Classical Techniques: Substitution Substitute a character, digit or symbol for each
Transcription
Classical Techniques: Substitution Substitute a character, digit or symbol for each
Classical Techniques: Substitution Substitute a character, digit or symbol for each character in the plaintext Discussed: The Caesar cipher Monoalphabetic cipher Playfair cipher Polyalphabetic cipher 1 Caesar Cipher 2000 years ago, by Julius Caesar A simple substitution cipher, known as Caesar cipher Replace each letter with the letter standing 3 places further down the alphabet Plain: meet me after the toga party Cipher: PHHW PH DIWHU WKH WRJD SDUWB No key, just one mapping (translation) 0123456... Plain: abcdefghijklmnopqrstuvwxyz Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC 3456789... ci=E(3,pi)=(pi+3) mod 26; pi=D(3,ci)=(ci-3) mod 26 2 Generalized Caesar Cipher Can use any shift from 1 to 25, i.e., replace each letter by a letter a fixed distance away ci=E(k,pi)=(pi+k) mod 26; pi=D(k,ci)=(ci-k) mod 26 Shift cipher Key = k Key letter: the letter a plaintext A maps to e.g. a key letter of F means A maps to F, B to G, …, Y to D, Z to E Hence have 26 (25 useful) ciphers Key space = 26 3 Brute-Force Cryptanalysis of Caesar Cipher Ciphertext only attack Charateristics for success 1. The encryption and decryption algorithms are known 2. There are only 25 keys to try 3. The language of the plaintext is known and easily recongnizable 4 Monoalphabetic Cipher Increased key space compared to Caesar cipher Alphabet sequence is not required What is the key space? 26! > 4 x 1026 Monoalphabetic ciphers are easier to break because they reflect frequency of alphabet E = 12.75, T = 9.25, R = 8.50, N = 7.75, etc. 5 Relative Frequency of Letters in English Text 6 Substitution Techniques Frequency Statistics of Language In addition to the frequency info of single letters, the frequency info of two-letter (digram) or threeletter (trigram) combinations can be used for the cryptanalysis Most frequent digrams TH, HE, IN, ER, AN, RE, ED, ON, ES, ST, EN, AT, TO, NT, HA, ND, OU, EA, NG, AS, OR, TI, IS, ET, IT, AR, TE, SE, HI, OF Most frequent trigrams THE, ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH, FOR, DTH 7 Playfair Cipher Best-known multiple-letter substitution cipher Digram cipher (digram to digram, i.e., E(pipi+1) = cici+1 through keyword-based 5x5 transformation table) Keyword = monarchy M O N A R C H Y B D E F G I/J K L P Q S T U V W X Z Plaintext: H S E A A R M U Ciphertext: B P I M R M C M Great advance over simple monoalphabetic cipher (26 letters 26x26=676 digrams) Can be generalized to polygram cipher 8 Playfair Cipher - Rules Repeating plaintext letters are separated with a filler letter, such as X. Plaintext letters that fall in the same row of the matrix are each replaced by the letter to the right, with the first element of the row circularly following the last. Plaintext letters that fall in the same column are each replaced by the letter beneath, with the top element of the row circularly following the last. Otherwise, each plaintext letter is replaced by the letter that lies in its own row and the column occupied by the other plaintext letter. 9 Polyalphabetic Cipher Typically a set of monoalphabetic substitution rules is used Key determines which rule to use 10 Vigenère cipher Best-known polyalphabetic ciphers Each key letter determines one of 26 Caesar (shift) ciphers ci = E(pi) = pi + ki mod(key length) mod 26 Example: Key: Plaintext: Cipheretxt: deceptivedeceptivedeceptive wearediscoveredsaveyourself ZICVTWQNGRZGVTWAVZHCQYGLMGJ Keyword is repeated to make a key as long as the plaintext 11 Vigenère cipher - 2 12 Example: Encryption Decryption 13 Vigenère cipher - 3 Vigenère autokey system: after key is exhausted, use plaintext for running key (to eliminate the periodic nature) Key: Plaintext: Cipheretxt: deceptivewearediscoveredsav wearediscoveredsaveyourself ZICVTWQNGKZEIIGASXSTSLVVWLA 14 Transposition (Permutation) Techniques Hide the message by rearranging the letter order without altering the actual letters used Rail Fence Cipher Write message on alternate rows, and read off cipher row by row Example: M e m a t r h t g p r y e t e f e t e o a a t MEMATRHTGPRYETEFETEOAAT Block (Columnar) Transposition Ciphers Message is written in rectangle, row by row, but read off column by column; The order of columns read off is the key Example: Key: 4 3 1 2 5 6 7 Plaintext: a t t a c k p o s t p o n e d u n t i l t w o a m x y z Ciphertext:TTNAAPTMTSUOAODWCOIXKNLYPETZ 15