Data Encryption Chris Mraovich Overview Purpose of Encryption
![Data Encryption Chris Mraovich Data Encryption Chris Mraovich](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-1.jpg)
![Overview • Purpose of Encryption • Permutations Bases and Factoradics • Project Summary Overview • Purpose of Encryption • Permutations Bases and Factoradics • Project Summary](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-2.jpg)
![Purpose of Encryption Purpose of Encryption](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-3.jpg)
![Protecting Digital Content • DVDs use CSS (Content Scramble System) • Weak Algorithm -Cracked Protecting Digital Content • DVDs use CSS (Content Scramble System) • Weak Algorithm -Cracked](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-4.jpg)
![Protecting Digital Content Arcade Printed Circuit Boards • Capcom Play System 2 (CPS 2) Protecting Digital Content Arcade Printed Circuit Boards • Capcom Play System 2 (CPS 2)](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-5.jpg)
![Protecting Digital Content Why use encryption on an arcade board? 1. ROM chips can Protecting Digital Content Why use encryption on an arcade board? 1. ROM chips can](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-6.jpg)
![Permutations, Bases, and Factoradics Permutations, Bases, and Factoradics](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-7.jpg)
![Permutations Goal is to rearrange bits into a different pattern Original Form: 1 0 Permutations Goal is to rearrange bits into a different pattern Original Form: 1 0](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-8.jpg)
![Bases and Factoradics Factoradic – mixed radix numbering system that uses multiple bases to Bases and Factoradics Factoradic – mixed radix numbering system that uses multiple bases to](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-9.jpg)
![Order & Total Permutations Order – number of objects (N) Total number of permutations Order & Total Permutations Order – number of objects (N) Total number of permutations](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-10.jpg)
![Total Permutations of order 4 Int Factoradic Permutation 0 1 2 3 4 5 Total Permutations of order 4 Int Factoradic Permutation 0 1 2 3 4 5](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-11.jpg)
![Bases – Generate Factoradic Base 10 Base 2 20 10100 Write 2010 in Base Bases – Generate Factoradic Base 10 Base 2 20 10100 Write 2010 in Base](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-12.jpg)
![From Base 2 to Factoradic Generalization of Base 2 Expansion ( 2 x 23) From Base 2 to Factoradic Generalization of Base 2 Expansion ( 2 x 23)](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-13.jpg)
![Factoradic Number System Factoradic Expansion ( 4 x 3!) + (C ( 3 x Factoradic Number System Factoradic Expansion ( 4 x 3!) + (C ( 3 x](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-14.jpg)
![Factoradic Number System Write 2010 in Factoradic notation (E 5 x 24) + (D Factoradic Number System Write 2010 in Factoradic notation (E 5 x 24) + (D](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-15.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-16.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-17.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-18.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-19.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-20.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-21.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-22.jpg)
![Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-23.jpg)
![Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-24.jpg)
![Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-25.jpg)
![Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-26.jpg)
![Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-27.jpg)
![Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-28.jpg)
![Project Summary Use the principles of factoradics to: • Encrypt/Decrypt any binary file on Project Summary Use the principles of factoradics to: • Encrypt/Decrypt any binary file on](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-29.jpg)
- Slides: 29
![Data Encryption Chris Mraovich Data Encryption Chris Mraovich](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-1.jpg)
Data Encryption Chris Mraovich
