CLASSICAL CRYPTOGRAPHY. A Brief Reference for Self Build Crypto assignment

Transcription

1 CLASSICAL CRYPTOGRAPHY A Brief Reference for Self Build Crypto assignment

2 CLASSICAL CRYPTOGRAPHY Cryptography is the study of secret (crypto-) writing (-graphy) Concerned with developing algorithms which may be used to: Conceal the context of some message from all except the sender and recipient (privacy or secrecy), and/or Verify the correctness of a message to the recipient (authentication or integrity) Basis of many technological solutions to computer and communications security problems

3 BASIC TERMINOLOGY Cryptography The art or science encompassing the principles and methods of transforming message an intelligible into one that is unintelligible, and then retransforming that message back to its original form Plaintext The original intelligible message Ciphertext The transformed message Cipher Cp An algorithm for transforming an intelligible message into one that is unintelligible by transposition and/or substitution methods Key Some critical information used by the cipher, known only to the sender & receiver

4 Basic Terminology - 2 Encipher (encode) Process of converting plaintext to ciphertext using a cipher and a key Decipher (decode) The process of converting ciphertext back into plaintext using a cipher and a key Cryptanalysis (codebreaking) The study of principles i and methods of transforming an unintelligible message back into an intelligible message without knowledge of the key. Cryptology The field encompassing both cryptography and cryptanalysis

5 Basic Terminology - 3 Encryption The mathematical function mapping plaintext to ciphertext using the specified key: Y = E K (X) Decryption The mathematical function mapping ciphertext to plaintext using the specified key: X = D (Y) = E -1 K K (Y) Cryptographic system The family of transformations from which the cipher function E K is chosen

6 SIMPLIFIED CONVENTIONAL ENCRYPTION MODEL Not secret Conventional Private-Key ( Public-Key) Secret-Key Single-Key Symmetric ( Asymmetric)

7 CONVENTIONAL CRYPTOSYSTEM MODEL

8 CRYPTANALYSIS Process of attempting ti to discover X or K or both. Various types of cryptanalytic attacks

9 EXHAUSTIVE KEY SEARCH Always theoretically possible to simply try every key Most basic attack, directly proportional to key size Assume either know or can recognize when plaintext t is found Average Time Required for Exhaustive Key Search

10 UNCONDITIONAL AND COMPUTATIONAL SECURITY Unconditionally secure No matter how much computer power is available, the cipher cannot be broken since the ciphertext t provides insufficient information to uniquely determine the corresponding plaintext Computationally secure The cost of breaking the security exceeds the value of the secured service or information. The time required to break the security exceeds the useful lifetime of the information

11 STEGANOGRAPHY The art of covered writing Security by obscurity Hide messages in other messages. Conceal the existence of message Conceal what you are communicating (Sending encrypted messages would make you a spy) Character marking. Overwrite with a pencil Invisible ink, - Pin punctures, - First letter of each word Letter position on page, - Drawings, - Codes Typewriter correction ribbon Microdots Digital steganography Digital steganography Spread spectrum

12 Steganography - Example News Eight Weather: Tonight increasing snow. Unexpected precipitation Smothers Eastern towns. Be extremely cautious and use snowtires especially heading east. The highways are knowingly slippery. Highway evacuation is suspected. Police report emergency situations in downtown ending near Tuesday First letter of each word yields: Newt is upset because he thinks he is President This example was created by Neil F. Johnson, and was published in Steganography,Technical Report TR_95_11_nfj, URL: From WWII German spy (Kahn): Apparently neutral s protest is thoroughly discounted and ignored. Isman hard hit. Blockade issue affects pretext for embargo on by products, ejecting suets and vegetable Oils. Second letter of each word yields: Pershing sails from NY June 1.

13 Steganography - Exercise What is the message embedded in the left figure?

14 CLASSICAL ENCRYPTION TECHNIQUES Substitution Techniques Caesar Cipher Monoalphabetic Ciphers Playfair Cipher Hill Cipher Polyalphabetic Ciphers Transposition (Permutation) ti Techniques Rail Fence Technique Block (Columnar) Transposition Technique Product Techniques Substitution and transposition ciphers are concatenated

15 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 c i =E(p i )=(p i +3) mod 26; p i =D(c i )=(c i -3) mod 26 No key, just one mapping (translation) Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC

16 GENERALIZED CAESAR CIPHER Can use any shift from 1 to 25, i.e., replace each letter by a letter a fixed distance away c i =E(p i )=(p i +k) mod 26; p=d(c i )=(c i -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

17 Brute-Force Cryptanalysis of Caesar Cipher

18 AFFINE CIPHER c i =E(p i )=(k 1 p i +k 2 ) mod 26; gcd(k 1,26)=1 p -1 i =D(c i )=(k 1 (c i -k 2 )) mod 26 Key = (k1, k2) Number of keys = 12x26 = 312 Caesar/Shift ciphers are special cases of affine ciphers

