Register to reply

Help me make a very mathematical encryption algorithm

by Jamin2112
Tags: algorithm, encryption, mathematical
Share this thread:
Jamin2112
#1
Apr18-13, 01:02 AM
Jamin2112's Avatar
P: 909
Suppose I make an application with a password of max 20 characters -- no special characters and not case-sensitive. So that means there is a 1-to-1 correspondence between the set of all passwords P and the set S = {1, 2, ..., 3720 - 1, 3720}. A simple bijective function f:P-->S could be constructed. Then I want to construct another bijective function g:S-->T for some set T. Any ideas?
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
chiro
#2
Apr18-13, 01:17 AM
P: 4,572
Hey Jamin2112.

What properties do you want your bijective function to have?
Jamin2112
#3
Apr18-13, 02:16 AM
Jamin2112's Avatar
P: 909
Quote Quote by chiro View Post
Hey Jamin2112.

What properties do you want your bijective function to have?
Actually, it doesn't have to be bijective, now that I think about it. Could be merely injective.

Maybe take the binary representation of the numbers and have each of those digits correspond to parameters in a differential equation?

chiro
#4
Apr18-13, 02:18 AM
P: 4,572
Help me make a very mathematical encryption algorithm

What is the quantization scheme you want to use for the parameters and what is the state space for the DE model?
Jamin2112
#5
Apr18-13, 02:41 AM
Jamin2112's Avatar
P: 909
Quote Quote by chiro View Post
What is the quantization scheme you want to use for the parameters and what is the state space for the DE model?
Scratch that. I'm gonna need something simpler than a differential equation.

Let's assume the ints 1, 2, ..., 3720 are represented with 64 bits. Convert the binary representation of each to an 8 x 8 matrix of 0's and 1's. Then raise that matrix to, say, the 69th power. Now we have to assume that this makes for an injective function. Is that too much to assume?
chiro
#6
Apr18-13, 02:50 AM
P: 4,572
One small problem:

log_2(37^20) = 20*log_2(37) = 30*ln(37)/ln(2) = 104.1891 which means if you have a uniform distribution with those values, you will need at least 105 bits to store them.
Jamin2112
#7
Apr18-13, 02:59 AM
Jamin2112's Avatar
P: 909
Quote Quote by chiro View Post
One small problem:

log_2(37^20) = 20*log_2(37) = 30*ln(37)/ln(2) = 104.1891 which means if you have a uniform distribution with those values, you will need at least 105 bits to store them.
Make 'em 16 x 16 matrices. We've got a 256-bit machine.
chiro
#8
Apr18-13, 03:02 AM
P: 4,572
So what do you want your function to be exactly (given this 16x16 matrix)?
Jamin2112
#9
Apr18-13, 03:13 AM
Jamin2112's Avatar
P: 909
Quote Quote by chiro View Post
So what do you want your function to be exactly (given this 16x16 matrix)?
g(M) = M69 where M ε ℝ16x16

Lets assume that if the only possible M in the domain are those binary matrix representations of the numbers 1 through 3720, we have an injective function.


Register to reply

Related Discussions
Example of encryption key pair algorithm? Programming & Computer Science 1
Help With Pseudo Coded Algorithm for The Diamond-Square Algorithm Engineering, Comp Sci, & Technology Homework 0
Prime Number finding Algorithm.How can we make things go faster? General Math 20
Matlab, mathematical algorithm Math & Science Software 2
Mathematical algorithm Math & Science Software 1