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[Java] An Idea - Polynomial Encryption

 
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Jorg hi
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PostPosted: Fri Aug 27, 2010 6:53 pm    Post subject: [Java] An Idea - Polynomial Encryption Reply with quote
I started reading some Alg2 stuff and thought of creating an encryption method based of Polynomial Equations to the outputs would have finite lengths. But my question is, would using this technique with a key work well?

I know it can be easily brute forced though by changing the key.

Equation Used:
Trinomial Encryption -> Output = (x+key)² + (x+key) + 1
Trinomial Decryption -> Output = (x+key)² + (x+key) + 1

Example:
Code:
    public static void PolyEnc(String input, int key){
        String Output = "";
        //Y = (x+key)² + (x+key) + 1
        for (int i = 0;i<input.length();i++){
            int coded = ((Integer.valueOf(input.charAt(i)))+key)^2 + ((Integer.valueOf(input.charAt(i)))+key) + 1;
            Output += "[" + String.valueOf(coded) + "]";
        }
        System.out.println(Output);
    }


I'm working on a decryption method. And I got some tables to start with it thats based of the trinomial.

Code:
--- chr = 1, key = 1; 7
--- chr = 2, key = 1; 10
--- chr = 3, key = 1; 13


--- chr = 1, key = 2; 10
--- chr = 2, key = 2; 13
--- chr = 3, key = 2; 16

--- chr = 1, key = 3; 13
--- chr = 2, key = 3; 16
--- chr = 3, key = 3; 19

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Last edited by Jorg hi on Sat Aug 28, 2010 8:35 am; edited 1 time in total
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tombana
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PostPosted: Sat Aug 28, 2010 6:20 am    Post subject: Re: [Java] An Idea - Polynomial Encryption Reply with quote
Jorghi wrote:
Trinomial Encryption -> Output = (x+key)2 + (x+key) + 1
Code:
int coded = ((Integer.valueOf(input.charAt(i)))+key)*2 + (

Isn't that code the same as (x+key)*3 + 1. Didn't you mean (x+key)² ?
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Jorg hi
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PostPosted: Sat Aug 28, 2010 8:14 am    Post subject: Reply with quote
Oh I didn't see that.
Thanks. Thats why the decryption had problems.

Code:
    public static void PolyEnc2(int input, int key){
        String Output = "";
        //Y = ((x+key)2 + (x+key) + 1) + x^key
        int coded = ((input+key)^2 + (input+key) + 1) + input^key;
        Output += "[" + String.valueOf(coded) + "]";
        System.out.println(Output);
    }


Edit: I removed the trinomial. It outputs the same values for different numbers. I'm adding a linear equation.

//Y = ((x+key)2 + (x+key) + 1) * ((x * key) + key)
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tombana
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PostPosted: Sat Aug 28, 2010 12:32 pm    Post subject: Reply with quote
Jorghi wrote:

int coded = ((input+key)^2 + (input+key) + 1) + input^key;

I don't know about Java, but in C the ^ operator is the xor operator. So in C (input+key)^2 would xor the output of (input+key) with 2. Might be different for Java though.
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