PART I Symmetric Ciphers

Transcription

1 PART I Symmetric Ciphers CHAPTER 2 Classical Encryption Techniques Cryptography, Cryptanalysis Caesar cipher, Monoalphabetic ciphers Playfair cipher, Hill cipher Polyalphabetic ciphers One-time Pad 2.3 Transposition Techniques 2.4 Rotor Machines 2.5 Steganography 23/55 KEY POINTS Symmetric encryption is a form of cryptosystem in which encryption and decryption are performed using the same key. It is also known as conventional encryption Symmetric encryption transforms plaintext into ciphertext using a secret key and an encryption algorithm. Using the same key and a decryption algorithm, the plaintext is recovered from the ciphertext. The two types of attack on the encryption algorithm are cryptanalysis based on properties of the encryption algorithm, and brute-force, which involves trying all possible keys. 24/56 1

2 KEY POINTS Traditional (precomputer) symmetric ciphers use substitution and/or transposition techniques. Substitution techniques map plaintext elements (characters, bits) into ciphertext elements. Transposition techniques systematically transpose the positions of plaintext elements. Rotor machines are sophisticated precomputer hardware devices that use substitution techniques. Steganography is a technique for hiding a secret message within a larger one in such a way that others cannot discern the presence or contents of the hidden message. 25/56 Some Basic Terminology plaintext - original message ciphertext - coded message cipher - algorithm for transforming plaintext to ciphertext. key - information used in cipher known only to sender/receiver encipher (encryption) - the process of converting plaintext to ciphertext decipher (decryption) - recovering ciphertext from plaintext cryptography - study of encryption principles/methods cryptographic system (cipher) - such a method cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext without knowing key cryptology - field of both cryptography & cryptanalysis 26/56 2

3 Fig Simplified Model of Conventional Encryption A symmetric encryption scheme consists of five ingredients Plaintext, Encryption algorithm, Secret key Ciphertext, Decryption algorithm 27/56 Two requirements for secure use of symmetric encryption: (1) a strong encryption algorithm (2) a secret key known only to sender / receiver Assuming encryption algorithm is known implies a secure channel to distribute key Mathematically have: P : Plaintext, C : Ciphertext, K : Secret key E : Encryption algorithm; D : Decryption algorithm Encryption : C = E K (P), C = E(K, P) Decryption : P = D K (C), P = D(K, C) 28/56 3

4 ˆP ˆK P C P Fig Model of Conventional Cryptosystem 29/56 Cryptography Cryptographic systems are characterized by: Type of encryption operations used Substitution / Transposition Product system : multiple stages of substitutions & Transpositions The number of keys used single-key (secret key) : symmetric cipher two-key (public, private-key): asymmetric cipher The way in which plaintext is processed block cipher stream cipher 30/56 4

5 Cryptanalysis The objective of attacking an encryption system is to recover key not just message. There are two general approaches to attacking a encryption scheme: Cryptanalytic attack : rely on the nature of the algorithm plus some knowledge of the general characteristics of the plaintext or even some sample plaintext-ciphertext pairs Brute-force attack : tries every possible key on a piece of ciphertext. On average, half of all possible keys must be tried to achieve success. 31/56 Table 2.1 Types of Attacks on Encrypted Messages 32/56 5

6 Two more definitions Unconditional security No matter how much computer power or time 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 (eg time needed for calculations is greater than age of universe), the cipher cannot be broken 33/56 Table 2.2 Average Time Required for Exhaustive Key Search 34/56 6

7 Caesar Cipher earliest known substitution cipher by Julius Caesar first attested use in military affairs replaces each letter of the alphabet with the letter standing three places further down the alphabet. Example : Plaintext : meet me after the toga party Ciphertext : PHHW PH DIWHU WKH WRJD SDUWB A numerical equivalent to each letter 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 /56 Caesar Cipher Caesar cipher as: p = a letter in plaintext; C = substituted letter; k = 3 C = E(p) = (p + k) mod (26) p = D(C) = (c k) mod (26) A brute force cryptanalysis is easily performed. (fig. 2.3) Three important characteristics enable us to use a brute force cryptanalysis: The encryption/decryption algorithms are known. There are only 26 keys to try The language of the plaintext is known and easily recognizable. 36/56 7

8 Monoalphabetic Cipher could shuffle (jumble) the letters arbitrarily; each plaintext letter maps to a different random ciphertext letter The cipher line can be any permutation of 26 letters; i.e. there are 26! Plain : abcdefghijklmnopqrstuvwxyz Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN Monoalphabetic Cipher Plaintext : ifwewishtoreplaceletters Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA 37/56 Monoalphabetic Cipher With so many keys, might think is secure; but would be!!!wrong!!! Problem is language characteristics (redundancy ) (eg) "th lrd shphrd shll nt wnt" Analyze relative frequency of letters in English text 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 & triple letter frequencies for various languages 38/56 8

