Implement Diffie-Hellmen Key exchange Method in c.

Introduction:

The first published public-key algorithm appeared in the seminal paper by Diffie and Hillman that defined public-key cryptography and is generally referred to as Diffie-Hillman key exchange.

The purpose of the algorithm is to enable two users to securely exchange a key that can then be used for subsequent symmetric encryption of messages. Its purpose is limited to exchange of secret value only.

The Diffie-Hillman algorithm depends for its effectiveness on the difficulty of computing discrete logarithms.

There are two publicly known numbers: a prime number q and an integer α that is primitive root of q.

Suppose the users A and B wish to exchange a key.

User A selects a random integer X_A < q and computes Y_{A =} α^XA mod q.

Similarly User B selects indepently a random integer X_B< q and computes Y_B = α^XB mod q.

Each side keeps X value Private and makes the Y value publicly available to other side.

User A computes the key as K=YB^XA mod q and user B computes K=YA^XB mod q.

We need to prove that K calculated on both side are equal.

K=YB^XA mod q

   = (α^XA mod q) ^XA mod q

=(α^XB )^XA  mod q

   =α^XBXA  mod q

=(α^XA )^XB  mod q

=(α^XA mod q)^XB  mod q

   = YA^XB mod q

 

C code:

// Diffie-Hillman

#include<stdio.h>

#include<conio.h>

#include<math.h>

long int power(long int a, long int j, long int c)

{

            long int f,i;

            f=1;

            for(i=1;i<=j;i++)

            {

                        f=(f*a)%c;

            }

            f=f%c;

            return f;

}

void main()

{

            long int q,alpha,xa,xb,ya,yb,key1,key2,ya1,yb1;

            clrscr();

            {

                        printf("enter the value of q:");

                        scanf("%ld",&q);

                        printf("enter the value of alpha:");

                        scanf("%ld",&alpha);

                        if(alpha<q)

                        {

                                    printf("enter the value of xa:");

                                    scanf("%ld",&xa);

                                    printf("enter the value of xb:");

                                    scanf("%ld",&xb);

                                    ya=(power(alpha,xa,q));

                                    printf("\nvalue of ya is:%ld",ya);

                                    yb=power(alpha,xb,q);

                                    printf("\nvalue of yb is:%ld",yb);

                                    key1=power(yb,xa,q);

                                    printf("\nvalue of key is:%ld",key1);

                                    key2=power(ya,xb,q);

                                    printf("\nvalue of key is:%ld",key2);

                        }

                        else

                        {

                                    printf("\n no result");

                        }

                        getch();

                        }

}

 

Output:

 

THANK YOU!!!!