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Diffie-Hellman Algorithm in C


  • A method of public-key encryption known as elliptic curve cryptography (ECC) is based on the algebraic structure of elliptic curves over finite fields.
  • To ensure equal security, ECC encryption requires fewer keys than non-ECC encryption (256-bit ECC security has the same security as 3072-bit RSA encryption).
  • Understanding the fundamentals of elliptic curves is crucial for understanding elliptic curve cryptography.
  • An equation of the type describes an elliptic curve, a planar algebraic curve.
    y^2 = x^3 + axe + b
  • where "a" denotes the x-coefficient and "b" denotes an expression constant.
  • It is not singular to the curve.
  • Thus, there are no peaks or self-intersections on the graph (if the coefficient array characteristic equals 2 or 3)
  • An elliptic curve typically resembles the image below.
  • When a straight line crosses the curve, an elliptic curve can nearly always intersect three locations.
  • The elliptic curve is symmetric about the x-axis, as you can see.
  • This characteristic is crucial to the elliptic curve method.

Algorithm Diffie-Hellman

  • The Diffie-Hellman technique creates a shared secret that may be utilised for confidential communication while exchanging data over public networks by using an elliptic curve to produce points and a private key to retrieve parameters.
  • we take only four variables into account for the algorithm's practical implementation and simplicity: prime figures P and G, as well as the two private values a and b, are the fundamental roots of P.
  • P and G are both open numbers. Users (like Alice and Bob) select private values a and b, create keys, and then publicly exchange them. The key is obtained by another party, who then creates a private key and encrypts it.

Step-by-step Guidelines

Public Keys Obtainable = P, GPublic Keys Obtainable = P, G  
Private key picked equals aPrivate key chosen = b  
produced key =x=Ga mod P.  produced key =Gb mod P = y  
Keys generated are traded  Keys generated are traded  
y = obtain key,x = get key  
private key produced = y a mod P = k a  private key produced = k b = P mod xb  

This is algebraically demonstrable.

k a = k b

In order to encrypt, the user now possesses a symmetric private key.

#include <stdio.h>
// Function to compute `i^t mod n`
int compute(int i, int t, int n)  {
    int q,z = 1;
    while (t> 0)  {
q= m % 2; 
        if (r == 1) {
z= (z*i) % n;  }
        a = i*i% n;
t= t / 2;}
    return y;}
// demonstrating the Diffie-Hellman algorithm in c language
int main()  {
    int f = 23;        // modulus
    int h = 5;        // base
    int i, j;    // `i` – Alice's secret key, `j` – Bob's secret key.
    int I, J;    // `I` – Alice's public key, `J` – Bob's public key
    // choose a secret integer for Alice's private key (only known to Alice)
i = 6;        // or, use `rand()`
    // Calculate Alice's public key (Alice will send `I` to Bob)
I = compute(h, i, f);
    // choose a secret integer for Bob's private key (only known to Bob)
j = 15;        // or, use `rand()`
    // Calculate Bob's public key (Bob will send `J` to Alice)
J = compute(h, j, f);
    // Alice and Bob Exchange their public key `I` and `J` with each other
    // Find secret key
    int keyI = compute(J, i, f);
    int keyJ = compute(I, j, f);
printf("Alice's secret key is %d\nBob's secret key is %d", keyI, keyJ);
    return 0;


Alice’s secret key is 2
Bob’s secret key is 2
  • The actual algorithm is really basic. Here is an example protocol with the secret value indicated in red, for when Alice wishes to communicate a secret with Bob.
  • In order to allow the resultant shared secret to have any value between 1 and p-1, Alice and Bob decide to use prime p = 23 and base g = 5. A = ga mod p (A = 56 mod 23 = 8) is the message Alice delivers to Bob using the secret number a = 6.
  • Alice transmits B = gb mod p (B = 515 mod 23 = 19) after Bob selects a secret integer of size b = 15 for him.
  • For Alice, s = Ba mod p equals 2 (s = 196 mod 23).
  • Bob discovers the formula s = Ab mod p (s = 815 mod 23 = 2).
  • Bob and Alice have a secret (number 2) The result Alice receives in step four is the same result Bob received in step five.
  • Bob does the math
  • Gave Ab mod p equals (ga mod p)b mod p and mod p.
  • Alice does the math
  • gba mod p = ba mod p = (gb mod p)a mod p
  • To exchange encryption keys for use with symmetric encryption techniques like AES, the Diffie-Hellman algorithm is typically utilised. Note that no data is sent while keys are being exchanged.
  • Here, the key is jointly created by the two parties.