lec 5-Cryptography

Cryptography

Cryptography

polyalphabetic cipher

Polyalphabetic Ciphers

• _{another approach to improving security is to use}

multiple cipher alphabets

• _{called polyalphabetic substitution ciphers}

• _{makes 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

• _{use each alphabet in turn}

Vigenère Cipher

• _{simplest polyalphabetic substitution cipher is}

the Vigenère Cipher

• _{effectively multiple caesar ciphers}

• _{key is multiple letters long K = k1 k2 ... kd} • _ith _{letter specifies i}th _{alphabet to use}

• _{use each alphabet in turn}

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}

Security of Vigenère Ciphers

• _{have multiple ciphertext letters for each}

Autokey Cipher

• _{ideally want a key as long as the message} • _{Vigenère proposed the autokey cipher}

• _{with keyword is prefixed to message as key}

• _{knowing keyword can recover the first few letters} • _{use these in turn on the rest of the message}

• _{but still have frequency characteristics to attack} • _{eg. given key deceptive}

One-Time Pad

• _{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

• _{since for any plaintext & any ciphertext there}

exists a key mapping one to other

• _{can only use the key once though}

Transposition Ciphers

• _{now consider classical transposition or}

permutation ciphers

• _{these hide the message by rearranging the}

letter order

• _{without altering the actual letters used} • _{can recognise these since have the same}

Rail Fence cipher

• _{write message letters out diagonally over a}

number of rows

• _{then read off cipher row by row} • _{eg. write 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

• _{giving ciphertext}

Columnar Transposition

Definition: Write the message in rows of a fixed length, and then read out again column by

column. The columns are chosen in some

scrambled order. Both the length of the rows and the permutation of the columns are

Columnar Transposition Cipher

• _{The columnar transposition cipher is a fairly simple, easy to}

implement cipher. It is a transposition cipher that follows a simple rule for mixing up the characters in the plaintext to form the ciphertext.

• _{Although weak on its own, it can be combined with other}

ciphers, such as a substitution cipher, the combination of

• The key for the columnar transposition cipher is a keyword e.g. GERMAN. The row length that is used is the same as the length of the keyword. To encrypt a piece of text, e.g.

• defend the east wall of the castle we write it out in a special way in a number of rows (the keyword here is GERMAN):

• In the above example, the plaintext has been padded so that it neatly fits in a rectangle. This is known as a regular columnar transposition. An irregular columnar transposition leaves these characters blank, though this makes decryption slightly more difficult. The columns are now reordered such that the letters in the key word are ordered alphabetically.

• _{nalcxehwttdttfseeleedsoaxfeahl}

Key Columnar Transposition

Example: Let the key word be: ZEBRA.

The message:

EODAEASRENEIELORCEECWDVFT.

Z E B R A

W E A R E

D I S C O

V E R E D

F L E E A

Row Transposition Ciphers

• _{a more complex scheme}

• _{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

Key: 3 4 2 1 5 6 7 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

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

Steganography

• _{an alternative to encryption} • _{hides existence of message}

– _{using only a subset of letters/words in a longer}

message marked in some way

– _{using invisible ink} – _{Pin punctures}

• _{has drawbacks}

Summary

• _{have considered:}

– _{classical cipher techniques and terminology} – _{monoalphabetic substitution ciphers}

– _{cryptanalysis using letter frequencies} – _{Playfair ciphers}

– _{polyalphabetic ciphers} – _{transposition ciphers} – _{product ciphers}