1 / 29

Data Encryption

Data Encryption. Chris Mraovich. Overview. Purpose of Encryption. Permutations Bases and Factoradics. Project Summary. Purpose of Encryption. Protecting Digital Content. DVDs use CSS (Content Scramble System). Weak Algorithm -Cracked by Jon Johansen in 1999. Protecting Digital Content.

zulema
Télécharger la présentation

Data Encryption

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. Data Encryption Chris Mraovich

  2. Overview • Purpose of Encryption • Permutations Bases and Factoradics • Project Summary

  3. Purpose of Encryption

  4. Protecting Digital Content • DVDs use CSS (Content Scramble System) • Weak Algorithm • -Cracked by Jon Johansen in 1999

  5. Protecting Digital Content Arcade Printed Circuit Boards • Capcom Play System 2 (CPS2) -Used in mid 1990s for 2D games • Uses encryption on program ROM chips • Graphic ROM chips are not encrypted • Cracked by team

  6. Protecting Digital Content Why use encryption on an arcade board? • ROM chips can be copied to a PC as binary data 2. Program can be written to interpret binary data 3. PC can then run the arcade without the board

  7. Permutations, Bases, and Factoradics

  8. 1 1 0 1 Permutations Goal is to rearrange bits into a different pattern 1 0 1 1 Original Form: Encrypted Form: Permutation – rearrangement of a set of objects

  9. Obtain permutation from factoradic Use permutation to rearrange bits Generate Factoradic Bases and Factoradics Factoradic – mixed radix numbering system that uses multiple bases to represent a single number Why are they important? • Factoradics provide a way of generating permutations Summary of Encryption Process

  10. Order & Total Permutations Order – number of objects (N) Total number of permutations for N objects is N! Suppose there are 4 objects N = 4, so there are 4! or 24 ways to rearrange 4 objects

  11. Total Permutations of order 4 Int Factoradic Permutation 0 { 0 0 0 0 } ( 0 1 2 3 ) 1 { 0 0 1 0 } ( 0 1 3 2 ) 2 { 0 1 0 0 } ( 0 2 1 3 ) 3 { 0 1 1 0 } ( 0 2 3 1 ) 4 { 0 2 0 0 } ( 0 3 1 2 ) 5 { 0 2 1 0 } ( 0 3 2 1 ) 6 { 1 0 0 0 } ( 1 0 2 3 ) 7 { 1 0 1 0 } ( 1 0 3 2 ) 8 { 1 1 0 0 } ( 1 2 0 3 ) 9 { 1 1 1 0 } ( 1 2 3 0 ) 10 { 1 2 0 0 } ( 1 3 0 2 ) 11 { 1 2 1 0 } ( 1 3 2 0 ) 12 { 2 0 0 0 } ( 2 0 1 3 ) 13 { 2 0 1 0 } ( 2 0 3 1 ) 14 { 2 1 0 0 } ( 2 1 0 3 ) 15 { 2 1 1 0 } ( 2 1 3 0 ) 16 { 2 2 0 0 } ( 2 3 0 1 ) 17 { 2 2 1 0 } ( 2 3 1 0 ) 18 { 3 0 0 0 } ( 3 0 1 2 ) 19 { 3 0 1 0 } ( 3 0 2 1 ) 20 { 3 1 0 0 } ( 3 1 0 2 ) 21 { 3 1 1 0 } ( 3 1 2 0 ) 22 { 3 2 0 0 } ( 3 2 0 1 ) 23 { 3 2 1 0 } ( 3 2 1 0 ) • Int is the base 10 representation of the factoradic • Each factoradic uniquely identifies a particular permutation • Walkthrough of how 2010 is converted to a permutation of order 4

  12. Bases – Generate Factoradic Base 10 Base 2 Multi-Base Factoradic 20 10100 3100 Write 2010 in Base 2 24 23 22 21 20 (16) (8) (4) (2) (1) 1 0 1 0 0 Expand the Binary Number (12 x 24) + (02 x 23) + (12 x 22) + (02 x 21) + (02 x 20) = 2010

