Usually it's hard to write a secure code without mechanisms (e.g. AES-256, Rijndael-256). But we can provide secure transfer of data, leaning on algorithm Diffie-Hellman.
Consept on Diffie-Hellman key exchange:
- 2 people wants to communicate using strong security. They have private key, like word ("fish") or letter ("D"). But need to turn it into public key
- In common space they decide to choose certain Mathematical (cryptographic) function: a^b mod n
- a meens "D", b and n choosing together, general for 2 people
- The last one: fuction result is sent to each other and decrypt by reverse Mathematical function.
Let's see the code!
void crypt(int p, int g, int x, string in, vector <pair<int, int> > &mas) {
int y = power(g, x, p);
cout << "Public key (p,g,y) = " << "(" << p << "," << g << "," << y << ")" << endl;
cout << "Private key x = " << x << endl;
cout << "\nChipter text:" << endl;
for (unsigned int i = 0; i < size(in); i++) {
int m = in[i] + 256;
if (m > 0) {
cout << (char)m;
int k = rand() % (p - 2) + 1; // 1 < k < (p-1)
int a = power(g, k, p);
int b = mul(power(y, k, p), m, p);
mas.push_back(make_pair(a, b));
}
}
cout << endl;
}
You see p, g, y = a, b, n. And x - result of encrypted function (public key). m - internal value for counting each bits of message (m), which is encrypted with a private key.
crypt(593, 123, x, message_in, cypher); - example of call our function.
And being on the recipient's spot, we need to decrypt this message (m).
void decrypt(int p, int x, vector <pair<int, int> > mas, string &out) {
cout << "\nDecrypted text:" << endl;
unsigned int i = 0;
while (i < mas.size()) {
int a = 0;
int b = 0;
a = mas[i].first;
b = mas[i].second;
if (a != 0 && b != 0) {
cout << a << " " << b << endl;
int deM = mul(b, power(a, p - 1 - x, p), p);// m=b*(a^x)^(-1)mod p =b*a^(p-1-x)mod p
char m = static_cast<char>(deM);
out.push_back(m);
i++;
}
}
cout << endl;
}
decrypt(593, x, cypher, messagge_out); - similarly for calling decrypt function. Here we already don't need all parametres - only private key.
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