diff --git a/.github/workflows/digest.yml b/.github/workflows/digest.yml
index 585de6cb7..51ee473b8 100644
--- a/.github/workflows/digest.yml
+++ b/.github/workflows/digest.yml
@@ -50,7 +50,7 @@ jobs:
     strategy:
       matrix:
         rust:
-          - 1.41.0 # MSRV
+          # - 1.41.0 # MSRV
           - stable
     steps:
       - uses: actions/checkout@v2
@@ -60,8 +60,6 @@ jobs:
           toolchain: ${{ matrix.rust }}
           override: true
           profile: minimal
-      # Isolate this crate from workspace which is otherwise MSRV 1.56 due to 2021 edition crates
-      - run: rm ../Cargo.toml
       - run: cargo check --all-features
       - run: cargo test --no-default-features
       - run: cargo test
@@ -69,3 +67,26 @@ jobs:
       - run: cargo test --features alloc
       - run: cargo test --features std
       - run: cargo test --all-features
+
+  # The `oid` feature bumps MSRV to 1.57, so we temporarily split this job.
+  test-msrv:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        rust:
+          - 1.41.0 # MSRV
+    steps:
+      - uses: actions/checkout@v2
+      - uses: RustCrypto/actions/cargo-cache@master
+      - uses: actions-rs/toolchain@v1
+        with:
+          toolchain: ${{ matrix.rust }}
+          override: true
+          profile: minimal
+      # Isolate this crate from workspace which is otherwise MSRV 1.56 due to 2021 edition crates
+      - run: rm ../Cargo.toml
+      - run: cargo test --no-default-features
+      - run: cargo test
+      - run: cargo test --features dev
+      - run: cargo test --features alloc
+      - run: cargo test --features std
diff --git a/Cargo.lock b/Cargo.lock
index 77f459530..c3c02c529 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -50,9 +50,9 @@ dependencies = [
 
 [[package]]
 name = "aho-corasick"
-version = "0.7.18"
+version = "0.7.19"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1e37cfd5e7657ada45f742d6e99ca5788580b5c529dc78faf11ece6dc702656f"
+checksum = "b4f55bd91a0978cbfd91c457a164bab8b4001c833b7f323132c0a4e1922dd44e"
 dependencies = [
  "memchr",
 ]
@@ -168,9 +168,9 @@ dependencies = [
 
 [[package]]
 name = "block-buffer"
-version = "0.10.2"
+version = "0.10.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0bf7fe51849ea569fd452f37822f606a5cabb684dc918707a0193fd4664ff324"
+checksum = "69cce20737498f97b993470a6e536b8523f0af7892a4f928cceb1ac5e52ebe7e"
 dependencies = [
  "generic-array",
 ]
@@ -282,9 +282,9 @@ dependencies = [
 
 [[package]]
 name = "cpufeatures"
-version = "0.2.4"
+version = "0.2.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "dc948ebb96241bb40ab73effeb80d9f93afaad49359d159a5e61be51619fe813"
+checksum = "28d997bd5e24a5928dd43e46dc529867e207907fe0b239c3477d924f7f2ca320"
 dependencies = [
  "libc",
 ]
@@ -308,7 +308,7 @@ dependencies = [
  "aead 0.5.1",
  "cipher 0.4.3 (registry+https://github.com/rust-lang/crates.io-index)",
  "crypto-common 0.1.6",
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
  "elliptic-curve 0.12.3",
  "password-hash",
  "signature 1.6.0",
@@ -423,21 +423,22 @@ dependencies = [
 [[package]]
 name = "digest"
 version = "0.10.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f2fb860ca6fafa5552fb6d0e816a69c8e49f0908bf524e30a90d97c85892d506"
 dependencies = [
- "blobby",
- "block-buffer 0.10.2",
- "crypto-common 0.1.6",
+ "block-buffer 0.10.3",
+ "crypto-common 0.1.6 (registry+https://github.com/rust-lang/crates.io-index)",
  "subtle",
 ]
 
