classical techniques: substitution
Post on 24-Feb-2016
37 Views
Preview:
DESCRIPTION
TRANSCRIPT
1
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
2
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
3
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
4
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
5
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.
6
Relative Frequency of Letters in English Text
7
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
8
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
9
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.
10
Polyalphabetic CipherTypically a set of monoalphabetic substitution rules is
usedKey determines which rule to use
11
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
12
Vigenère cipher - 2
13
Example: Encryption
Decryption
14
Vigenère cipher - 3
Vigenère autokey system: after key is exhausted, use plaintext for running key (to eliminate the periodic nature)
Key: deceptivewearediscoveredsavPlaintext: wearediscoveredsaveyourselfCipheretxt: ZICVTWQNGKZEIIGASXSTSLVVWLA
15
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
top related