Finish challenge 39 without invmod

src/set5.rs

@@ -5,6 +5,7 @@ use crate::srp;
 use num_bigint::BigUint;
 use num_bigint::RandBigInt;
 use num_bigint::ToBigUint;
+use openssl::bn::BigNum;
 use openssl::sha::sha256;
 use rand::Rng;
 
@@ -509,6 +510,33 @@ pub fn challenge38() -> Option<()> {
     Some(())
 }
 
-pub fn challenge39() {
-    println!("[xxxx] Challenge 39: Implement RSA");
+pub fn challenge39() -> Option<()> {
+    // I recommend you not bother with primegen,
+    // but do take the time to get your own EGCD and
+    // invmod algorithm working.
+    let a = BigNum::from_u32(17).ok()?;
+    let n = BigNum::from_u32(3120).ok()?;
+    let r = BigNum::from_u32(2753).ok()?;
+    assert_eq!(rsa::invmod(&a, &n).ok()?, r, "invmod does not work");
+
+    let (public_key, private_key) = rsa::rsa_gen_keys().ok()?;
+
+    // Test this out with a number, like "42".
+    let i = BigNum::from_u32(1337).ok()?;
+    let c = rsa::rsa_encrypt(&i, &public_key).ok()?;
+    let m = rsa::rsa_decrypt(&c, &private_key).ok()?;
+    assert_eq!(i, m, "rsa is broken");
+
+    let i = "Party, party, party, all night long. Yuah!";
+    let c = rsa::rsa_encrypt_str(&i, &public_key).ok()?;
+    let m = rsa::rsa_decrypt_str(&c, &private_key).ok()?;
+    assert_eq!(i, &m, "string rsa is broken");
+
+    println!("[okay] Challenge 39: implement RSA");
+    Some(())
+}
+
+pub fn challenge40() -> Option<()> {
+    // println!("[xxxx] Challenge 40: implement an E=3 RSA Broadcast attack");
+    None
 }