diff --git a/src/ecdsa/serialized_signature.rs b/src/ecdsa/serialized_signature.rs
index 4fd0449..e89faf3 100644
--- a/src/ecdsa/serialized_signature.rs
+++ b/src/ecdsa/serialized_signature.rs
@@ -5,6 +5,8 @@
 //! unable to run on platforms without allocator. We implement a special type to encapsulate
 //! serialized signatures and since it's a bit more complicated it has its own module.
 
+pub use into_iter::IntoIter;
+
 use core::{fmt, ops};
 use crate::Error;
 use super::Signature;
@@ -62,6 +64,16 @@ impl ops::Deref for SerializedSignature {
 
 impl Eq for SerializedSignature {}
 
+impl IntoIterator for SerializedSignature {
+    type IntoIter = IntoIter;
+    type Item = u8;
+
+    #[inline]
+    fn into_iter(self) -> Self::IntoIter {
+        IntoIter::new(self)
+    }
+}
+
 impl<'a> IntoIterator for &'a SerializedSignature {
     type IntoIter = core::slice::Iter<'a, u8>;
     type Item = &'a u8;
@@ -107,3 +119,131 @@ impl SerializedSignature {
     /// Check if the space is zero.
     pub fn is_empty(&self) -> bool { self.len() == 0 }
 }
+
+/// Separate mod to prevent outside code accidentally breaking invariants.
+mod into_iter {
+    use super::*;
+
+    /// Owned iterator over the bytes of [`SerializedSignature`]
+    ///
+    /// Created by [`IntoIterator::into_iter`] method.
+    // allowed because of https://github.com/rust-lang/rust/issues/98348
+    #[allow(missing_copy_implementations)]
+    #[derive(Debug, Clone)]
+    pub struct IntoIter {
+        signature: SerializedSignature,
+        // invariant: pos <= signature.len()
+        pos: usize,
+    }
+
+    impl IntoIter {
+        #[inline]
+        pub(crate) fn new(signature: SerializedSignature) -> Self {
+            IntoIter {
+                signature,
+                // for all unsigned n: 0 <= n
+                pos: 0,
+            }
+        }
+
+        /// Returns the remaining bytes as a slice.
+        ///
+        /// This method is analogous to [`core::slice::Iter::as_slice`].
+        #[inline]
+        pub fn as_slice(&self) -> &[u8] {
+            &self.signature[self.pos..]
+        }
+    }
+
+    impl Iterator for IntoIter {
+        type Item = u8;
+
+        #[inline]
+        fn next(&mut self) -> Option<Self::Item> {
+            let byte = *self.signature.get(self.pos)?;
+            // can't overflow or break invariant because if pos is too large we return early
+            self.pos += 1;
+            Some(byte)
+        }
+
+        #[inline]
+        fn size_hint(&self) -> (usize, Option<usize>) {
+            // can't underlflow thanks to the invariant
+            let len = self.signature.len() - self.pos;
+            (len, Some(len))
+        }
+
+        // override for speed
+        #[inline]
+        fn nth(&mut self, n: usize) -> Option<Self::Item> {
+            if n >= self.len() {
+                // upholds invariant becasue the values will be equal
+                self.pos = self.signature.len();
+                None
+            } else {
+                // if n < signtature.len() - self.pos then n + self.pos < signature.len() which neither
+                // overflows nor breaks the invariant
+                self.pos += n;
+                self.next()
+            }
+        }
+    }
+
+    impl ExactSizeIterator for IntoIter {}
+
+    impl core::iter::FusedIterator for IntoIter {}
+
+    impl DoubleEndedIterator for IntoIter {
+        #[inline]
+        fn next_back(&mut self) -> Option<Self::Item> {
+            if self.pos == self.signature.len() {
+                return None;
+            }
+
+            // if len is 0 then pos is also 0 thanks to the invariant so we would return before we
+            // reach this
+            let new_len = self.signature.len() - 1;
+            let byte = self.signature[new_len];
+            self.signature.set_len(new_len);
+            Some(byte)
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::SerializedSignature;
+
+    #[test]
+    fn iterator_ops_are_homomorphic() {
+        let mut fake_signature_data = [0; 72];
+        // fill it with numbers 0 - 71
+        for (i, byte) in fake_signature_data.iter_mut().enumerate() {
+            // up to 72
+            *byte = i as u8;
+        }
+
+        let fake_signature = SerializedSignature { data: fake_signature_data, len: 72 };
+
+        let mut iter1 = fake_signature.into_iter();
+        let mut iter2 = fake_signature.iter();
+
+        // while let so we can compare size_hint and as_slice
+        while let (Some(a), Some(b)) = (iter1.next(), iter2.next()) {
+            assert_eq!(a, *b);
+            assert_eq!(iter1.size_hint(), iter2.size_hint());
+            assert_eq!(iter1.as_slice(), iter2.as_slice());
+        }
+
+        let mut iter1 = fake_signature.into_iter();
+        let mut iter2 = fake_signature.iter();
+
+        // manual next_back instead of rev() so that we can check as_slice()
+        // if next_back is implemented correctly then rev() is also correct - provided by `core`
+        while let (Some(a), Some(b)) = (iter1.next_back(), iter2.next_back()) {
+            assert_eq!(a, *b);
+            assert_eq!(iter1.size_hint(), iter2.size_hint());
+            assert_eq!(iter1.as_slice(), iter2.as_slice());
+        }
+    }
+}