Introduction to Cryptography - PowerPoint PPT Presentation

1 / 14
About This Presentation
Title:

Introduction to Cryptography

Description:

Using the square we encrypt plaintext and get the message: RWPUPJOMIIIZZDMENKMCWSMIIIZ. ... Calculate distance between those groups ... – PowerPoint PPT presentation

Number of Views:42
Avg rating:3.0/5.0
Slides: 15
Provided by: Eliz179
Category:

less

Transcript and Presenter's Notes

Title: 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.
Write a Comment
User Comments (0)
About PowerShow.com