Diffie Hellman Key exchange algorithm Implementation in C

Diffie Hellman algorithm is a public-key algorithm used to establish a shared secret that can be used for secret communications while exchanging data over a public network. 

It is primarily used as a method of exchanging cryptography keys for use in symmetric encryption algorithms. It was Proposed in 1976 by Whitfield Diffie and Martin Hellman. Diffie-Hellman is currently used in many protocols like Secure Sockets Layer (SSL)/Transport Layer Security (TLS), Secure Shell (SSH), Internet Protocol Security (IPSec), Public Key Infrastructure (PKI).

Steps of Diffie Hellman key exchange Algorithm

  1.      Requires two large numbers, one prime (P), and (G), a primitive root of P

  2.      P and G are both publicly available numbers

a.       P is at least 512 bits

  3.      Users pick private values a and b

  4.      Compute public values

a.       x = g^a mod p

b.      y = g^b mod p

  5.      Public values x and y are exchanged

  6.      Compute shared, private key

a.       k_a = y^amod p

b.      k_b = x^bmod p

c.       Algebraically it can be shown that k_a = k_b 

Users now have a symmetric secret key to encrypt.

Example

1. Alice and Bob get public numbers
1. P = 23, G = 9
2. Alice and Bob compute public values
3. X = 94 mod 23 = 6561 mod 23 = 6
4. Y = 93 mod 23 ⁼ 729 mod 23    = 16
5. Alice and Bob exchange public numbers
2. Alice and Bob compute symmetric keys
1. k_a = y^a mod p = 16⁴ mod 23 = 9
2. k_b = x^b mod p = 63 mod 23 = 9

            3.       9 is the shared secret.

Implementing the Diffie Hellman Key exchange algorithm in C Program

/* this program calculates the Key for two persons using the Diffie Hellman Key exchange algorithm */ #include<stdio.h> long int power(int a,int b,int mod) { long long int t; if(b==1) return a; t=power(a,b/2,mod); if(b%2==0) return (t*t)%mod; else return (((t*t)%mod)*a)%mod; } long long int calculateKey(int a,int x,int n) { return power(a,x,n); } int main() { int n,g,x,a,y,b; // both the persons will be agreed upon the common n and g printf("Enter the value of n and g : "); scanf("%d%d",&n,&g); // first person will choose the x printf("Enter the value of x for the first person : "); scanf("%d",&x); a=power(g,x,n); // second person will choose the y printf("Enter the value of y for the second person : "); scanf("%d",&y); b=power(g,y,n); printf("key for the first person is : %lld\n",power(b,x,n)); printf("key for the second person is : %lld\n",power(a,y,n)); return 0; }

Output will be

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