Implement challenge 33 Diffie-Hellman

src/set5.rs

@@ -1,3 +1,67 @@
+use crate::rsa;
+use num_bigint::{BigUint, RandBigInt, ToBigUint};
+use rand::Rng;
+use std::fs;
+
 pub fn challenge33() {
-    println!("[xxxx] Challenge 33: now we talking!");
+    #![allow(non_snake_case)]
+
+    fn simple_diffie_hellman() {
+        let mut rng = rand::thread_rng();
+
+        // Set a variable "p" to 37 and "g" to 5.
+        let p: u32 = 37;
+        let g: u32 = 5;
+
+        // Generate "a", a random number mod 37. Now generate "A", which is "g" raised to the "a"
+        // power mode 37 --- A = (g**a) % p.
+        let a: u32 = rng.gen::<u32>() % p;
+        let A = rsa::expmod(g, a, p);
+
+        // Do the same for "b" and "B".
+        let b: u32 = rng.gen::<u32>() % p;
+        let B = rsa::expmod(g, b, p);
+
+        // "A" and "B" are public keys. Generate a session key with them; set "s" to "B" raised to
+        // the "a" power mod 37 --- s = (B**a) % p.
+        let s = rsa::expmod(B, a, p);
+
+        // Do the same with A**b, check that you come up with the same "s".
+        let s_ = rsa::expmod(A, b, p);
+
+        assert_eq!(s, s_, "crypto is broken");
+        // To turn "s" into a key, you can just hash it to create 128 bits of key material (or
+        // SHA256 it to create a key for encrypting and a key for a MAC).
+    }
+
+    fn serious_diffie_hellman() {
+        let mut rng = rand::thread_rng();
+
+        let s = fs::read_to_string("data/33.txt").expect("run from git root dir");
+        let b: Vec<u8> = s
+            .chars()
+            .filter(|c| *c != '\n')
+            .map(|c| c.to_digit(16).unwrap().try_into().unwrap())
+            .collect();
+        let p = BigUint::from_radix_be(&b, 16).unwrap();
+        let g = 2_u8.to_biguint().unwrap();
+
+        let a = rng.gen_biguint_below(&p);
+        let A = g.modpow(&a, &p);
+
+        let b = rng.gen_biguint_below(&p);
+        let B = g.modpow(&b, &p);
+
+        let s = B.modpow(&a, &p);
+        let s_ = A.modpow(&b, &p);
+        assert_eq!(s, s_, "crypto is broken");
+    }
+
+    simple_diffie_hellman();
+    serious_diffie_hellman();
+    println!("[okay] Challenge 33: implemented Diffie-Hellman");
+}
+
+pub fn challenge34() {
+    println!("[xxxx] Challenge 34: tbd");
 }