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The major problem of private-key encryption is how to pass the key between Bob and Alice, without Eve listening (Figure 1). This problem was solved by Whitfield Diffie in 1975, who created the Diffie-Hellman method. With this method, Bob and Eve generate two random values, and perform some calculations (Figure 2 and Figure 3), and pass the result of the calculations to each other (Figure 4). Once these values have been received at either end, Bob and Alice will have the same secret key, which Eve cannot compute (without extensive computation).
Figure 1 How to pass the private key?
Figure 2 Diffie-Helman method
Figure 3 Diffie-Hellman process
Figure 4 Example Diffie-Hellman process For example, please try your own values:
A simple .NET program to calculate small values of G and n is [Click here to download of the solution]: using System;
namespace diffie
{
class Class1
{
public static Random r= new Random();
static void Main (string[] args)
{
long x,y,A,B,n,G,K1, K2 ;
G= 20;
n= 99;
x = random(10)+1;
y = random((int)x);
double val1= Math.Pow((double)G,(double)x);
double val2= Math.Pow((double)G,(double)y);
Math.DivRem((long)val1,n,out A);
Math.DivRem((long)val2,n,out B);
Math.DivRem((long)Math.Pow((double)B,(double)x),n,out K1);
Math.DivRem((long)Math.Pow((double)A,(double)y),n,out K2 );
Console.WriteLine("x is {0} and A is {1}",x,A);
Console.WriteLine("y is {0} and B is {1}",y,B);
Console.WriteLine("K1 is: " + K1);
Console.WriteLine("K2 is: " + K2 );
Console.ReadLine();
}
public static int random(int max)
{
try
{
return(r.Next(max));
}
catch {};
return(0);
}
}
}
which gives a sample run of: x is 6 and A is 64 It can be seen that the values of G and n (20 and 99, respectively) are relevantly small as larger values will typically overflow the calculations, as the Math.DivRem() method can only support long integers, whereas many more bits are required to support the large values involved, especially with the A and B to the power of x and y, respectively. A run of values of x and y between 1 and 3 shows that the values of K1 and K2 are the same for these values of G and n (the code for this is in Tutorial 4.10.4): x y A B K1 K2 1 1 20 20 20 20 1 2 20 4 4 4 1 3 20 80 80 80 2 1 4 20 4 4 2 2 4 4 16 16 2 3 4 80 64 64 3 1 80 20 80 80 3 2 80 4 64 64 3 3 80 80 71 71 The code is: using System;
namespace diffie
{
class Diffie
{
static void Main (string[] args)
{
long x,y,A,B,n,G,K1, K2 ;
G= 20;
n= 99;
Console.WriteLine("x\ty\tA\tB\tK1\tK2");
for (x=1;x<4;x++)
for (y=1;y<4;y++)
{
double val1= Math.Pow((double)G,(double)x);
double val2= Math.Pow((double)G,(double)y);
Math.DivRem((long)val1,n,out A);
Math.DivRem((long)val2,n,out B);
Math.DivRem((long)Math.Pow((double)B,(double)x),n,out K1);
Math.DivRem((long)Math.Pow((double)A,(double)y),n,out K2 );
Console.WriteLine("{0}\t{1}\t{2}\t{3}\t{4}\t{5}",x,y,A, B, K1, K2 );
}
Console.ReadLine();
}
}
}
Diffie-Hellman is used in many applications, such as in VPN (Virtual Private Networks), SSH, and secure FTP. The following shows a trace of a connection to a secure FTP site: STATUS:> Getting listing ""... Magic!!!! Hail to the Whitfield Diffie ... a true genius! Other related .NET articles I've written include:
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