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CryptographyCryptography andand Chapter 2 – Classical Encryption NetworkNetwork SecuritySecurity Techniques ChapterChapter 22 • "I am fairly familiar with all the forms of secret writings, and am myself the author of a trifling monograph upon the subject, in which I analyze Fifth Edition one hundred and sixty separate ciphers," said by William Stallings Holmes. Lecture slides by Lawrie Brown —The Adventure of the Dancing Men , Sir Arthur (with edits by RHB) Conan Doyle Outline Symmetric Encryption • We will consider: • or conventional / private -key / single -key – classical cipher techniques and terminology • sender and recipient share a common key – monoalphabetic substitution ciphers • all classical encryption algorithms are – cryptanalysis using letter frequencies private -key – Playfair cipher – polyalphabetic ciphers • was only type prior to invention of public - – transposition ciphers key in 1970 ’s – product ciphers and rotor machines • and by far most widely used – steganography Some Basic Terminology Symmetric Cipher Model • plaintext - original message • ciphertext - 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 ) - study of principles/ methods of deciphering ciphertext without knowing key • cryptology - field of both cryptography and cryptanalysis Requirements • two requirements for secure use of symmetric encryption: – a strong encryption algorithm – a secret key known only to sender / receiver • mathematically have: Y = E(K,X) X = D(K,Y) • assume encryption algorithm is known • implies a secure channel to distribute key Cryptography Cryptanalysis • can characterize cryptographic system by: • objective to recover key not just message – type of encryption operations used – type of encryption operations used • general approaches: • substitution • transposition – cryptanalytic attack • product – brute -force attack – number of keys used • if either succeed all key use compromised • single -key or private • two -key or public – way in which plaintext is processed • block • stream Cryptanalytic Attacks More Definitions • ciphertext only • unconditional security – only know algorithm & ciphertext , is statistical, must – no matter how much computer power or time is know or be able to identify plaintext available, the cipher cannot be broken … since the • known plaintext ciphertext provides insufficient information to – attacker knows/suspects plaintext & ciphertext uniquely determine the corresponding plaintext • chosen plaintext • computational security – attacker selects plaintext and gets ciphertext • given limited computing resources ( eg . time • chosen ciphertext needed for calculations is greater than age of – attacker selects ciphertext and gets plaintext universe (usually defined via polynomial time • chosen text algorithms)), the cipher cannot be broken – attacker selects plaintext or ciphertext to en/decrypt Brute Force Search Classical Substitution Ciphers • always possible to simply try every key • letters of plaintext are replaced by other • most basic attack, proportional to key size letters or by numbers or symbols • assume able to know / recognise plaintext or Number of Time Required at 10 9 Time Required at • plaintext is viewed as a sequence of Key size (bits) Cipher Alternative Keys decryptions/s 10 13 decryptions/s 56 DES 256 ᱌ 7.2 x 10 16 255 ns = 1.125 years 1 hour bits, and substitution involves replacing 128 AES 2128 ᱌ 3.4 x 10 38 2127 ns = 5.3 x 10 21 years 5.3 x 10 17 years 168 Triple DES 2168 ᱌ 3.7 x 10 50 2167 ns = 5.8 x 10 33 years 5.8 x 10 29 years plaintext bit patterns with ciphertext bit 192 AES 2192 ᱌ 6.3 x 10 57 2191 ns = 9.8 x 10 40 years 9.8 x 10 36 years patterns 256 AES 2256 ᱌ 1.2 x 10 77 2255 ns = 1.8 x 10 60 years 1.8 x 10 56 years 26 characters Monoalphabetic 26! = 4 x 10 26 2 ᠯ 10 26 ns = 6.3 x 10 9 years 6.3 x 10 6 years (permutation) Caesar Cipher Caesar Cipher • earliest known substitution cipher • can define transformation as: • by Julius Caesar 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 z D 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 • first attested use in military affairs • mathematically give each letter a number • replaces each letter by 3rd letter along 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 z 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 • example: • then have Caesar cipher as: meet me after the toga party c = E(k,p ) = (p + k) mod 26 PHHW PH DIWHU WKH WRJD SDUWB p = D(k,c ) = (c – k) mod 26 Cryptanalysis of Caesar Cipher • only have 25 possible ciphers … 25 keys – a maps to (A),B...Z (obviously avoid a A) • could simply try each in turn • a brute force search • given ciphertext , just try all shifts of letters • do need to recognize when have plaintext • eg. break ciphertext "GCUA VQ DTGCM " Monoalphabetic Cipher Monoalphabetic Cipher Security • rather than just shifting the alphabet • now have a total of 26! = 4 x 10 26 keys • could shuffle (jumble) the letters arbitrarily • with so many keys, might think is secure • each plaintext letter maps to a different random ciphertext letter • but would be !!!WRONG!!! • hence key is 26 letters long • problem is language characteristics Plain: abcdefghijklmnopqrstuvwxyz Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN Plaintext: ifwewishtoreplaceletters Ciphertext : WIRFRWAJUHYFTSDVFSFUUFYA Language Redundancy and English Letter Frequencies Cryptanalysis • human languages are redundant • eg " th lrd s m shphrd shll nt wnt " • letters are not equally commonly used • in English E is by