Diffie Hellman Key exchange algorithm Implementation in C

Diffie Hellman Key exchange algorithm:

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. 

Diffie Hellman Key exchange algorithm

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

.       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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