From 450131c6fa4178c067505724fd35dd01b831a4d6 Mon Sep 17 00:00:00 2001
From: theBreadCompany <contact@thebread.dev>
Date: Wed, 4 Dec 2024 13:56:14 +0100
Subject: [PATCH] use 16-bit n and add comments

---
 src/main.rs        |  8 ++++--
 src/pollard_rho.rs | 66 +++++++++++++++++++++++++++++-----------------
 2 files changed, 48 insertions(+), 26 deletions(-)

diff --git a/src/main.rs b/src/main.rs
index fd0ca05..2029d5d 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,7 +1,11 @@
 mod pollard_rho;
 
 fn main() {
-    let n = rand::random::<u8>();
+    let mut n = 0;
+    while n % 2 == 0 { n = rand::random::<u16>(); }
     let n_primediv = pollard_rho::pollard_rho(n.into());
-    eprintln!("Generated random number {}, got prime divisor {}", n, n_primediv);
+    eprintln!(
+        "Generated random number {}, got prime divisor {}",
+        n, n_primediv
+    );
 }
diff --git a/src/pollard_rho.rs b/src/pollard_rho.rs
index 91ca656..3dff6f9 100644
--- a/src/pollard_rho.rs
+++ b/src/pollard_rho.rs
@@ -1,53 +1,71 @@
 use gcd::Gcd;
 
 /**
- * Calculate the primedivisor for some number `n`
+ * Calculate the prime divisor for some number `n`
+ *
+ * Uses cycle finding
 */
-pub fn pollard_rho(n: u16) -> u16 {
-    if n == 1 { return 1; } // 1 only has 1 as prime divisor
-    if n % 2 == 0 { return 2; } // even numbers have at least 2 as prime divisor
-    if is_prime(n) { return n; }
+pub fn pollard_rho(n: u32) -> u32 {
+    if n == 1 {
+        return 1;
+    } // 1 only has 1 as prime divisor
+    if n % 2 == 0 {
+        return 2;
+    } // even numbers have at least 2 as prime divisor
+    if is_prime(n) {
+        return n;
+    } // need to detect to be able to decide if we have bad random numbers or the
 
-    let mut x = rand::random::<u16>() % 2;
-    let mut y = x;
+    let mut x = rand::random::<u32>() % n; // cycle finding: tortoise
+    let mut y = x; // cycle finding: hare
 
-    let c = rand::random::<u16>() % 2;
-    let mut div = 1;
+    let c = rand::random::<u32>() % n; // random number to add to the cycle finding moves
+    let mut div = 1; // divisor - 1 applies to all numbers and is our failed and start value
 
     while div == 1 {
+        // tortoise move
         x = (mod_pow(x, 2, n) + c + n) % n;
+        // hare move
         y = (mod_pow(y, 2, n) + c + n) % n;
         y = (mod_pow(y, 2, n) + c + n) % n;
-        div = u16::try_from((i16::try_from(x).unwrap()-i16::try_from(y).unwrap()).abs()).unwrap().gcd(n);
-        eprintln!("Got div {}", div);
-        if div == n { return pollard_rho(n); }
+        // divisor is the greatest common divisor between |x-y| and n
+        div = u32::try_from((i32::try_from(x).unwrap() - i32::try_from(y).unwrap()).abs())
+            .unwrap()
+            .gcd(n);
+        // bad random numbers, try again
+        if div == n {
+            return pollard_rho(n);
+        }
     }
 
-    return div;
+    div
 }
 
 /**
  * Discrete/Modular exponentiation
- * 
- * Highly memory efficient because the full result is never stored, but shortened by defined modulo instead. 
+ *
+ * Highly memory efficient because the full result is never stored, but shortened by defined modulo instead.
  * We can use that because the prime divisor required for our algorithm is guarenteed to be smaller
  * than n.
- * 
+ *
  * Counterpart function to the discrete logarithm.
  */
-fn mod_pow(base: u16, exp: u16, r#mod: u16) -> u16 {
-    let mut result = 1; 
-
-    for _ in 0..exp-1 {
+fn mod_pow(base: u32, exp: u32, r#mod: u32) -> u32 {
+    let mut result = 1;
+    for _ in 0..exp - 1 {
         result = (result * base) % r#mod;
     }
-
     result
 }
 
-fn is_prime(n: u16) -> bool {
-    for i in (3..=(n as f32).sqrt() as u16).step_by(2) {
-        if n % i == 0 {  return false; }
+/**
+ * very primitive prime checker
+ */
+fn is_prime(n: u32) -> bool {
+    for i in (3..=(n as f32).sqrt() as u32).step_by(2) {
+        if n % i == 0 {
+            return false;
+        }
     }
     true
 }