longest period finder

src/main.rs

@@ -3,7 +3,7 @@ mod period;
 mod tea3;
 
 use lfsr::Lfsr;
-use period::{period_bruteforce, period_floyd, period_paper};
+use period::{longest_period, period_bruteforce, period_floyd, period_paper};
 use tea3::Tea3;
 
 fn main() {
@@ -50,9 +50,22 @@ fn main() {
     println!("Decrypted : {:?}", decrypted);
 
     println!(
-        "\nPaper period: {}",
-        // period_paper(vec![0xc2, 0xc2, 0xc2, 0xc2, 0xc2])
-        // period_paper(vec![0xa3, 0xe1, 0x6f, 0x58, 0x05])
+        "\nPaper period p0: {}",
+        period_paper(vec![0xc2, 0xc2, 0xc2, 0xc2, 0xc2])
+    );
+    println!(
+        "Paper period p1: {}",
+        period_paper(vec![0xa3, 0xe1, 0x6f, 0x58, 0x05])
+    );
+    println!(
+        "Paper period p14: {}",
         period_paper(vec![0xe3, 0x61, 0x62, 0x00, 0x00])
     );
+
+    // println!("\nPaper period p20: {}", period_paper(vec![0x7a, 0x02, 0x00, 0x00, 0x00]));
+    // println!("\nPaper period p27: {}", period_paper(vec![0x00, 0x00, 0x00, 0x00, 0x00]));
+
+    let (p, seed) = longest_period();
+    println!("\nLongest period: {}", p);
+    println!("Seed: {:02x?}", seed);
 }

src/period.rs

@@ -66,6 +66,19 @@ pub fn period_floyd(key: Vec<u8>, iv: Vec<u8>) -> u64 {
 struct Reg5([u8; 5]);
 
 impl Reg5 {
+    fn from_u40(x: u64) -> Self {
+        assert!(x < (1u64 << 40), "value must fit in 40 bits");
+
+        // Internal order: byte 0 is the first register byte.
+        Self([
+            ((x >> 32) & 0xFF) as u8,
+            ((x >> 24) & 0xFF) as u8,
+            ((x >> 16) & 0xFF) as u8,
+            ((x >> 8) & 0xFF) as u8,
+            (x & 0xFF) as u8,
+        ])
+    }
+
     fn step_h(&mut self) -> u8 {
         let out = self.0[0];
         let feedback = out ^ Tea3::p(self.0[2]);
@@ -145,3 +158,22 @@ pub fn period_paper(key: Vec<u8>) -> u64 {
     let start = Decomposed::from_key(&[0, 0, 0, 0, 0, key[0], key[1], key[2], key[3], key[4]]);
     period_h(start.h) // p
 }
+
+/// Exhaustively scan all 2^40 initial values of h and returns:
+/// (longest period found, 5-bytes initial value)
+pub fn longest_period() -> (u64, [u8; 5]) {
+    let mut best_period = 0u64;
+    let mut best_seed = [0u8; 5];
+
+    for x in 0u64..(1u64 << 40) {
+        let seed = Reg5::from_u40(x);
+        let p = period_h(seed);
+
+        if p > best_period {
+            best_period = p;
+            best_seed = seed.0;
+        }
+    }
+
+    (best_period, best_seed)
+}