Chapter 2 – Classical Encryption TechniquesSymmetric EncryptionBasic TerminologySymmetric Cipher ModelRequirementsCryptographyTypes of Cryptanalytic AttacksBrute Force SearchMore DefinitionsTypes of CiphersClassical Substitution CiphersCaesar CipherSlide 13Cryptanalysis of Caesar CipherPolyalphabetic CiphersVigenère CipherExampleSecurity of Vigenère CiphersKasiski MethodAutokey CipherOne-Time PadTransposition CiphersRail Fence cipherProduct CiphersSteganographySummaryChapter 2 – Classical EncryptionTechniques•Symmetric encryption•Secret key encryption•Shared key encryptionSymmetric Encryption•or conventional / secret-key / single-key•sender and recipient share a common key•was the only type of cryptography, prior to invention of public-key in 1970’sBasic Terminology•plaintext - the original message •ciphertext - the coded message •cipher - algorithm for transforming plaintext to ciphertext •key - info used in cipher known only to sender/receiver •encipher (encrypt) - converting plaintext to ciphertext •decipher (decrypt) - recovering ciphertext from plaintext•cryptography - study of encryption principles/methods•cryptanalysis (codebreaking) - the study of principles/ methods of deciphering ciphertext without knowing key•cryptology - the field of both cryptography and cryptanalysisSymmetric Cipher ModelRequirements•Two requirements for secure use of symmetric encryption:–a strong encryption algorithm–a secret key known only to sender / receiverY = EK(X)X = DK(Y)•assume encryption algorithm is known•implies a secure channel to distribute keyCryptography•can be characterized by:–type of encryption operations used•substitution / transposition / product–number of keys used•single-key or secret-key vs two-key or public-key–way in which plaintext is processed•block / streamTypes of Cryptanalytic Attacks•ciphertext only –only know algorithm / ciphertext, statistical, can identify plaintext •known plaintext –know/suspect plaintext & ciphertext to attack cipher •chosen plaintext –select plaintext and obtain ciphertext to attack cipher•chosen ciphertext –select ciphertext and obtain plaintext to attack cipher•chosen text –select either plaintext or ciphertext to en/decrypt to attack cipherBrute Force Search•always possible to simply try every key •most basic attack, proportional to key size •assume either know / recognise plaintextMore Definitions•unconditional security –no matter how much computer power is available, the cipher cannot be broken since the ciphertext provides insufficient information to uniquely determine the corresponding plaintext •computational security –given limited computing resources (e.g., time needed for calculations is greater than age of universe), the cipher cannot be brokenTypes of Ciphers•Substitution ciphers•Permutation (or transposition) ciphers•Product ciphersClassical Substitution Ciphers•where letters of plaintext are replaced by other letters or by numbers or symbols•or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patternsCaesar Cipher•earliest known substitution cipher•by Julius Caesar (?)•first attested use in military affairs•replaces each letter by 3rd letter on•example:meet me after the toga partyPHHW PH DIWHU WKH WRJD SDUWB•What’s the key?Caesar Cipher•can define transformation as:a b c d e f g h i j k l m n o p q r s t u v w x y zD E F G H I J K L M N O P Q R S T U V W X Y Z A B C•mathematically give each letter a numbera b c d e f g h i j k l m0 1 2 3 4 5 6 7 8 9 10 11 12n o p q r s t u v w x y Z13 14 15 16 17 18 19 20 21 22 23 24 25•then have Caesar cipher as:C = E(p) = (p + k) mod (26)p = D(C) = (C – k) mod (26)Cryptanalysis of Caesar Cipher •only have 26 possible ciphers –A maps to A,B,..Z •could simply try each in turn •a brute force search •given ciphertext, just try all shifts of letters•e.g., break ciphertext "GCUA VQ DTGCM"Polyalphabetic Ciphers•another approach to improving security is to use multiple cipher alphabets •called polyalphabetic substitution ciphers •makes cryptanalysis harder with more alphabets to guess and flatter frequency distribution •use a key to select which alphabet is used for each letter of the message •use each alphabet in turn •repeat from start after end of key is reachedVigenère Cipher•simplest polyalphabetic substitution cipher is the Vigenère Cipher •effectively multiple caesar ciphers •key is multiple letters long K = k1 k2 ... kd •ith letter specifies ith alphabet to use •use each alphabet in turn •repeat from start after d letters in message•decryption simply works in reverseExample•write the plaintext out •write the keyword repeated above it•use each key letter as a caesar cipher key •encrypt the corresponding plaintext letter•eg using keyword deceptivekey: deceptivedeceptivedeceptiveplaintext: wearediscoveredsaveyourselfciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJSecurity of Vigenère Ciphers•have multiple ciphertext letters for each plaintext letter•hence letter frequencies are obscured•but not totally lost•start with letter frequencies–see if look monoalphabetic or not•if not, then need to determine the ‘number of alphabets’ in the key string (aka. the period of the key), since then can attach eachKasiski Method•method developed by Babbage / Kasiski •repetitions in ciphertext give clues to period •so find same plaintext an exact period apart •which results in the same ciphertext •e.g., repeated “VTW” in previous example•suggests size of 3 or 9•then attack each monoalphabetic cipher individually using same techniques as beforeAutokey Cipher•ideally want a key as long as the message•Vigenère proposed the autokey cipher •with keyword is prefixed to message as key•knowing keyword can recover the first few letters •use these in turn on the rest of the message•but still have frequency characteristics to attack •e.g., given key ‘deceptive’key: deceptivewearediscoveredsavplaintext: wearediscoveredsaveyourselfciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLAOne-Time Pad•if a truly random key as long as the message is used, the cipher will be secure •called a One-Time Pad•is unbreakable since ciphertext bears no statistical relationship to the plaintext•since for any plaintext & any