![Overview Purpose of Encryption Permutations Bases and Factoradics Project Summary Overview • Purpose of Encryption • Permutations Bases and Factoradics • Project Summary](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-2.jpg)
Overview • Purpose of Encryption • Permutations Bases and Factoradics • Project Summary
![Purpose of Encryption Purpose of Encryption](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-3.jpg)
Purpose of Encryption
![Protecting Digital Content DVDs use CSS Content Scramble System Weak Algorithm Cracked Protecting Digital Content • DVDs use CSS (Content Scramble System) • Weak Algorithm -Cracked](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-4.jpg)
Protecting Digital Content • DVDs use CSS (Content Scramble System) • Weak Algorithm -Cracked by Jon Johansen in 1999
![Protecting Digital Content Arcade Printed Circuit Boards Capcom Play System 2 CPS 2 Protecting Digital Content Arcade Printed Circuit Boards • Capcom Play System 2 (CPS 2)](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-5.jpg)
Protecting Digital Content Arcade Printed Circuit Boards • Capcom Play System 2 (CPS 2) -Used in mid 1990 s for 2 D games • Uses encryption on program ROM chips • Graphic ROM chips are not encrypted • Cracked by team
![Protecting Digital Content Why use encryption on an arcade board 1 ROM chips can Protecting Digital Content Why use encryption on an arcade board? 1. ROM chips can](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-6.jpg)
Protecting Digital Content Why use encryption on an arcade board? 1. 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
![Permutations Bases and Factoradics Permutations, Bases, and Factoradics](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-7.jpg)
Permutations, Bases, and Factoradics
![Permutations Goal is to rearrange bits into a different pattern Original Form 1 0 Permutations Goal is to rearrange bits into a different pattern Original Form: 1 0](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-8.jpg)
Permutations Goal is to rearrange bits into a different pattern Original Form: 1 0 1 1 Encrypted Form: 1 1 0 1 Permutation – rearrangement of a set of objects
![Bases and Factoradics Factoradic mixed radix numbering system that uses multiple bases to Bases and Factoradics Factoradic – mixed radix numbering system that uses multiple bases to](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-9.jpg)
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 Generate Factoradic Obtain permutation from factoradic Use permutation to rearrange bits
![Order Total Permutations Order number of objects N Total number of permutations Order & Total Permutations Order – number of objects (N) Total number of permutations](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-10.jpg)
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
![Total Permutations of order 4 Int Factoradic Permutation 0 1 2 3 4 5 Total Permutations of order 4 Int Factoradic Permutation 0 1 2 3 4 5](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-11.jpg)
Total Permutations of order 4 Int Factoradic Permutation 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 {0000} {0010} {0100} {0110} {0200} {0210} {1000} {1010} {1100} {1110} {1200} {1210} {2000} {2010} {2100} {2110} {2200} {2210} {3000} {3010} {3100} {3110} {3200} {3210} (0123) (0132) (0213) (0231) (0312) (0321) (1023) (1032) (1203) (1230) (1302) (1320) (2013) (2031) (2103) (2130) (2301) (2310) (3012) (3021) (3102) (3120) (3201) (3210) • 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
![Bases Generate Factoradic Base 10 Base 2 20 10100 Write 2010 in Base Bases – Generate Factoradic Base 10 Base 2 20 10100 Write 2010 in Base](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-12.jpg)
Bases – Generate Factoradic Base 10 Base 2 20 10100 Write 2010 in Base 2 Multi-Base Factoradic 3100 24 2 3 2 2 2 1 2 0 (16) (8) 1 0 (4) (2) (1) 1 0 0 Expand the Binary Number (12 x 24) + (0 ( 2 x 23) + (1 ( 2 x 22) + (0 ( 2 x 21) + (0 ( 2 x 20) = 2010
![From Base 2 to Factoradic Generalization of Base 2 Expansion 2 x 23 From Base 2 to Factoradic Generalization of Base 2 Expansion ( 2 x 23)](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-13.jpg)
From Base 2 to Factoradic Generalization of Base 2 Expansion ( 2 x 23) + (C ( 2 x 22) + (B ( 2 x 21) + (A ( 2 x 2 0) … (E 2 x 24) + (D A 2, B 2, C 2, D 2, E 2 are all numbers in base 2 (0 or 1) 2 n are powers of 2 What Changes : 1. ) The bases of A 2, B 2, C 2, D 2, E 2 increase from right to left 2. ) 2 n n! Factoradic Expansion ( 4 x 3!) + (C ( 3 x 2!) + (B ( 2 x 1!) + (A ( 1 x 0!) … (E 5 x 4!) + (D (Mixed Radix - multiple bases used)
