Announcements:

1
DTTF/NB479 Dszquphsbqiz Day 2

• Announcements
• Class is cancelled ThursFri while Im at the
  SIGCSE conference
• Assignment 1 is posted, due next Tuesday in
  class.
• Use the time to familiarize yourself with the
  Matlab/Maple/Mathematica tools.
• You should have subscribed to Angel forums
• Questions?
• Roll Call
• Today shift ciphers

2
Sherlock Holmes, The Adventure of the Dancing Men
(1898)Who got it?
In a letter
2 weeks later
2 mornings later
3 days later
4 days later
3
Comments

• A simple substitution cipher
• Used knowledge of linguistics
• The letter E.
• Used domain knowledge Elsie
• Issue with ____________
• Sherlock masqueraded as Elsie.
• Others are confidentiality, integrity,
  non-repudiation.
• There is a problem with original source
• One symbol is used twice (for V and P).
• Perhaps needs error-correcting?
• Read Section 2.5 in TW for the solution

4
Non-secure channels
Encryption Key (1)
Decryption Key (-1)
Alice
Bob
Encrypt
Decrypt
plaintext
CIPHERTEXT
DSZQUPHSBQIZ
cryptography
cryptography
Eve
Trappe and Washington, p. 3
5
Shift ciphers

• Attributed to Julius Caesar
• Letters represented as 0-25.
• x ? x k (mod 26)
• Relatively weak cryptosystem. Consider 4 typical
  attacks to find the decryption key
• Ciphertext only (the discussion forums)
• Known plaintext
• Chosen plaintext
• Chosen ciphertext

6
1. Ciphertext only

• Consider dszquphsbqiz
• dszquphsbqiz
• etarvqitcrja
• fubswrjudskb
• gvctxskvetlc
• hwduytlwfumd
• ixevzumxgvne
• jyfwavnyhwof
• kzgxbwozixpg
• lahycxpajyqh
• mbizdyqbkzri
• ncjaezrclasj
• odkbfasdmbtk
• pelcgbtencul
• qfmdhcufodvm
• rgneidvgpewn
• shofjewhqfxo
• tipgkfxirgyp

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2. Known plaintext

• Say I know sample of plaintext and corresponding
  ciphertext.
• How long does the sample need to be to find the
  key?

8
3. Chosen plaintext

• Say I have access to the encryption machine and
  can choose a sample of plaintext to encode. How
  can I deduce the key?
• Just encode a.

4. Chosen ciphertext
Say I can choose a sample of ciphertext to
decode. Just decode A that gives decryption key
the encryption key is the negative.
9
Affine ciphers

• Somewhat stronger since scale, then shift
• x ? ax b (mod 26)
• Say y 5x 3 x hellothere
• Then y mxggv

10
Affine ciphers x ? ax b (mod 26)

• Consider the 4 attacks
• How many possibilities must we consider in brute
  force attack?

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Restrictions on a

• Consider y 2x, y 4x, or y 13x
• The problem is that gcd(a, 26) 1.
• The function has no inverse.

12
Finding the decryption key

• Whats the inverse of y 5x 3?
• Remember this is Integer mod 26 World.

13
Affine ciphers x ? ax b (mod 26)

• Consider the 4 attacks
• Ciphertext only
• How long is brute force?
• Known plaintext
• How many characters do we need?
• Chosen plaintext
• Wow, this is easy.
• Chosen ciphertext
• Could be even easier!

14
Assignment 1

• Enjoy using the Maple/Matlab tools!
• Have fun reading the posts
• Email if you get stuck
• See you Monday!