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Protoman Guest
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Posted: Sun Jul 30, 2006 9:11 am Post subject: Diffie-Hellman-Merkle Key Exchange Program |
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I'm writing a Diffie-Hellman-Merkle Key Exchange Program, and,
sometimes (I haven't figured out how to predict it yet), Alice's and
Bob's shared symmetric key are different! This shouldn't happen!
Code:
#include <iostream>
#include <cstdlib>
using std::cout;
using std::cin;
using std::endl;
using std::system;
long long Exp(const long long& base,long long exp)
{
long long i=1;
for(;i<exp;i++)
i*=base;
return i;
}
int main()
{
long long A,B;
long long base,mod;
for(;
{
cout << "Base: " << endl;
cin >> base;
cout << "Modulus: " << endl;
cin >> mod;
cout << "Alice, choose your secret number: " << endl;
cin >> A;
cout << "Bob, choose your secret number: " << endl;
cin >> B;
long long a=Exp(base,A)%mod;
long long b=Exp(base,B)%mod;
cout << "Alice's value: " << a << endl;
cout << "Bob's value: " << b << endl;
long long akey=Exp(b,A)%mod;
long long bkey=Exp(a,B)%mod;
cout << "Alice's key: " << akey << endl;
cout << "Bob's key: " << bkey << endl;
}
system("PAUSE");
return EXIT_SUCCESS;
}
Here's an link to explain DHM Key Exchange:
http://en.wikipedia.org/wiki/Diffie-Hellman
Thanks!!!! |
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Kai-Uwe Bux Guest
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Posted: Sun Jul 30, 2006 9:11 am Post subject: [OT] Re: Diffie-Hellman-Merkle Key Exchange Program |
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Protoman wrote:
| Quote: | I'm writing a Diffie-Hellman-Merkle Key Exchange Program, and,
sometimes (I haven't figured out how to predict it yet), Alice's and
Bob's shared symmetric key are different! This shouldn't happen!
Code:
#include <iostream
#include <cstdlib
using std::cout;
using std::cin;
using std::endl;
using std::system;
long long Exp(const long long& base,long long exp)
{
long long i=1;
for(;i<exp;i++)
i*=base;
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on topic remarks:
=================
If this loop overflows, you have undefined behavior.
You should use unsigned long long instead. Then it will wrapand give the
correct result mod 2^N where N is the bitlength.
However, even that will not do, for reasons explained below.
| Quote: | return i;
}
int main()
{
long long A,B;
long long base,mod;
for(;
{
cout << "Base: " << endl;
cin >> base;
cout << "Modulus: " << endl;
cin >> mod;
cout << "Alice, choose your secret number: " << endl;
cin >> A;
cout << "Bob, choose your secret number: " << endl;
cin >> B;
long long a=Exp(base,A)%mod;
|
more off topic remarks:
=======================
when you take the overflown result from Exp(base,A) and pass it to %mod, you
do not really compute the correct remainder because for x > 2^N, in general
x % mod != ( x % 2^N ) % mod
You need to either use a library for arbitrary precision integers or write a
function exp_mod( base, exponent, modulus ) that computes
base**exponent mod modulus
correctly.
| Quote: | long long b=Exp(base,B)%mod;
cout << "Alice's value: " << a << endl;
cout << "Bob's value: " << b << endl;
long long akey=Exp(b,A)%mod;
long long bkey=Exp(a,B)%mod;
cout << "Alice's key: " << akey << endl;
cout << "Bob's key: " << bkey << endl;
}
system("PAUSE");
return EXIT_SUCCESS;
}
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Also, your question is on the borderline to purely algorithmic problems. You
might want to ask in comp.programming instead.
Best
Kai-Uwe Bux |
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