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Cryptography Classical Ciphers Caesar Cipher Monoalphabetic Ciphers Playfair Cipher Classical Ciphers Polyalphabetic Ciphers Vigen`ereCipher Cryptography Vernam Cipher One Time Pad School of Engineering and Technology Transposition CQUniversity Australia Techniques Prepared by Steven Gordon on 19 Feb 2020, classical.tex, r1789 1/64 Cryptography Contents Classical Ciphers Caesar Cipher Caesar Cipher Monoalphabetic Ciphers Playfair Cipher Monoalphabetic Ciphers Polyalphabetic Ciphers Playfair Cipher Vigen`ereCipher Vernam Cipher Polyalphabetic Ciphers One Time Pad Transposition Techniques Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 2/64 Cryptography Caesar Cipher (algorithm) Classical Ciphers To encrypt with a key k, shift each letter of the plaintext k Caesar Cipher positions to the right in the alphabet, wrapping back to the Monoalphabetic Ciphers start of the alphabet if necessary. To decrypt, shift each Playfair Cipher letter of the ciphertext k positions to the left (wrapping if Polyalphabetic Ciphers necessary). Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 3/64 Cryptography Caesar Cipher Encryption (exercise) Classical Ciphers Using the Caesar cipher, encrypt plaintext hello with key 3. Caesar Cipher Monoalphabetic Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 4/64 Cryptography How many keys are possible in the Caesar Classical Ciphers cipher? (question) Caesar Cipher Monoalphabetic If the Caesar cipher is operating on the characters a{z, then Ciphers how many possible keys are there? Is a key of 0 possible? Is Playfair Cipher it a good choice? What about a key of 26? Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 5/64 Cryptography Caesar Cipher Decryption (exercise) Classical Ciphers You have received the ciphertext TBBQOLR. You know the Caesar Cipher Caesar cipher was used with key n. Find the plaintext. Monoalphabetic Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 6/64 Cryptography Caesar Cipher, formal (algorithm) Classical Ciphers Caesar Cipher C = E(K; P) = (P + K) mod 26 (1) Monoalphabetic Ciphers P = D(K; C) = (C − K) mod 26 (2) Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 7/64 Cryptography Caesar Cipher, formal (exercise) Classical Ciphers Consider the following mapping. Caesar Cipher abcdefghijklm Monoalphabetic Ciphers 0 1 2 3 4 5 6 7 8 9 10 11 12 Playfair Cipher nopqrstuvwxyz Polyalphabetic Ciphers 13 14 15 16 17 18 19 20 21 22 23 24 25 Vigen`ereCipher Use the the formal (mathematical) algorithm for Caesar Vernam Cipher cipher to decrypt SDV with key p. One Time Pad Transposition Techniques 8/64 Cryptography Caesar Encrypt and Decrypt (python) Classical Ciphers Caesar Cipher 1 >>> pycipher.Caesar(3).encipher("hello") 2 Monoalphabetic 'KHOOR' Ciphers 3 >>> pycipher.Caesar(3).decipher("khoor") Playfair Cipher 4 'HELLO' Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 9/64 Cryptography Brute Force Attack (definition) Classical Ciphers Try all combinations (of keys) until the correct plaintext/key Caesar Cipher is found. Monoalphabetic Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 10/64 Cryptography Caesar Brute Force (exercise) Classical Ciphers The ciphertext FRUURJVBCANNC was obtained using the Caesar Cipher Caesar cipher. Find the plaintext using a brute force attack. Monoalphabetic Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 11/64 Cryptography Caesar Brute Force (python) Classical Ciphers Caesar Cipher 1 for k in range(0,26): 2 Monoalphabetic pycipher.Caesar(k).decipher("FRUURJVBCANNC") Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 12/64 Cryptography Caesar Brute Force Results (text) Classical Ciphers Caesar Cipher 0: FRUURJVBCANNC 13: SEHHEWIOPNAAP Monoalphabetic 1: EQTTQIUABZMMB 14: RDGGDVHNOMZZO Ciphers 2: DPSSPHTZAYLLA 15: QCFFCUGMNLYYN Playfair Cipher 3: CORROGSYZXKKZ 16: PBEEBTFLMKXXM Polyalphabetic 4: BNQQNFRXYWJJY 17: OADDASEKLJWWL Ciphers 5: AMPPMEQWXVIIX 18: NZCCZRDJKIVVK Vigen`ereCipher 6: ZLOOLDPVWUHHW 19: MYBBYQCIJHUUJ Vernam Cipher 7: YKNNKCOUVTGGV 20: LXAAXPBHIGTTI 8: XJMMJBNTUSFFU 21: KWZZWOAGHFSSH One Time Pad 9: WILLIAMSTREET 22: JVYYVNZFGERRG Transposition Techniques 10: VHKKHZLRSQDDS 23: IUXXUMYEFDQQF 11: UGJJGYKQRPCCR 24: HTWWTLXDECPPE 12: TFIIFXJPQOBBQ 25: GSVVSKWCDBOOD 13/64 Cryptography How many attempts for Caesar brute force? Classical Ciphers (question) Caesar Cipher Monoalphabetic What is the worst, best and average case of number of Ciphers attempts to brute force ciphertext obtained using the Caesar Playfair Cipher cipher? Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 14/64 Cryptography Recognisable Plaintext upon Decryption Classical Ciphers (assumption) Caesar Cipher Monoalphabetic The decrypter will be able to recognise that the plaintext is Ciphers correct (and therefore the key is correct). Decrypting Playfair Cipher ciphertext using the incorrect key will not produce the Polyalphabetic Ciphers original plaintext. The decrypter will be able to recognise Vigen`ereCipher that the key is wrong, i.e. the decryption will produce Vernam Cipher unrecognisable output. One Time Pad Transposition Techniques 15/64 Cryptography Is plaintext always recognisable? (question) Classical Ciphers Caesar cipher is using recognisably correct plaintext, i.e. Caesar Cipher English words. But is the correct plaintext always Monoalphabetic Ciphers recognisable? What if the plaintext was a different Playfair Cipher language? Or compressed? Or it was an image or video? Or Polyalphabetic Ciphers binary file, e.g. .exe? Or a set of characters chosen Vigen`ereCipher randomly, e.g. a key or password? Vernam Cipher One Time Pad Transposition Techniques 16/64 Cryptography How to improve upon the Caesar cipher? Classical Ciphers Caesar Cipher 1. Increase the key space so brute force is harder Monoalphabetic Ciphers 2. Change the plaintext (e.g. compress it) so harder to Playfair Cipher recognise structure Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 17/64 Cryptography Contents Classical Ciphers Caesar Cipher Caesar Cipher Monoalphabetic Ciphers Playfair Cipher Monoalphabetic Ciphers Polyalphabetic Ciphers Playfair Cipher Vigen`ereCipher Vernam Cipher Polyalphabetic Ciphers One Time Pad Transposition Techniques Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 18/64 Cryptography Permutation (definition) Classical Ciphers A permutation of a finite set of elements is an ordered Caesar Cipher sequence of all the elements of S, with each element Monoalphabetic Ciphers appearing exactly once. In general, there are n! Playfair Cipher permutations of a set with n elements. Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 19/64 Cryptography Permutation (example) Classical Ciphers Consider the set S = fa; b; cg. There are six permutations Caesar Cipher of S: Monoalphabetic Ciphers abc, acb, bac, bca, cab, cba Playfair Cipher This set has 3 elements. There are 3! = 3 × 2 × 1 = 6 Polyalphabetic Ciphers permutations. Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 20/64 Cryptography Monoalphabetic (Substitution) Cipher Classical Ciphers (definition) Caesar Cipher Monoalphabetic Given the set of possible plaintext letters (e.g. English Ciphers alphabetc, a{z), a single permutation is chosen and used to Playfair Cipher determine the corresponding ciphertext letter. Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 21/64 Cryptography Monoalphabetic (Substitution) Cipher (example) Classical Ciphers In advance, the sender and receiver agree upon a Caesar Cipher permutation to use, e.g.: Monoalphabetic Ciphers P:abcdefghijklmnopqrstuvw Playfair Cipher x y z Polyalphabetic Ciphers C:HPWNSKLEVAYCXOFGTBQRUID Vigen`ereCipher JZM Vernam Cipher To encrypt the plaintext hello, the agreed upon One Time Pad permutation (or mapping) is used to produce the ciphertext Transposition ESCCF. Techniques 22/64 Cryptography Decrypt Monoalphabetic Cipher (exercise) Classical Ciphers Decrypt the ciphertext QSWBSR using the permutation Caesar Cipher chosen in the previous example. Monoalphabetic Ciphers Playfair Cipher Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 23/64 Cryptography How many keys in English monoalphabetic Classical Ciphers cipher? (question) Caesar Cipher Monoalphabetic How many possible keys are there for a monoalphabetic Ciphers cipher that uses the English lowercase letters? What is the Playfair Cipher length of an actual key? Polyalphabetic Ciphers Vigen`ereCipher Vernam Cipher One Time Pad Transposition Techniques 24/64 Cryptography Brute Force on Monoalphabetic Cipher (exercise) Classical Ciphers You have intercepted a ciphertext message that was Caesar Cipher obtained with an English monoalphabetic cipher. You have a Monoalphabetic Ciphers Python function called: Playfair Cipher mono decrypt and check(ciphertext,key) Polyalphabetic Ciphers that decrypts the ciphertext with a key, and returns the Vigen`ereCipher plaintext if it is correct,
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