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tidmiste
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I was just using three digit numbers for examples, but they could be two digit numbers or even one digit numbers. I will use an example here.

I will encrypt the phrase "We are at the inn."

Let's let the letters equal:
Code:
 
A=21
E=32
H=33
I=41
N=44
R=62
T=64
W=71


That will be Key 1. Now the encryption method would represent Key 2.
Code:
 
y1=x-1
y2=2x
y3=2x-2

(y#- # is the placement of the equation in the list.)


Now, to encrypt, I would send each letter through the equations, first letter going through the first equation, the second through the second, the third in the third, the fourth in the first, and so on.
Code:
 
WE ARE AT THE INN
W=(71) - 1=70
E=2 x (32)=64
A=2 x (21) - 2=40
R=(62) - 1=61
E=2 x (32)=64
A=2 x (21) - 2=40
T=(64) - 1=63
T=2 x (64)=128
H=2 x (33) - 2=64
E=(32) - 1=31
I=2 x (41)=82
N=2 x (44) - 2=86
N=(44) - 1=43


70644 06164 40631 28643 18286 43000
As you can see, this wasn't a very good example because both the first and second E and first and second A were in the same position in the equation list, therefore having the same numbers. It is easily untraceable though with the five number groups. It can still be spotted and analyzed, but without the key, it won't do much to help, except maybe give the cryptanalyst the number of equations. However, as shown with the T's back to back, the numbers aren't always the same, and it's possible that two letters may equal the same value.

Now for decryption. It's just as simple as long as you have both of the keys. You could separate it first by bigrams. So it would end up like:
Code:
 
70/64/40/61/64/40/63/12/86/43/18/28/64/30

Here's the kicker. The recipient would know immediately that this isn't the correct message, because there is no way any of the numbers would equal 12, so he could easily find out that it's a trigram in that instance, and then make the rest bigrams, changing the message to this:
Code:
 
70/64/40/61/64/40/63/128/64/31/82/86/43

Then, after this separation, all the numbers are sent through the equations, but in the y value instead of the x. Once you're done, it is easily readable.

For nulls in this example, you could use "18", because, even if they used the trigram rule above, it would rule out the number as a whole because no number going through those equations would be over 142.

Hopefully that clears things up.

(PS: I'm not sure if I said it, but it is not mod-1000. Also, it isn't strictly limited to using prime numbers, as you can see with the list of values for letters. I kind of dodged it, it seemed. Sorry.)
Ancient chinese wise man once told me...
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