Computer security

Section 3

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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

• the Playfair Cipher is an example • invented by Charles Wheatstone in 1854, but

named after his friend Baron Playfair

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Playfair Key Matrix

• a 5X5 matrix of letters based on a keyword • fill in letters of keyword• fill rest of matrix with other letters• eg. using the keyword MONARCHY

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

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Playfair Cipher Con.,

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

•Plaintext is encrypted two letters at a time•If a pair is a repeated letter, insert filler like 'X’. •e.g. BALLOON will be treated as:

BA LX LO ON

• If both letters m1 and m2 fall in the same row, then c1 and c2 replace each with letter to the right of m1 and m2, respectively.

m1 c1 m2 c2(wrapping back to start from end)

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If both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom)

If the plaintext has an odd number of characters, a null letter is appended to the end of plaintext.

Playfair Cipher Con., m1

c1

m2

c2

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Playfair Cipher Con.,

• Otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair.

• Ex. Encrypt the message “ playfair invented by Charles” using Playfair cipher.

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

pl ay fa ir in ve nt ed by ch ar le sx

qp nb io ka ga uf rq kc db hy rm ul xa

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Playfair Cipher Con.,

• Encipher the following word “ RENAISSANCE” using Playfair key as shown.

RE NA IS SA NC EX

HG WC BH HR WF GV

H A R P SI C O D BE F G K LM N Q T UV W X Y Z

Vigenère Cipher

• Simplest polyalphabetic substitution cipher is the Vigenère Cipher

• Effectively multiple caesar ciphers • Given a key letter X and a plain text Y, the

cipher text letter is at inspection of the row labelled x and the column labelled y in this case the cipher text is V.

• Decryption simply works in reverse

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Example

• Write the plaintext out • Write the keyword repeated above it• Use each key letter as a caesar cipher key • Encrypt the corresponding plaintext letter• eg using keyword deceptive

key: deceptivedeceptivedeceptiveplaintext: wearediscoveredsaveyourselfciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ

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Security of Vigenère Ciphers

• Have multiple ciphertext letters for each plaintext letter

• Hence letter frequencies are obscured• But not totally lost• Start with letter frequencies

– see if look monoalphabetic or not

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Row Transposition ciphers

– In general write message in a number of columns and then use some rule to read off from these columns.

– Key could be a series of number being the order to: read off the cipher; or write in the plaintext

– Plain: THE SIMPLEST POSSIBLE TRANSPOSITIONSXX

– Key (R Cipher): 41532Key (W Plain) : 4 1 5 3 2

1 2 3 4 5 1 2 3 4 5 T H E S I S T I E H M P L E S E M S L P T P O S S S T S O P I B L E T E I T L B R A N S P S R P N A O S I T I T O I I S O N S X X X O X S N

– Cipher: STIEH EMSLP STSOP EITLB SRPNA TOIIS XOXSN

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Example

– We can use a word, with letter order giving sequence: to write in the plaintext; or read off the cipher

– Plain: A,CONVENIENT,WAY,TO,EXPRESS, THE,PERMUTATION

– Key (W): C O M P U T E R – Key (W): 1 4 3 5 8 7 2 6 –

A C O N V E N I A N O C N I E V E N T W A Y T O E T T N W O Y A E X P R E S S T E S P X R T S E H E P E R M U T H U P E E T M RA T I O N Z Z Z A Z I T O Z Z N

-Cipher: ANOCN IEVET TNWOY AESPX RTSEH UPEET MRAZI TOZZN