Use new BIP340 domain separation scheme

Abandoned the old one (mention by real-or-random) to the one suggested
here:

sipa/bips#207 (comment)

schnorr_fun/src/schnorr.rs

@@ -30,6 +30,7 @@ pub struct Schnorr<CH, NG = (), GT = BasePoint> {
     ///
     /// [`NonceGen`]: crate::nonce::NonceGen
     nonce_challenge_bundle: NonceChallengeBundle<CH, NG>,
+    application_tag: Option<[u8; 64]>,
 }
 
 /// Describes the kind of messages that will be signed with a [`Schnorr`] instance.
@@ -48,7 +49,12 @@ pub enum MessageKind {
     Plain {
         /// You must provide a tag to separate signatures from your application
         /// from other applications. If two [`Schnorr`] instances are created
-        /// with a different `tag` then a signature valid for one will never be valid for the other.
+        /// with a different `tag` then a signature valid for one will never be
+        /// valid for the other. It will also never be valid for `Prehashed`
+        /// instances. The specific method of domain separation used is
+        /// described [here].
+        ///
+        /// [here]: https://github.com/sipa/bips/issues/207#issuecomment-673681901
         tag: &'static str,
     },
 }
@@ -107,13 +113,24 @@ where
         }
         .add_protocol_tag("BIP0340");
 
-        if let MessageKind::Plain { tag } = msgkind {
-            nonce_challenge_bundle = nonce_challenge_bundle.add_application_tag(tag);
-        }
+        let application_tag = match msgkind {
+            MessageKind::Prehashed => None,
+            MessageKind::Plain { tag } => {
+                assert!(tag.len() <= 64);
+                // Only add the application tag to nonce gen since we will be
+                // separately adding the tag to the challenge hash in self.challenge()
+                nonce_challenge_bundle.nonce_gen =
+                    nonce_challenge_bundle.nonce_gen.add_application_tag(tag);
+                let mut application_tag = [0u8; 64];
+                application_tag[..tag.len()].copy_from_slice(tag.as_bytes());
+                Some(application_tag)
+            }
+        };
 
         Self {
             G: fun::G.clone(),
             nonce_challenge_bundle,
+            application_tag,
         }
     }
 }
@@ -213,7 +230,14 @@ impl<NG, CH: Digest<OutputSize = U32> + Clone, GT> Schnorr<CH, NG, GT> {
     /// ```
     pub fn challenge<S: Secrecy>(&self, R: &XOnly, X: &XOnly, m: Slice<'_, S>) -> Scalar<S, Zero> {
         let hash = self.nonce_challenge_bundle.challenge_hash.clone();
-        let challenge = Scalar::from_hash(hash.add(R).add(X).add(&m));
+        let mut hash = hash.add(R).add(X);
+
+        if let Some(tag) = self.application_tag {
+            hash.update(&tag[..]);
+        }
+
+        let challenge = Scalar::from_hash(hash.add(&m));
+
         challenge
             // Since the challenge pre-image is adversarially controlled we
             // conservatively allow for it to be zero
@@ -258,6 +282,8 @@ impl<NG, CH: Digest<OutputSize = U32> + Clone, GT> Schnorr<CH, NG, GT> {
 
 #[cfg(test)]
 pub mod test {
+    use fun::nonce::Deterministic;
+
     use super::*;
     use crate::fun::TEST_SOUNDNESS;
     crate::fun::test_plus_wasm! {
@@ -304,5 +330,22 @@ pub mod test {
                 assert_ne!(signature_1.R, signature_4.R);
             }
         }
+
+        fn deterministic_nonces_for_different_message_kinds() {
+            use sha2::Sha256;
+            let schnorr_1 = Schnorr::<Sha256,_>::new(Deterministic::<Sha256>::default(), MessageKind::Prehashed);
+            let schnorr_2 = Schnorr::<Sha256,_>::new(Deterministic::<Sha256>::default(), MessageKind::Plain { tag: "two" });
+            let schnorr_3 = Schnorr::<Sha256,_>::new(Deterministic::<Sha256>::default(), MessageKind::Plain { tag: "three" });
+            let x =  Scalar::from_str("18451f9e08af9530814243e202a4a977130e672079f5c14dcf15bd4dee723072").unwrap();
+            let keypair = schnorr_1.new_keypair(x);
+            let message = b"foo".as_ref().mark::<Public>();
+            assert_ne!(schnorr_1.sign(&keypair, message).R, schnorr_2.sign(&keypair, message).R);
+            assert_ne!(schnorr_1.sign(&keypair, message).R, schnorr_3.sign(&keypair, message).R);
+
+            // make sure deterministic signatures don't change
+            use core::str::FromStr;
+            assert_eq!(schnorr_1.sign(&keypair, message), Signature::<Public>::from_str("fe9e5d0319d5d221988d6fd7fe1c4bedd2fb4465f592f1002f461503332a266977bb4a0b00c00d07072c796212cbea0957ebaaa5139143761c45d997ebe36cbe").unwrap());
+            assert_eq!(schnorr_2.sign(&keypair, message), Signature::<Public>::from_str("6cad3863f4d01494ce4c40f3422e4916c616356d730bc4ffe33e386f038b328ba1dc9621e626992c2612f33cdb35f4be4badc464c1f4bf3de15517e7aedcf615").unwrap());
+        }
     }
 }