![Factoradic Number System Factoradic Expansion 4 x 3 C 3 x Factoradic Number System Factoradic Expansion ( 4 x 3!) + (C ( 3 x](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-14.jpg)
Factoradic Number System Factoradic Expansion ( 4 x 3!) + (C ( 3 x 2!) + (B ( 2 x 1!) + (A ( 1 x 0!) … (E 5 x 4!) + (D Simplify Factorials (E 5 x 24) + (D ( 4 x 6) + (C ( 3 x 2) + (B ( 2 x 1) + (A ( 1 x 1) 0 1 2 3 4 0 1 2 3 0 1 2 0 1 0 Since A, B, C, D, and E have different bases, they have different ranges of valid values
![Factoradic Number System Write 2010 in Factoradic notation E 5 x 24 D Factoradic Number System Write 2010 in Factoradic notation (E 5 x 24) + (D](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-15.jpg)
Factoradic Number System Write 2010 in Factoradic notation (E 5 x 24) + (D ( 4 x 6) + (C ( 3 x 2) + (B ( 2 x 1) + (A ( 1 x 1) 0 1 2 3 4 0 1 2 3 0 1 2 0 1 0 (3 x 3!) + (1 ( x 2!) + (0 ( x 1!) + (0 ( x 0!) = (3 x 6) + (1 ( x 2) + (0 ( x 1) = 20 Final Factoradic for 2010: 3 1 0 0
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-16.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-17.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-18.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 1
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-19.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 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
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-20.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 1 3)This 1 is the “new value” (N) 12 If any red value to the right of N is >= N, it gets incremented by 1
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-21.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 1 3)This 1 is the “new value” (N) 12 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
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-22.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 1 3)This 1 is the “new value” (N) 12 If any red value to the right of N is 21 3 >= N, it gets incremented by 1 4) Repeat step 3 until all red numbers have been used
![Obtain Permutation from Factoradic Initial Factoradic 3 1 0 0 1 Increment every digit Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-23.jpg)
Obtain Permutation from Factoradic Initial Factoradic: 3 1 0 0 1) Increment every digit by 1 4 2 1 1 2) Replace right-most digit with a 1 4 2 1 3)This 1 is the “new value” (N) 1 If any red value to the right of N is 21 >= N, it gets incremented by 1 4 21 4) Repeat step 3 until all red numbers have been used 4) Decrement all numbers by 1 3 1 0 2 1 2 3 3
![Use Permutation to swap bits Obtained Permutation 3 1 0 2 Original Binary Data Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-24.jpg)
Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: 1 0 Encrypted Bit Array Data: 0 1 2 3
![Use Permutation to swap bits Obtained Permutation 3 1 0 2 Original Binary Data Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-25.jpg)
Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: 1 0 Encrypted Bit Array Data: 1 0 1 2 3
![Use Permutation to swap bits Obtained Permutation 3 1 0 2 Original Binary Data Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-26.jpg)
Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: 1 0 Encrypted Bit Array Data: 0 0 1 1 2 3
![Use Permutation to swap bits Obtained Permutation 3 1 0 2 Original Binary Data Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-27.jpg)
Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: 1 0 Encrypted Bit Array Data: 1 0 0 1 1 2 3
![Use Permutation to swap bits Obtained Permutation 3 1 0 2 Original Binary Data Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data:](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-28.jpg)
Use Permutation to swap bits Obtained Permutation: 3 1 0 2 Original Binary Data: 1 0 Encrypted Bit Array Data: 1 0 0 1 2 3
![Project Summary Use the principles of factoradics to EncryptDecrypt any binary file on Project Summary Use the principles of factoradics to: • Encrypt/Decrypt any binary file on](https://slidetodoc.com/presentation_image_h/22b355bf43337796bdaa9b813776333b/image-29.jpg)
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
Chris mraovich
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