High-level Diffie-Hellman key exchange

DiffieHellman

// public (primitive root) base¹, known to Alice, Bob, and Eve
const long G = 5;
// public (prime) modulus², known to Alice, Bob, and Eve
const long P = 23;

var aliceCalc = new Calc(6, G, P);
var bobCalc = new Calc(5, G, P);

// Alice's public key, known to Alice, Bob, and Eve. A = g^a mod p
long A = aliceCalc.GetPublicKey(bobCalc.OutgoingSharedKey);

// Bob's public key, known to Alice, Bob, and Eve. B = g^b mod p
long B = bobCalc.GetPublicKey(aliceCalc.OutgoingSharedKey);

System.Console.WriteLine($"Alice's secret key: {A}\nBob's secret key: {B}\nEve can only guess.");

class Calc
{
    private long _privateKey;

    public Calc(long privateKey, long primeBase, long primeModulus)
    {
        _privateKey = privateKey;
        PrimeBase = primeBase;
        PrimeModulus = primeModulus;
    }

    public long PrimeBase { get; }

    public long PrimeModulus { get; }

    public long OutgoingSharedKey => PrimeBase.PowMod(_privateKey, PrimeModulus);

    public long GetPublicKey(long incomingSharedKey) => incomingSharedKey.PowMod(_privateKey, PrimeModulus);
}

static class LongEx
{
    public static long PowMod(this long self, long i, long m) =>
        i == 1 ? self : ((long)System.Math.Pow(self, i)) % m;
}

// Footnotes (see https://brilliant.org/wiki/diffie-hellman-protocol)
// 1. The base G should be chosen so that G has large order
// 2. The prime P should be chosen so that the largest prime factor of P-1 is large,
//    in order to negate the Pohlig-Hellman algorithm