  13. From Base 2 to Factoradic Generalization of Base 2 Expansion (E2 x 24) + (D2 x 23) + (C2 x 22) + (B2 x 21) + (A2 x 20) … A2, B2, C2, D2, E2 are all numbers in base 2 (0 or 1) 2nare powers of 2 1.) The bases of A2, B2, C2, D2, E2increase from right to left What Changes : 2n n! 2.) Factoradic Expansion (E5 x 4!) + (D4 x 3!) + (C3 x 2!) + (B2 x 1!) + (A1 x 0!) … (Mixed Radix - multiple bases used)

  14. Factoradic Number System Factoradic Expansion (E5 x 4!) + (D4 x 3!) + (C3 x 2!) + (B2 x 1!) + (A1 x 0!) … Simplify Factorials (E5 x 24) + (D4 x 6) + (C3 x 2) + (B2 x 1) + (A1 x 1) 0 0 0 0 0 1 1 1 1 2 2 2 3 3 4 Since A, B, C, D, and E have different bases, they have different ranges of valid values

  15. Factoradic Number System Write 2010 in Factoradic notation (E5 x 24) + (D4 x 6) + (C3 x 2) + (B2 x 1) + (A1 x 1) 0 0 0 0 0 1 1 1 1 2 2 2 3 3 4 (3 x 3!) + (1 x 2!) + (0 x 1!) + (0 x 0!) = (3 x 6) + (1 x 2) + (0 x 1) + (0 x 1) = 20 Final Factoradic for 2010: 3 1 0 0

  16. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0

  17. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1

  18. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1

  19. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 1 1 2) Replace right-most digit with a 1 3)This 1 is the “new value” (N) If any red value to the right of N is >= N, it gets incremented by 1

  20. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 3)This 1 is the “new value” (N) 1 2 If any red value to the right of N is >= N, it gets incremented by 1

  21. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 2 2) Replace right-most digit with a 1 3)This 1 is the “new value” (N) 1 1 2 2 If any red value to the right of N is >= N, it gets incremented by 1 4) Repeat step 3 until all red numbers have been used

  22. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 4 2) Replace right-most digit with a 1 3)This 1 is the “new value” (N) 1 2 If any red value to the right of N is >= N, it gets incremented by 1 2 2 1 1 3 3 4) Repeat step 3 until all red numbers have been used

  23. Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 4 2 1 1 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 3)This 1 is the “new value” (N) 1 2 If any red value to the right of N is >= N, it gets incremented by 1 2 1 3 4 2 1 3 4) Repeat step 3 until all red numbers have been used 3 1 0 2 4) Decrement all numbers by 1

  24. Use Permutation to swap bits 3 1 0 2 Obtained Permutation: Original Binary Data: 1 0 1 0 Encrypted Bit Array Data: 2 3 0 1

  25. Use Permutation to swap bits 3 1 0 2 Obtained Permutation: Original Binary Data: 1 0 1 0 Encrypted Bit Array Data: 1 2 3 0 1

  26. Use Permutation to swap bits 3 1 0 2 Obtained Permutation: Original Binary Data: 1 0 1 0 Encrypted Bit Array Data: 0 1 2 3 0 1

  27. Use Permutation to swap bits 3 1 0 2 Obtained Permutation: Original Binary Data: 1 0 1 0 Encrypted Bit Array Data: 0 1 1 2 3 0 1

  28. Use Permutation to swap bits 3 1 0 2 Obtained Permutation: Original Binary Data: 1 0 1 0 Encrypted Bit Array Data: 0 0 1 1 2 3 0 1

  29. Project Summary Use the principles of factoradics to: • Encrypt/Decrypt any binary file on the Windows platform • Generate keys to decrypt files Like a really long password stored in a text file

More Related