From 596adf5d3243975aa719e897d02db93da28709c8 Mon Sep 17 00:00:00 2001
From: jacekpoz <jacekpoz@proton.me>
Date: Tue, 14 May 2024 15:03:12 +0200
Subject: [PATCH] improve printing and actually find the private key

---
 l4/z1/rsa-rs/src/main.rs | 35 ++++++++++++++++++++++++++++-------
 1 file changed, 28 insertions(+), 7 deletions(-)

diff --git a/l4/z1/rsa-rs/src/main.rs b/l4/z1/rsa-rs/src/main.rs
index 7fda804..7bf0a07 100644
--- a/l4/z1/rsa-rs/src/main.rs
+++ b/l4/z1/rsa-rs/src/main.rs
@@ -114,7 +114,7 @@ fn pow_mod(a: &BigUint, exp: &BigUint, n: &BigUint) -> BigUint {
     res
 }
 
-fn find_private_key(n: &BigUint, e: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
+fn find_primes(n: &BigUint, e: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
     let kphi = d * e - 1u32;
     let mut t = kphi.clone();
     while &t % 2u32 == BigUint::zero() {
@@ -145,6 +145,14 @@ fn find_private_key(n: &BigUint, e: &BigUint, d: &BigUint) -> (BigUint, BigUint)
     (p, q)
 }
 
+fn find_private_key(p1: &BigUint, p2: &BigUint, e: &BigUint) -> BigUint {
+    let phi = (p1 - 1u32) * (p2 - 1u32);
+
+    let d = euclid(e, &phi);
+
+    d
+}
+
 fn main() {
     let n = env::args().nth(1)
         .expect(format!("usage: {} <key_length>", env::args().nth(0).unwrap()).as_str())
@@ -152,25 +160,38 @@ fn main() {
         .expect("key length must be usize");
 
     let p1: BigUint = thread_rng().gen_prime_exact(n, Some(PrimalityTestConfig::strict()));
-    println!("p1 ({b} bits): {p1}", b = p1.bits());
+    println!("p1 ({b} bits): 0x{p1:X}", b = p1.bits());
 
     let p2: BigUint = thread_rng().gen_prime_exact(n, Some(PrimalityTestConfig::strict()));
-    println!("p2 ({b} bits): {p2}", b = p1.bits());
+    println!("p2 ({b} bits): 0x{p2:X}", b = p1.bits());
+
+    println!();
 
     let pair_a = generate_key_pair(&p1, &p2)
         .expect("failed to generate key pair a");
     println!("private key A: {}", pair_a.private);
     println!("public key A: {}", pair_a.public);
 
+    println!();
+
     let pair_b = generate_key_pair(&p1, &p2)
         .expect("failed to generate key pair b");
     println!("private key B: {}", pair_b.private);
     println!("public key B: {}", pair_b.public);
 
-    let found_secret = find_private_key(&pair_a.public.n, &pair_a.public.key, &pair_a.private.key);
-    println!("found_b: (0x{:X}, 0x{:X})", found_secret.0, found_secret.1);
-    if (&found_secret.0 == &p1 && &found_secret.1 == &p2)
-        || (&found_secret.0 == &p2 && &found_secret.1 == &p1) {
+    println!();
+
+    let found_primes = find_primes(&pair_a.public.n, &pair_a.public.key, &pair_a.private.key);
+    println!("found_primes: (0x{:X}, 0x{:X})", found_primes.0, found_primes.1);
+
+    println!();
+
+    let found_private_key = find_private_key(&found_primes.0, &found_primes.1, &pair_b.public.key);
+    println!("found_private_key: 0x{:X}", found_private_key);
+
+    println!();
+
+    if found_private_key == pair_b.private.key {
         println!("cracked B)");
     } else {
         println!("uncracked B(");