Writing a code for decryption key.

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I have the following expression for calculating the decryption key in a Public Key Encryption System :

d = N^-1 mod LCM(p-1,q-1)

where N = p²q.

I wrote the follwing code to find d ,

C#

long long int gendecrypkey(long long int modulo,long long int p,long long int q)
    {
        long long int dk = 0;


        while(!(dk * modulo == fmod(1,lcm((p-1),(q-1)))))
        {
            ++dk ;
        }

        return dk;

    }

but is this the right way of finding d ? If not please suggest a C++ code for finding d.
Upon execution of this function the console wont show anything (blank).What could be the mistake?

[updated]

C#

sscrypto(long long int &publkey, long long int &privtkey,long long int &pq)
    {
        publickey = publkey =0;
        privatekey = privtkey = 0;
        long long int  p = genrndprimes(50,200);
        long long int q = genrndprimes(200,300);
        long long int n = (p*p)*q; //Modulus.
        long long int d = fmod((1/n),lcm(p-1,q-1)); //Problematic code
        pq = p*q;
        publkey =   publickey = n;
        privtkey = privatekey = d;
    }

Posted 11-Jun-13 16:10pm

compuknow

Updated 11-Jun-13 17:38pm

v3

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Ron Beyer · Answer 1 · 2013-06-11T16:20:00

Solution 1

Wouldn't it be

C++

fmod((1/(p*p*q)), lcm((p-1), (q-1)))

?

Also, you are getting a blank screen because your while loop never converges, so you are stuck in an infinite loop. I'm also not sure what the "modulo" value is based on the information you gave, so I can't really tell you if that part is right or wrong...

Posted 11-Jun-13 16:20pm

Ron Beyer

Updated 11-Jun-13 16:21pm

v2

Comments

compuknow 11-Jun-13 22:52pm

Are you asking the modulo in the function signature ? That modulo is p*p*q.
Any way this is a method which i had already tried "fmod((1/p*p*q),lcm((p-1),(q-1)))" but please understand i got 0 as the decryption key (in fact Always , generating p and q at random) , or is it something that I did not understand the formula properly ?

Ron Beyer 11-Jun-13 22:57pm

What is it that you are really trying to do here? Reverse engineer the private encryption key from a public key? This looks like RSA encryption, and if you are trying to brute force it then I hope you have years of processor time. If you are trying to decrypt data in a public key encryption system, you are supposed to give the public key with the encrypted data, the private key remains private... Not sure what you are really trying to do with the formula...

compuknow 11-Jun-13 23:12pm

No , I am not a cryptanalyst , infact i am new to cryptography. This is not at all RSA , its Schmidt - Samoa public key encryption , the article is in wikipedia (http://en.wikipedia.org/wiki/Schmidt-Samoa_cryptosystem).
I am trying to implement it using C++. According to the article , this is the way i should generate the Private key using the publickey (ie., N itself).

Ron Beyer 11-Jun-13 23:27pm

Ok, I read that and understand it now, you don't need a loop or anything at all, what you are doing is generating a public key and a private key. The public key (N) is p*p*q where P and Q are "distinct large primes". Its important that they are prime numbers, distinct, and large. You then generate the private key by using d = 1/N mod lcm(p-1, q-1). There should be no looping or modulus.

compuknow 11-Jun-13 23:32pm

Why do i get a zero if i am going by 1/N mod lcm(p-1,q-1) , i always get zero regardless of what p,q or n are. I tried this earlier.

Ron Beyer 11-Jun-13 23:36pm

what are the values you are using for p and q when you get zero? Where did you get the lcm function?

compuknow 11-Jun-13 23:40pm

p and q are random. I have updated my question. Please note that genrndprimes(a,b) is function which would generate prime numbers within a the range 'a' and 'b'.
I will give the values (i have to modify code.).

compuknow 11-Jun-13 23:47pm

The values for example are : p = 83 q = 241 publickey = 1660249 privatekey = 0 (the problem).

compuknow 11-Jun-13 23:37pm

I have updated my question with the method you suggest but i get zero as answer.

Ron Beyer 11-Jun-13 23:51pm

fmod takes two floating point values and returns a floating point value, if N, p or q are small enough, this returns a fractional value which casts back to zero in an integer. I would add some debug output statements and see what you get for p, q, and N so you can hand run it and get d.

compuknow 12-Jun-13 0:24am

How should I modify my code ?

Ron Beyer 12-Jun-13 0:39am

Add some printf statements to output the values of p, q, and N as soon as you calculate them. Make note of them in the output window and then run through the next step by hand (pencil/paper) to see what the issue might be.