1 / 12

Announcements: Pass in Assignment 1 now Meet my assistant Kevin Reed

DTTF/NB479: Dszquphsbqiz Day 6. Announcements: Pass in Assignment 1 now Meet my assistant Kevin Reed Assignment 2 (tentative) posted Questions? Today: Finish Vigenere, start Hill ciphers. Vigenere Ciphers. Idea: the key is a vector of shifts Ex. Use a word like hidden (7 8 3 3 4 13) .

korene
Download Presentation

Announcements: Pass in Assignment 1 now Meet my assistant Kevin Reed

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DTTF/NB479: Dszquphsbqiz Day 6 • Announcements: • Pass in Assignment 1 now • Meet my assistant Kevin Reed • Assignment 2 (tentative) posted • Questions? • Today: Finish Vigenere, start Hill ciphers

  2. Vigenere Ciphers • Idea: the key is a vector of shifts • Ex. Use a word like hidden (7 8 3 3 4 13). • Example: • The recent development of various methods of 7 8 3 3 413 7 8 3 3 413 7 8 3 3 413 7 8 3 3 413 7 8 3 3 4 13 7 8 3 3 413 7 8 015 7 20 815112122 6 8 811191718161720 1 17 8 25132416172322 2511 11017 7 5 2113 • aph uiplvw giiltrsqrub ri znyqrxw zlbkrhf vn • Encryption: • Repeat the vector as many times as needed to get the same length as the plaintext • Add this repeated vector to the plaintext. • Demo

  3. Summary from yesterday • What makes a Vigenere cipher more secure than a shift cipher? • How do we find the key length? • Why does the max of dot(A0,Ai) occur when i==0? • What are the advantages and disadvantages of using the dot product method (method 2) vs. method 1 to decrypt the key?

  4. English letter frequencies H 0.061 I 0.070 J 0.002 K 0.008 L 0.040 M 0.024 N 0.067 O 0.075 P 0.019 Q 0.001 R 0.060 S 0.063 T 0.091 U 0.028 V 0.010 W 0.023 X 0.001 Y 0.020 Z 0.001 A 0.082 B 0.015 C 0.028 D 0.043 E 0.127 F 0.022 G 0.020 Graph:

  5. Finding the key length • What if the frequency of letters in the plaintext approximates A? • Then for each k, frequency of each group of letters in position p = k (mod L) in the ciphertext approximates A. • Then loop, displacing the ciphertext by i, and counting the number of coincidences. • Get max when displace by correct key length • So just look for the max! shift APHUIPLVWGIILTRSQRUBRIZNYQRXWZLBKRHFVN (0) NAPHUIPLVWGIILTRSQRUBRIZNYQRXWZLBKRHFV (1) VNAPHUIPLVWGIILTRSQRUBRIZNYQRXWZLBKRHF (2) … KRHFVNAPHUIPLVWGIILTRSQRUBRIZNYQRXWZLB (6) 5matches

  6. Visualization • http://www.usafa.af.mil/df/dfcs/acis/applets/Vigenere.html • Play with now and for homework • Thanks to Dr. Dino Schweitzer, USAFA, who I met last Friday, for pointing me to his demo! • Aren’t you glad I was at SIGCSE?

  7. Vigenere Closing Thought • What if we modified the Vigenere cipher so that each individual letter was not simply shifted, but the result of an affine function?

  8. Block Ciphers • So far, changing 1 character in the plaintext changes ___ characters in the ciphertext. • Shannon outlined qualities of good ciphers: • Diffusion: Changing one character of the plaintext changes _____ characters in the ciphertext • Makes frequency analysis much tougher! • Confusion: Each character of the ciphertext interacts with several parts of the key • Block ciphershave both qualities: • DES (64 bits), AES (128 bits), Hill ciphers (smaller; today)

  9. Hill Ciphers • Lester Hill, 1929. Not used much, but first time linear algebra used in crypto • Use an n x n matrix M. Encrypt by breaking plaintext into blocks of length n (padding with x’s if needed) and multiplying each by M. • Example: Encrypt “hereissomeonetoencrypt” using M • her eis som eon eto enc ryp txx • (7, 4, 17) (4, 8, 18) … (19, 23, 23) • (2, 5, 25) (0, 2, 22) … (0, 22, 15) • cfz acw yga vns ave anc sdd awp • “CFZACWYGAVNSAVEANCSDDAWP”

  10. Decrypting • Reverse the process, multiplying each block by M inverse • Theorem: If a matrix M is invertible mod n, then gcd(det(M), n) = 1 • Proof on board (uses a lemma from Ch 3)

  11. How to break via known plaintext? • Think about this…

  12. Does this cipher exhibit diffusion?

More Related