From 70cecb0d9e4d2f865c7e21cc3a7fde90054a2428 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Sat, 14 Jan 2023 10:37:37 -0500
Subject: [PATCH] Solve challenge 45 DSA parameter tampering

---
 src/dsa.rs  | 15 +++++++-------
 src/main.rs |  1 +
 src/set6.rs | 60 ++++++++++++++++++++++++++++++++++++++++++++++++++++-
 3 files changed, 68 insertions(+), 8 deletions(-)

diff --git a/src/dsa.rs b/src/dsa.rs
index 5c6193e..0e82275 100644
--- a/src/dsa.rs
+++ b/src/dsa.rs
@@ -59,13 +59,14 @@ impl DsaKeys {
         let mut k = BigNum::new()?;
         let mut r = BigNum::from_u32(0)?;
         let zero = BigNum::from_u32(0)?;
-        while r == zero {
-            // Choose an integer k randomly from { 1 … q − 1 }
-            params.q.rand_range(&mut k)?;
-            // Compute r := (g^k mod p) mod q. In the unlikely case that r=0, start again.
-            r.mod_exp(&params.g, &k, &params.p, &mut ctx)?;
-            r = &r % &params.q;
-        }
+
+        // Choose an integer k randomly from { 1 … q − 1 }
+        params.q.rand_range(&mut k)?;
+        // Compute r := (g^k mod p) mod q.
+        r.mod_exp(&params.g, &k, &params.p, &mut ctx)?;
+        r = &r % &params.q;
+        // In the unlikely case that r=0, crash.
+        assert!(r != zero, "r is zero");
 
         // Compute s := (k^(−1) * ( H ( m ) + x r ) ) mod q.
         let s = &(&rsa::invmod(&k, &params.q)? * &(&h(msg)? + &(&self.x * &r))) % &params.q;
diff --git a/src/main.rs b/src/main.rs
index af6fcb1..30488d8 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -75,4 +75,5 @@ fn main() {
     set6::challenge43().unwrap_or_else(|| println!("[fail] challenge 43"));
     set6::challenge44().unwrap_or_else(|| println!("[fail] challenge 44"));
     set6::challenge45().unwrap_or_else(|| println!("[fail] challenge 45"));
+    set6::challenge46().unwrap_or_else(|| println!("[fail] challenge 46"));
 }
diff --git a/src/set6.rs b/src/set6.rs
index 9902958..90fe093 100644
--- a/src/set6.rs
+++ b/src/set6.rs
@@ -282,6 +282,64 @@ pub fn challenge44() -> Option<()> {
 }
 
 pub fn challenge45() -> Option<()> {
-    println!("[xxxx] Challenge 45: DSA parameter tampering");
+    // Part 1: 0 mod p
+    //
+    // Use the parameters from the previous exercise, but substitute 0 for "g". Generate a
+    // signature. You will notice something bad.
+    //
+    // Observation:
+    //
+    // - If g=0, because of r := (g^k mod p) mod q, it follows r=0.
+    // - When verifying, v := ((g^u1 * y^u2) % p) % q).
+    // - Therefore, v=0, and v == r is always true for any signature.
+    //
+    // Our implementation catches this case, both for signing and verifying.
+
+    // Part 2: 1 mod p
+    let mut params = dsa::DsaParameters::new().ok()?;
+    fn generate_magic_signature(
+        params: &mut dsa::DsaParameters,
+    ) -> Result<dsa::DsaSig, ErrorStack> {
+        let mut ctx = BigNumContext::new()?;
+
+        //Now, try (p+1) as "g". With this "g", you can generate a magic signature s, r for any DSA
+        //public key that will validate against any string.
+        params.g = &params.p + &BigNum::from_u32(1)?;
+
+        // For arbitrary z:
+        // r = ((y**z) % p) % q
+        let mut r = BigNum::from_u32(0)?;
+        let z = BigNum::from_u32(1337)?;
+        r.mod_exp(&params.g, &z, &params.p, &mut ctx)?;
+        r = &r % &params.q;
+
+        //       r
+        // s =  --- % q
+        //       z
+        let s = &rsa::invmod(&z, &params.q)? * &r;
+
+        // k doesn't matter
+        let k = BigNum::from_u32(0)?;
+
+        Ok(dsa::DsaSig { r, s, k })
+    }
+
+    let sig = generate_magic_signature(&mut params).ok()?;
+    let keys = dsa::DsaKeys::new(&params).ok()?;
+
+    let msg = Bytes::from_utf8("Hello, world");
+    let result = keys.verify(&params, &msg, &sig).ok()?;
+    assert!(result, "verify failed unexpectedly");
+
+    let msg = Bytes::from_utf8("Goodbye, world");
+    let result = keys.verify(&params, &msg, &sig).ok()?;
+    assert!(result, "verify failed unexpectedly");
+
+    println!("[okay] Challenge 45: DSA parameter tampering");
+    Some(())
+}
+
+pub fn challenge46() -> Option<()> {
+    println!("[xxxx] Challenge 46: RSA parity oracle");
     None
 }