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Help me make a very mathematical encryption algorithm 
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#1
Apr1813, 01:02 AM

P: 909

Suppose I make an application with a password of max 20 characters  no special characters and not casesensitive. So that means there is a 1to1 correspondence between the set of all passwords P and the set S = {1, 2, ..., 37^{20}  1, 37^{20}}. 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?



#2
Apr1813, 01:17 AM

P: 4,572

Hey Jamin2112.
What properties do you want your bijective function to have? 


#3
Apr1813, 02:16 AM

P: 909

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


#4
Apr1813, 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?



#5
Apr1813, 02:41 AM

P: 909

Let's assume the ints 1, 2, ..., 37^{20} 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? 


#6
Apr1813, 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. 


#8
Apr1813, 03:02 AM

P: 4,572

So what do you want your function to be exactly (given this 16x16 matrix)?



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