secret key A by: Create the plaintext vector p for the message sus Encrypt the plaintext vector to form the ciphertext vector e Decrypt the ciphertext vector to obtain the vector d'and validate that d = p

Compute A² and hence determine A-¹. Demonstrate this cryptography scheme using the secret key A by: Create the plaintext vector p for the message sus Encrypt the plaintext vector to form the ciphertext vector e Decrypt the ciphertext vector to obtain the vector d'and validate that d = p

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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In this question, we will use the following cryptography scheme: 1. An invertible matrix M will be used as the secret key shared between between the Alice and Bob. 2. Alice creates plaintext vector p by assigning each letter in the alphabet a numerical value. In this case, we use a →1,b2,...,2 → 26. For example, the phrase 'red' will translate into p= (1854) 3. The ciphertext vector is creating by encrypting the plaintext vector via c = Mp. 4. The ciphertext vector is sent to Bob via a communication channel. = 5. Upon receiving the ciphertext, Bob decrypts to obtained the decipheredtext d via d = M-¹c. If d = p, then Bob can decode the numerical vector to recover the initial message. For Parts (a), (b), (c), we will use the secret key A = 3 2 0 -4 -3 0 00 -1
Transcribed Image Text:In this question, we will use the following cryptography scheme: 1. An invertible matrix M will be used as the secret key shared between between the Alice and Bob. 2. Alice creates plaintext vector p by assigning each letter in the alphabet a numerical value. In this case, we use a →1,b2,...,2 → 26. For example, the phrase 'red' will translate into p= (1854) 3. The ciphertext vector is creating by encrypting the plaintext vector via c = Mp. 4. The ciphertext vector is sent to Bob via a communication channel. = 5. Upon receiving the ciphertext, Bob decrypts to obtained the decipheredtext d via d = M-¹c. If d = p, then Bob can decode the numerical vector to recover the initial message. For Parts (a), (b), (c), we will use the secret key A = 3 2 0 -4 -3 0 00 -1
(a) Compute A² and hence determine A-¹. (b) Demonstrate this cryptography scheme using the secret key A by: • Create the plaintext vector p for the message sus Encrypt the plaintext vector to form the ciphertext vector • Decrypt the ciphertext vector to obtain the vector d and validate that d = p
Transcribed Image Text:(a) Compute A² and hence determine A-¹. (b) Demonstrate this cryptography scheme using the secret key A by: • Create the plaintext vector p for the message sus Encrypt the plaintext vector to form the ciphertext vector • Decrypt the ciphertext vector to obtain the vector d and validate that d = p
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