Introduction to Cryptography

1
Introduction to Cryptography

• Lecture 8

2
Polyalphabetic Substitutions

• Definition Let be different
  substitution ciphers. Then to encrypt the message
  apply .
• If the length of the message is longer than
  number of different ciphers, then repeat same
  ciphers in the same order.

3
Polyalphabetic Substitutions

• Example Let the message be Today is Tuesday.
  Let , where is a shift
  cipher with ki.
• The message UQGEZKUXVGVHBA.
• Two same letters encrypted to different letters
• Can not use English properties directly

4
Vigenere Square
5
Vigenere Square

• Example Let the message be APRIL SHOWERS BRING
  MAY FLOWERS. Let the key word be RHYME.
• Using the square we encrypt plaintext and get the
  message RWPUPJOMIIIZZDMENKMCWSMIIIZ.

6
Vigenere Cipher

• Suppose the key word has n letters.
• Let the key letters be
• Let the plaintext be
• Let the cipher text be
• Then

7
Index of Coincidence

• Definition The index of coincidence, I, is the
  probability that two randomly selected letters in
  ciphertext are identical.
• Formula
• If I is close to 0.065, then most probably the
  cipher is monoalphabetic
• If I is close to 0.0385, then most probably the
  cipher is polyalphabetic

8
Index of Coincidence

• Example Let the message be WSPGMHHEHMCMTGPNROVXW
  ISCQTXHKRVESQTIMMKWBMTKWCSTVLTGOPZXGTQMCXHCXHSMGXW
  MNIAXPLVYGROWXLILNFJXTJIRIRVEXRTAXWETUSBITJMCKMCOT
  WSGRHIRGKPVDNIHWOHLDAIVXJVNUSJX.

9
Index of Coincidence

• Example Build a table of letter frequencies
  (there are 152 letters)

A B C D E F G H I J K L M
3 2 7 2 4 1 8 9 10 5 5 5 11
N O P Q R S T U V W X Y Z
5 5 5 3 8 8 12 2 8 9 13 1 1
10
Vigenere Cipher

• Vigenere cipher uses a keyword
• Let length of the keyword be k
• Assume the ciphertext is given
• We know message encrypted using Vigenere Cipher
• We can find estimated key size using

11
Vegenere Cipher

• Example For last example with n152.
• The keyword may be about 4 letters.

12
The Kasiski Test

• The Kasiski test relies on the occasional
  coincidental alignment of letter groups in
  plaintext with the keyword
• Find groups of same letters of size 3 or more
• Calculate distance between those groups
• The greatest common divisor of those distances
  have a good chance to be the length of the key

13
The Kasiski Test

• Example Let the message be WCZOUQNAHYYEDBLWOSHMA
  UCERCELVELXSSUZLQWBSVYXARRMJFIAWFNAHBZOUQNAHULKHGY
  LWQISTBHWLJCYVEIYWVYJPFNTQQYYIRNPHSHZORWBSVYXARRMJ
  FIAWF.
• For NAH distances 48 and 8
• For WBSVYXARRMJFIAWF 72
• The keyword can be of size 2,4 or 8.

14
Homework

• Read pg.107-117.
• Exercises 1(a), 3(c) on pg.118.
• Read pg.134-141.
• Exercises 3, 8 on pg.141-143.
• Those questions will be a part of your collected
  homework.