9 Fig Relative Frequency of Letters in English Text 39/56 Monoalphabetic Cipher Cryptanalysis of Monoalphabetic Cipher key concept - monoalphabetic substitution ciphers do not change relative letter frequencies discovered by Arabian scientists in 9 th century Example : given ciphertext: P=e, Z=t, ZW=th UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ t a e e t e a t h a t e e a a t VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX e t t a t h a e e e a e t h t a EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ e e e t a t e t h e e t Plaintext : it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow 40/56 9

10 Playfair Cipher Not even the large number of keys in a monoalphabetic cipher provides security; one approach to improving security was to encrypt multiple letters invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair. Key Matrix; keyword is monachy M O N A R C H Y B D E L F P G Q I/J S K T U V W X Z 41/56 Playfair Cipher Encryption/Decryption : ( plaintext is encrypted two letters at a time) 1) if a pair is a repeated letter, insert filler like x ex) balloon ba lx lo on 2) if both letters fall in the same row, replace each with letter to right (wrapping back to start from end) ex) plaintext : ar ciphertext : RM 3) if both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom) ex) plaintext : mu ciphertext : CM 4) Otherwise, each letter is replaced by the letter in the same row and in the column of the other letter of the pair. ex) plaintext : hs ciphertext : BP 42/56 10

11 Playfair Cipher Security much improved over simple monoalphabetic cipher There are 26 x 26 = 676 digrams so that identification of individual diagrams is more difficult; making frequency analysis much more difficult. was for a long time considered unbreakable, widely used for many years; British Army in WW1, US Army & Allied forces in WW2 it can be broken, given a few hundred letters since still has much of plaintext structure (Fig. 2.6) 43/56 Hill Cipher Developed by the mathematician Lester Hill in 1929 The substitution is determined by m linear equations. C = KP mod 26 P = K 1 C mod 26 P & C are column vectors of length m, representing the plaintext and ciphertext, and K is an m m matrix, key. Example : Plaintext : paymoremoney K = Ciphertext = LNSHDLEWMTRW p L K a = K 0 = 819 = 13 = N y S 44/56 11

12 Polyalphabetic Cipher improve security using multiple cipher alphabets make 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 Vigenère Cipher simplest polyalphabetic substitution cipher effectively multiple Caesar ciphers key is multiple letters long K = k 1 k 2... k d i th letter specifies i th alphabet to use repeat from start after d letters in message decryption simply works in reverse 45/56 Polyalphabetic Cipher Vigenère Cipher eg using keyword deceptive key = deceptivedeceptivedeceptive Plaintext = wearediscoveredsaveyourself Ciphertext = ZICVTWQNGRZGVTWAVZHCQYGLMGJ Vigenère proposed the autokey cipher, in which a keyword is concatenated with the plaintext itself to provide a running key. Security of Vigenère Ciphers; method developed by Babbage / Kasiski (Kasiski method) 46/56 12

13 Polyalphabetic Cipher One-Time Pad AT&T engineer named Gilbert Vernam in 1918 Encryption : c i = p i k i p i, k i, c i = ith binary digit of plaintext, key, ciphertext 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; can only use the key once though. Problems in generation & safe distribution of key. 47/ Transposition Ciphers Consider classical transposition or permutation ciphers These hide the message by rearranging the letter order; without altering the actual letters used. Can recognize these since they have the same frequency distribution as the original text. Rail Fence cipher Write message letters out diagonally over a number of rows; then read off cipher row by row eg. write plaintext message out as: m e m a t r h t g p r y e t e f e t e o a a t ciphertext : MEMATRHTGPRYETEFETEOAAT 48/56 13

14 2.3 Transposition Ciphers Row Transposition Ciphers Write letters of message out in rows over a specified number of columns; then reorder the columns according to some key before reading off the rows. A more complex transposition. eg. message : attack postponed until two am Key : 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 49/ Transposition Ciphers Row Transposition Ciphers eg. message : attack postponed until two am Key : plaintext t t n a a p t m t s u o a o d w c o i x k n l y p e t z ciphertext: NSCYAUOPTTWLTMDNAOIEPAXTTOKZ 50/56 14

15 Product Ciphers Ciphers using substitutions or transpositions are not secure because of language characteristics. Hence, consider using several ciphers in succession to make harder, but: two substitutions make a more complex substitution two transpositions make more complex transposition but a substitution followed by a transposition makes a new much harder cipher This is bridge from classical to modern ciphers 51/ Rotor Machines Before modern ciphers, rotor machines were most common complex ciphers in use widely used in WW2 German Enigma, Allied Hagelin, Japanese Purple implemented a very complex, varying substitution cipher is used a series of cylinders, each giving one substitution, which rotated and changed after each letter was encrypted with 3 cylinders have 26 3 =17,576 alphabets 52/56 15

16 2.4 Rotor Machines Fig Three rotor machine 53/56 Hagelin Rotor Machine 2.4 Rotor Machines 54/56 16

17 German Enigma 2.4 Rotor Machines 55/56 an alternative to encryption hides existence of message 2.5 Steganography using only a subset of letters/words in a longer message marked in some way using invisible ink hiding in LSB in graphic image or sound file has drawbacks high overhead to hide relatively few information bits 56/56 17