# Diffie Hellman

Hard

0.0% Acceptance

Diffie-Hellman key exchange.

Alice and Bob use Diffie-Hellman key exchange to share secrets. They

start with prime numbers, pick private keys, generate and share public

keys, and then generate a shared secret key.

## Step 0

The test program supplies prime numbers p and g.

## Step 1

Alice picks a private key, a, greater than 1 and less than p. Bob does

the same to pick a private key b.

## Step 2

Alice calculates a public key A.

```
A = g**a mod p
```

Using the same p and g, Bob similarly calculates a public key B from his

private key b.

## Step 3

Alice and Bob exchange public keys. Alice calculates secret key s.

```
s = B**a mod p
```

Bob calculates

```
s = A**b mod p
```

The calculations produce the same result! Alice and Bob now share

secret s.