Implement a binary search for BatchVerifier blame

Adds helper functions to verify and, on failure, blame, which move an 
unwrap from callers into multiexp where it's guaranteed to be safe and 
easily verified to be proper.

Closes https://github.com/serai-dex/serai/issues/10.

crypto/multiexp/src/lib.rs

@@ -106,27 +106,51 @@ impl<Id: Copy, G: Group> BatchVerifier<Id, G> {
 
   pub fn verify(&self) -> bool {
     multiexp(
-      self.0.iter().flat_map(|sets| sets.1.iter()).cloned(),
+      self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned(),
       self.1
     ).is_identity().into()
   }
 
   pub fn verify_vartime(&self) -> bool {
     multiexp_vartime(
-      self.0.iter().flat_map(|sets| sets.1.iter()).cloned(),
+      self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned(),
       self.1
     ).is_identity().into()
   }
 
-  // Solely has a vartime variant as there shouldn't be any reason for this to not be vartime, yet
-  // we should explicitly label vartime software as vartime
-  // TODO: Binary search, or at least randomly sort
+  // A constant time variant may be beneficial for robust protocols
   pub fn blame_vartime(&self) -> Option<Id> {
-    for value in &self.0 {
-      if !bool::from(multiexp_vartime(value.1.clone(), self.1).is_identity()) {
-        return Some(value.0);
+    let mut slice = self.0.as_slice();
+    while slice.len() > 1 {
+      let split = slice.len() / 2;
+      if multiexp_vartime(
+        slice[.. split].iter().flat_map(|pairs| pairs.1.iter()).cloned(),
+        self.1
+      ).is_identity().into() {
+        slice = &slice[split ..];
+      } else {
+        slice = &slice[.. split];
       }
     }
-    None
+
+    slice.get(0).filter(
+      |(_, value)| !bool::from(multiexp_vartime(value.clone(), self.1).is_identity())
+    ).map(|(id, _)| *id)
+  }
+
+  pub fn verify_with_vartime_blame(&self) -> Result<(), Id> {
+    if self.verify() {
+      Ok(())
+    } else {
+      Err(self.blame_vartime().unwrap())
+    }
+  }
+
+  pub fn verify_vartime_with_vartime_blame(&self) -> Result<(), Id> {
+    if self.verify_vartime() {
+      Ok(())
+    } else {
+      Err(self.blame_vartime().unwrap())
+    }
   }
 }