# Step 0: Encryption Obtain an English plaintext message of 50,000

#### Step 0: Encryption

Obtain an English plaintext message of 50,000 plaintext characters, where the characters consist only of lowercase a through z (i.e., remove all punctuation, special characters, and spaces, and convert all upper case to lower case). Set a key yourself and encrypt this plaintext using a simple substitution cipher.

#### Step 1: Generate a digraph frequency matrix A for English text

Use an English text with 1,000,000 characters (only 26 letters in lowercases) to compute a digraph frequency matrix A, where aij is the count of the number of times that letter i is followed by letter j. Here, we assume that a is letter 0, b is letter 1, c is letter 2, and so on. Next, add five to each element in your 26×26 matrix A. Finally, normalize your matrix A by dividing each element by its row sum. The resulting matrix A will be row stochastic, and it will not contain any 0 probabilities.

#### Step 2: Train an HMM with M = N = 26

Using the first 1000 characters of ciphertext you generated in step 0 as O to train an HMM, where the A matrix is initialized with your A matrix from step 1. That is, in your HMM, do not re-estimate A. For B & pi, randomly initialize them so each element is about 1/26 (recall they also need to be row stochastic! and do NOT make all elements the same). Train using 200 iterations of the Baum-Welch re-estimation algorithm.

#### Step 3: Analyze Result

Use the final B matrix you get from step 2 to determine a putative key and give the fraction of putative key elements that match the actual key (as a decimal, to four places). For example, if 22 of the 26 key positions are correct, then your answer would be 22/26 = 0.8462. If the accuracy is low (<80%), you can do several tries.

separate files:

• Your source code (in any language you like)
• A report in .doc or .pdf that includes screenshot(s) of the result, and your analysis. The format doesn’t matter, just make sure the screenshots are clear and easy to read.

Pages (275 words)
Standard price: \$0.00

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