19 MONOALPHABETIC SUBSTITUTION CIPHERS Further generalization of the Caesar cipher, Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC is obtained bti by allowing any permutation ti of 26 characters for the cipher Key size = 26 Key space = 26! 4x10 26 Unique mapping of plaintext alphabet to ciphertext alphabet Monoalphabetic For a long time thought secure, but easily breakable by frequency analysis attack

20 RELATIVE FREQUENCY OF LETTERS IN ENGLISH TEXT

21 FREQUENCY STATISTICS OF LANGUAGE In addition to the frequency info of single letters, the frequency info of two-letter (digram) or three-letter (trigram) combinations i can be used for the cryptanalysis Most frequent digrams TH, HE, IN, ER, RE, AN, ON, EN, AT Most frequent trigrams THE, ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH, FOR, DTH

22 HOMOPHONES Monoalphabetic substitution ciphers are easy to cryptanalyze through letter frequency analysis Multiple l substitutes t (homophones) h for a single letter can be used to hide the single-letter frequency information But even with homophones, h multiple-letter l ltt patterns (e.g. digram frequencies) still survive in the ciphertext Two approaches for this problem Encrypt multiple letters of plaintext Playfair cipher Hill cipher Use multiple cipher alphabets Polyalphabetic cipher

23 PLAYFAIR CIPHER Best-known multiple-letter substitution cipher Digram cipher (diagram to digram, i.e., E(p i p i+1 )=c i c i+1 through h key-based 5x55 transformation ti table) 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 Keyword = monarchy 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) Still leaves much of the structure of the plaintext language relatively easy to break Can be generalized to polygram cipher

24 Relative Frequency of Occurrence of Letters

25 HILL CIPHER Multiletter cipher Takes m successive plaintext letters and substitutes for them m ciphertext letters 3x3 Hill cipher: c 1 = (k 11 p 1 + k 12 p 2 + k 13 p 3 ) mod 26 c 2 = (k 21 p 1 + k 22 p 2 + k 23 p 3 ) mod 26 c 3 = (k 31 p 1 + k 32 p 2 + k 33 p 3 ) mod 26 C = E K (P) = KP; P=D K (C)=K -1 C = K -1 KP = P m x m Hill cipher hides (m-1)-letter frequency info Strong against for the plaintext-only attack, but easily broken with known plaintext attack with m plaintext-ciphertext pairs, each of length m; K = CP -1

26 POLYALPHABETIC CIPHER Typically a set of monoalphabetic substitution rules is used Key determines which rule to use

27 VIGENÈRE CIPHER Best-known polyalphabetic ciphers Each key letter determines one of 26 Caesar (shift) ciphers c i = E(p i ) = p i + k i mod(key length) Example: Key: Plaintext: Cipheretxt: deceptivedeceptivedeceptive wearediscoveredsaveyourself ZICVTWQNGRZGVTWAVZHCQYGLMGJ Keyword is repeated to make a key as long as the plaintext Given a sufficient amount of ciphertext, common sequences are repeated, exposing the period (keyword length) Target of the cryptanalysis

28 Vigenère cipher - 2

29 VIGENÈRE CIPHER -3 If the keyword length is N, then Vigenère cipher, in effect, consists of N monoalphabetic substitution ciphers Improvement over the Playfair cipher, but language g structure and frequency information still remain Vigenère autokey system: after key is exhausted, use plaintext for running key (to eliminate the periodic nature) Key: deceptivewearediscoveredsav di d Plaintext: wearediscoveredsaveyourself Cipheretxt: ZICVTWQNGKZEIIGASXSTSLVVWLA Key and plaintext share the same frequency distribution of letters a statistical technique can be used for the cryptanalysis, (e.g., e enciphered with e would occur with a frequency of (0.1275) , t enciphered with t would occur with a frequency of (0.0925) 0925) , 0086 etc.)

30 ONE-TIME PAD Perfect substitution cipher Use a random key (pad) which is as long as the message, with no repetitions. Key distribution is a problem Or, random key stream generation is a problem With such key, plaintext and ciphertext are statistically independent Unconditionally secure

31 TRANSPOSITION (PERMUTATION) TECHNIQUES Hide the message by rearranging the letter order without t 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 Block (Columnar) Transposition Ciphers MEMATRHTGPRYETEFETEOAAT 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: 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 Generalization: multiple l transpositions

32 ROTOR MACHINES Mechanical cipher machines, extensively used in WWII; Germany (Enigma), Japan (Purple), Sweden (Hagelin) Each rotor corresponds to a substitution cipher A one-rotor machine produces a polyalphabetic cipher with period 26 Output of each rotor is input to next rotor After each symbol, the fast rotor is rotated After a full rotation, the adjacent rotor is rotated t (like odometer) ) - An n rotor machine produces a polyalphabetic cipher with period 26 n

33 Three-Rotor Machines