Classical Techniques: Substitution

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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

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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 alphabetPlain: meet me after the toga partyCipher: 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

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Generalized Caesar Cipher Can use any shift from 1 to 25, i.e., replace each letter by a

letter a fixed distance awayci=E(k,pi)=(pi+k) mod 26; pi=D(k,ci)=(ci-k) mod 26

Shift cipher Key = kKey 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) ciphersKey space = 26

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Brute-Force Cryptanalysis of Caesar Cipher

Ciphertext only attack Charateristics for

success1. 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

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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.

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Relative Frequency of Letters in English Text

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Frequency Statistics of LanguageIn addition to the frequency info of single letters,

the frequency info of two-letter (digram) or three-letter (trigram) combinations can be used for the cryptanalysis

Most frequent digramsTH, 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 trigramsTHE, ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH,

FOR, DTH

Substitution Techniques

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Playfair CipherBest-known multiple-letter substitution cipherDigram cipher (digram to digram, i.e., E(pipi+1) =

cici+1 through keyword-based 5x5 transformation table)

Great advance over simple monoalphabetic cipher(26 letters 26x26=676 digrams)

Can be generalized to polygram cipher

Keyword = monarchy

Plaintext: H S E A A R M UCiphertext: B P I M R M C M

M O N A RC H Y B DE F G I/J KL P Q S TU V W X Z

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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.

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Polyalphabetic CipherTypically a set of monoalphabetic substitution rules is

usedKey determines which rule to use

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Vigenère cipher Best-known polyalphabetic ciphers Each key letter determines one of 26 Caesar (shift) ciphersci = E(pi) = pi + ki mod(key length) mod 26 Example:

Keyword is repeated to make a key as long as the plaintext

Key: deceptivedeceptivedeceptivePlaintext: wearediscoveredsaveyourselfCipheretxt: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

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Vigenère cipher - 2

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Example: Encryption

Decryption

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Vigenère cipher - 3

Vigenère autokey system: after key is exhausted, use plaintext for running key (to eliminate the periodic nature)

Key: deceptivewearediscoveredsavPlaintext: wearediscoveredsaveyourselfCipheretxt: ZICVTWQNGKZEIIGASXSTSLVVWLA

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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:

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:

M e m a t r h t g p r y e t e f e t e o a a t MEMATRHTGPRYETEFETEOAAT

Key: 4 3 1 2 5 6 7Plaintext: a t t a c k p

o s t p o n ed u n t i l tw o a m x y z

Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