Introduction to Cryptography Lecture 8. Polyalphabetic Substitutions Definition: Let be different substitution ciphers. Then to encrypt the message apply.

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Presentation transcript:

Introduction to Cryptography Lecture 8

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.

Polyalphabetic Substitutions Example: Let the message be: Today is Tuesday. Let, where is a shift cipher with k=i. The message: UQGEZKUXVGVHBA. Two same letters encrypted to different letters Can not use English properties directly

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.

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

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 , then most probably the cipher is polyalphabetic

Index of Coincidence Example: Let the message be: WSPGMHHEHMCMTGPNROVXWISCQ TXHKRVESQTIMMKWBMTKWCSTVLT GOPZXGTQMCXHCXHSMGXWMNIAX PLVYGROWXLILNFJXTJIRIRVEXRTAX WETUSBITJMCKMCOTWSGRHIRGKP VDNIHWOHLDAIVXJVNUSJX.

Index of Coincidence Example: Build a table of letter frequencies (there are 152 letters): ABCDEFGHIJKLM NOPQRSTUVWXYZ

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:

Vegenere Cipher Example: For last example with n=152. The keyword may be about 4 letters.

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

The Kasiski Test Example: Let the message be: WCZOUQNAHYYEDBLWOSHMAUCER CELVELXSSUZLQWBSVYXARRMJFIA WFNAHBZOUQNAHULKHGYLWQISTB HWLJCYVEIYWVYJPFNTQQYYIRNPH SHZORWBSVYXARRMJFIAWF. For NAH distances: 48 and 8 For WBSVYXARRMJFIAWF: 72 The keyword can be of size: 2,4 or 8.

Homework Read pg Exercises: 1(a), 3(c) on pg.118. Read pg Exercises: 3, 8 on pg Those questions will be a part of your collected homework.