I need help to finish my introduction to the science and history of secret writing (cryptography)
Homework 4 CSC 233 We talked about modular arithmetic and the shift and affine ciphers, and then entered the Renaissance. We discussed various Renaissance systems including nomenclators, Alberti’s cipher disk, and ideas contained in Trithemius’s Polygraphia, in particular the influential tabula recta. We saw variants of that due to Porta and Belaso. Next week, we will talk about Cardano, Bacon and the Vigenere cipher (including the kappa test, and counting coincidences) and the move on to the Playfair system. Handing it in: Submit to the d2l submission folder. Use some standard format for your homework (Word or pdf, for example). If necessary you can include handwritten answers as pictures, but please make sure the writing is legible (pencils often do not show up well in pictures). The vast majority of your assignment should be typed. Please include all work in a single file (don’t use zip). The class information folder contains a sample homework submission (hwexample.docx or hwexample.pdf). Note how I cropped and resized the image to make it more readable. 1. (Reading Assignment) Read Section 2.12 (1st edition) or 1.16 (2nd edition) on the affine cipher, and Sections 3.1 and 3.2 (1st edition), or 2.1 and 2.2 (2nd edition) covering Alberti, Thrithemius, and Porta (and Vigenere, who we will talk about next). If you want to look ahead, check out Bacon’s Biliteral Cipher (5.1 in the 1st edition, 4.1 in the 2nd edition). Make sure every explanation you give as part of your solution is detailed and clear enough to be used to teach someone who is learning the method demonstrated in your solution. Any solutions whose explanation does not meet this standard will lose points. 2. (Affine Cipher, 10pt) You have intercepted the ciphertext “UVHTG” encrypted using an affine cipher. You bribed the right person, and found out that the encryption key was (a,b) = (7,17). a) [2pt] What is the inverse of 7 modulo 26? (You can do trial/error, try all possibilities, or write a loop, like we did in class). Explain how you found it. b) [4pt] What is the decryption key corresponding to encryption key (7,17)? Hint: you can use the formula we saw, or derive it the same way we did, but show your work. c) [4pt] With the decryption key from b) decrypt the ciphertext. Do this by hand and show your work (including the numerical values of each letter: a = 0, b = 1, etc.). 3. (Alberti/NSA Cipher disk, 12pt) For this problem, we are working with the NSA toy version of Alberti’s cipher disk we saw in class; it’s pictured below, but for doing the problem, you can download the higher-quality version from d2l. a) [5pt] You’ve intercepted the text zMLYdZYGbXYH which you suspect to has been encrypted with the cipher disk above (and using the index letter K on the inner disk). Decrypt. Explain how you found your solution in detail. b) [7pt] You have intercepted the ciphertext “CJTSFEDCTY” again encrypted with our modernized Alberti disk. You do not know the key letter that was used for this piece of text (but apparently it didn’t change through this piece of text). Decrypt and determine the key letter used (the letter aligned with the index letter K). Describe how you found the solution in detail. 4. (Tabula Recta 10pt) IMPORTANT! Both of the plaintext words in parts a) and b) of this problemare fairly obscure English words, but both are found in the scrabble dictionary. To test if a word is in the scrabble dictionary, go to https://scrabble.merriam.com/ and enter the word in the search bar at the top of the page. a) [5pt] You have intercepted part of a ciphertext which was encrypted using the standard tabula recta on d2l using it as a progressive cipher, that is, switching to the next row/alphabet after each step). You observed the ciphertext “CQQQPF” Since you don’t know where the ciphertext started you can’t be sure that the first letter was encoded with the A alphabet. Decode the message nevertheless. (You can try all 26 possibilities, or you can try some likely candidates first.) Include a description of how you found the solution. b) [5pt] You’ve found another ciphertext encrypted using the standard tabula recta: “NNNDE” Again you don’t know with which alphabet of the tabula recta the encryption started. Find the plaintext. Include a description of how you found the solution. 5. (Belaso’s Cipher, 7pt) You see the ciphertext “CYLPNXG”, and you know it’s a place-name encrypted using Belaso’s cipher. Your (lucky) guess is that the keyword used was “gio”. Find the plaintext. Note: The substitution alphabets you need are should be on or near slide 27 (entitled “Giovan Batista Belaso”) of the Week 4 Slideshow posted on our D2L. Please note that some letters are missing in the substitution alphabets! In particular, V, W, J and K are missing. When decrypting, if you get a U the actualy plaintext letter might letter may be either U, V or W. Similarly, if you get a I in your decryption the actual that plaintext letter may be either I, J or K. Explain how you found your solution.
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