far the most common letter – followed by T,R,N,I,O,A,S • other letters like Z,J,K,Q,X are fairly rare • have tables of single, double and triple letter frequencies for various languages Use in Cryptanalysis Example Cryptanalysis • key concept - monoalphabetic substitution • given ciphertext : ciphers do not change relative letter frequencies UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ • discovered by Arabian scientists in 9 th century VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ • calculate letter frequencies for ciphertext • count relative letter frequencies (see text) • compare counts/plots against known values • guess P and Z are e and t • if caesar cipher look for common peaks/troughs • guess ZW is th and hence ZWP is the – peaks at: A-E-I triple, NO pair, RST triple • proceeding with trial and error finally get: – troughs at: JK , X-Z it was disclosed yesterday that several informal but direct contacts have been made with political • for monoalphabetic must identify each letter representatives of the viet cong in moscow – tables of common double/triple letters help Playfair Cipher Playfair Key Matrix • not even the large number of keys in a • a 5X5 matrix of letters based on a keyword monoalphabetic cipher provides security • fill in letters of keyword (no duplicates) • one approach to improving security was to • fill rest of matrix with other letters encrypt multiple letters • eg. using the keyword MONARCHY • the Playfair Cipher is an example • invented by Charles Wheatstone in 1854, M O N A R C H Y B D but named after his friend Baron Playfair E F G I/J K L P Q S T U V W X Z Encrypting and Decrypting Security of Playfair Cipher • plaintext is encrypted two letters at a time • security much improved over monoalphabetic 1. if a pair is a repeated letter, insert filler like ''X’ • since have 26 x 26 = 676 digrams 2. if both letters fall in the same row, replace • would need a 676 entry frequency table to each with letter to right (wrapping back to start analyse (verses 26 for a monoalphabetic ) from end) from end) • and correspondingly more ciphertext 3. if both letters fall in the same column, replace each with the letter below it (wrapping to top • was widely used for many years from bottom) – eg. by US & British military in WW1 4. otherwise each letter is replaced by the letter • it can be broken, given a few hundred letters in the same row and in the column of the other • since still has much of plaintext structure letter of the pair Polyalphabetic Ciphers Vigen ère Cipher • polyalphabetic substitution ciphers • simplest polyalphabetic substitution cipher • improve security using multiple cipher alphabets • effectively multiple caesar ciphers • make cryptanalysis harder with more alphabets • key is many letters long K = k k ... k to guess and flatter frequency distribution 1 2 d • ith letter specifies ith alphabet to use • use a key to select which alphabet is used for each letter of the message • use each alphabet in turn • use each alphabet in turn • repeat from start after d letters in message • repeat from start after end of key is reached • decryption simply works in reverse Example of Vigen ère Cipher Aids to Vigen ère Encryption • write the plaintext out • simple aids can assist with en/decryption • write the keyword repeated above it • a Saint -Cyr Slide is a simple manual aid • use each key letter as a caesar cipher key – a slide with repeated alphabet • encrypt the corresponding plaintext letter – line up plaintext ' A'' withwith keykey letter,letter, egeg '' C'' deceptive • eg . using keyword deceptive – then read off any mapping for key letter key: deceptivedeceptivedeceptive • can bend round into a cipher disk plaintext: wearediscoveredsaveyourself • can bend
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  • Traditional Symmetric-Key Ciphers

    Traditional Symmetric-Key Ciphers

    Traditional Symmetric-Key Ciphers A Biswas, IT, BESU Shibpur General idea of symmetric-key cipher The original message from Alice to Bob is called plaintext; the message that is sent through the channel is called the ciphertext. To create the ciphertext from the plaintext, Alice uses an encryption algorithm and a shared secret key. To create the plaintext from ciphertext, Bob uses a decryption algorithm and the same secret key. If P is the plaintext, C is the ciphertext, and K is the key, We assume that Bob creates P1; we prove that P1 = P: Locking and unlocking with the same key Kerckhoff’s Principle Based on Kerckhoff’s principle, one should always assume that the adversary, Eve, knows the encryption/decryption algorithm. The resistance of the cipher to attack must be based only on the secrecy of the key. Cryptanalysis As cryptography is the science and art of creating secret codes, cryptanalysis is the science and art of breaking those codes. Cryptanalysis attacks Ciphertext-Only Attack Ciphertext-only attack Known-Plaintext Attack Known-plaintext attack Chosen-Plaintext Attack Chosen-plaintext attack Chosen-Ciphertext Attack Chosen-ciphertext attack SUBSTITUTION CIPHERS A substitution cipher replaces one symbol with another. Substitution ciphers can be categorized as either monoalphabetic ciphers or polyalphabetic ciphers. Note A substitution cipher replaces one symbol with another. 1 Monoalphabetic Ciphres 2 Polyalphabetic Ciphers Monoalphabetic Ciphers Note In monoalphabetic substitution, the relationship between a symbol in the plaintext to a symbol in the ciphertext is always one-to-one. Example The following shows a plaintext and its corresponding ciphertext.