# Cellular Encryption(MS PowerPoint presentation)

AI and Robotics

Dec 1, 2013 (4 years and 7 months ago)

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Cellular Encryption

CREU Project

Team:

Alburn Brown

Orkun Kaya

Isaac Rieksts

Eric Thorpe

2004

Kutztown University

2

Overview

Construct software simulation

Compare 3 cellular encryption algorithms

Choose the best one

Implement it in hardware

2004

Kutztown University

3

Background :: Cellular
Computation

Cellular Automata

Cellular Automata with Shadow Cells

Hybrid Cellular Automata

Integer Functions

Cellular Encryption

2004

Kutztown University

4

Cellular Automata

John von Neumann

Uniform cells

“Peer Pressure Automata”

Uniform transition function

Turing Machine computing power

2004

Kutztown University

5

Cellular Automata

Need to compute integer functions

Limitation of classic CAs

Shadow cells enable integer computation

Wasted memory

2004

Kutztown University

6

Hybrid Cellular Automata

Relaxing the uniform transition rule

Memory savings

All integer functions computable

2004

Kutztown University

7

Integer Functions

Block cipher = integer function

Example: RSA

How many integer functions?

How many identity avoiding functions?

2004

Kutztown University

8

Block Cipher = Integer Function

An integer can represent any text string

Let p represent a given plaintext

Let c represent the corresponding ciphertext

Then f(p) = c represents the encryption

And f
-
1
(c) = p represents the decryption

Both f and f
-
1

are integer functions

2004

Kutztown University

9

RSA is an integer function

Encryption: f(p) = p
e

mod n

e is encryption key

n = p*q

p & q, two very large primes

Decryption: f
-
1
(c) = c
d

mod n

d is decryption key

e*d mod
f
(n) = 1

f
(n) is Euler totient function

f
(n) = (p
-
1)*(q
-
1)

Clearly an integer function

2004

Kutztown University

10

How Many Integer Functions?

Consider all 1
-
1 and onto functions

Let range be 0 to N
-
1.

Each function is one arrangement of integers
0 to N
-
1, i.e., a permutation.

Number of functions = number of
permutations

How many?
N!

2004

Kutztown University

11

How Many Are Identity
Avoiding?

Want to avoid:

f(p) = p, for all p within the range

We call such functions “identity avoiding”

How many such functions?

1
-
1, onto, identity avoiding functions

Over the integers: 0 to N
-
1

N! / e

2004

Kutztown University

12

Identity Avoiding Integer
Functions

Over the integers 0 to M
-
1

There are :: N! / e

e is a constant

Order of magnitude ::
O
(N!)

2004

Kutztown University

13

Cellular Encryption

Integers 0 to 2
k

1 represent:

Plain text

Cipher text

Choose at random from 2
k
!/e possibilities

k cells of hybrid CA

Will encrypt

By computing chosen integer function

Each cell computes one Boolean function

2004

Kutztown University

14

Encryption Cell Details

Represent integer in binary

3 bit example

Base 10:: f(3) = 5

Binary:: f(011) = 101

Work is spread among 3 cells

Cell
0
:: f
0
(
0
11) = 1

Cell
1
:: f
1
(0
1
1) = 0

Cell
2
:: f
2
(01
1
) = 1

2004

Kutztown University

15

Integer

Boolean

An integer function

base 10 & binary:

f(0) = 3

f(000) = 011

f(1) = 6

f(001) = 110

f(2) = 7

f(010) = 111

f(3) = 5

f(011) = 101

f(4) = 2

f(100) = 010

f(5) = 1

f(101) = 001

f(6) = 0

f(110) = 000

f(7) = 4

f(111) = 100

2004

Kutztown University

16

Integer

Boolean

Cell by cell

f(000) =
0
1
1

f
0
(000) =
0

f
1
(000) =
1

f

2
(000) =
1

f(001) =
1
1
0

f
0
(001) =
1

f
1
(001) =
1

f
2
(001) =
0

f(010) =
1
1
1

f
0
(010) =
1

f
1
(010) =
1

f
2
(010) =
1

f(011) =
1
0
1

f
0
(011) =
1

f
1
(011) =
0

f
2
(011) =
1

f(100) =
0
1
0

f
0
(100) =
0

f
1
(100) =
1

f
2
(100) =
0

f(101) =
0
0
1

f
0
(101) =
0

f
1
(101) =
0

f
2
(101) =
1

f(110) =
0
0
0

f
0
(110) =
0

f
1
(110) =
0

f
2
(110) =
0

f(111) =
1
0
0

f
0
(111) =
1

f
1
(111) =
0

f
2
(111) =
0

2004

Kutztown University

17

Hardware Implementation

Plain text is k bits long

There are k cells

Each cell gets k bits of input

Each cell computes its own Boolean function

Together cells compute k
-
bit integer function

THE END

brow8558@kutztown.edu

kaya0015@kutztown.edu

riek7902@kutztown.edu

thor2668@kutztown.edu

rieksts@kuztown.edu