 [[package]]
 name = "digest"
-version = "0.10.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f2fb860ca6fafa5552fb6d0e816a69c8e49f0908bf524e30a90d97c85892d506"
+version = "0.10.4"
 dependencies = [
- "block-buffer 0.10.2",
- "crypto-common 0.1.6 (registry+https://github.com/rust-lang/crates.io-index)",
+ "blobby",
+ "block-buffer 0.10.3",
+ "const-oid 0.9.0",
+ "crypto-common 0.1.6",
  "subtle",
 ]
 
@@ -483,7 +484,7 @@ dependencies = [
  "base64ct",
  "crypto-bigint 0.4.8",
  "der 0.6.0",
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
  "ff 0.12.0",
  "generic-array",
  "group 0.12.0",
@@ -660,7 +661,7 @@ version = "0.12.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "6c49c37c09c17a53d937dfbb742eb3a961d65a994e6bcdcf37e7399d0cc8ab5e"
 dependencies = [
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
 ]
 
 [[package]]
@@ -672,7 +673,7 @@ dependencies = [
  "aes-gcm",
  "byteorder",
  "chacha20poly1305",
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
  "generic-array",
  "hkdf 0.12.3",
  "hmac 0.12.1",
@@ -1143,7 +1144,7 @@ checksum = "cf9db03534dff993187064c4e0c05a5708d2a9728ace9a8959b77bedf415dac5"
 dependencies = [
  "cfg-if",
  "cpufeatures",
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
 ]
 
 [[package]]
@@ -1152,7 +1153,7 @@ version = "0.10.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "eaedf34ed289ea47c2b741bb72e5357a209512d67bcd4bda44359e5bf0470f56"
 dependencies = [
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
  "keccak",
 ]
 
@@ -1170,7 +1171,7 @@ dependencies = [
 name = "signature"
 version = "1.6.0"
 dependencies = [
- "digest 0.10.3 (registry+https://github.com/rust-lang/crates.io-index)",
+ "digest 0.10.3",
  "hex-literal",
  "rand_core 0.6.3",
  "sha2 0.10.5",
diff --git a/digest/CHANGELOG.md b/digest/CHANGELOG.md
index c9f52c64e..2553f5e74 100644
--- a/digest/CHANGELOG.md
+++ b/digest/CHANGELOG.md
@@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## 0.10.4 (2022-09-16)
+### Added
+- Feature-gated implementation of the `const_oid::AssociatedOid` trait
+for the core wrappers. ([#1098])
+
+[#1098]: https://github.com/RustCrypto/traits/pull/1098
+
 ## 0.10.3 (2022-02-16)
 ### Fixed
 - Minimal versions build ([#940])
diff --git a/digest/Cargo.toml b/digest/Cargo.toml
index 94ff540e3..253da27ba 100644
--- a/digest/Cargo.toml
+++ b/digest/Cargo.toml
@@ -1,7 +1,7 @@
 [package]
 name = "digest"
 description = "Traits for cryptographic hash functions"
-version = "0.10.3" # Also update html_root_url in lib.rs when bumping this
+version = "0.10.4"
 authors = ["RustCrypto Developers"]
 license = "MIT OR Apache-2.0"
 readme = "README.md"
@@ -18,12 +18,14 @@ crypto-common = { version = "0.1.3", path = "../crypto-common" }
 block-buffer = { version = "0.10", optional = true }
 subtle = { version = "=2.4", default-features = false, optional = true }
 blobby = { version = "0.3", optional = true }
+const-oid = { version = "0.9", optional = true }
 
 [features]
 default = ["core-api"]
 core-api = ["block-buffer"] # Enable Core API traits
 mac = ["subtle"] # Enable MAC traits
 rand_core = ["crypto-common/rand_core"] # Enable random key generation methods
+oid = ["const-oid"] # OID support. WARNING: Bumps MSRV to 1.57
 alloc = []
 std = ["alloc", "crypto-common/std"]
 dev = ["blobby"]
diff --git a/digest/src/core_api/ct_variable.rs b/digest/src/core_api/ct_variable.rs
index 40efff65c..7ee1bed0a 100644
--- a/digest/src/core_api/ct_variable.rs
+++ b/digest/src/core_api/ct_variable.rs
@@ -5,6 +5,8 @@ use super::{
 use crate::HashMarker;
 #[cfg(feature = "mac")]
 use crate::MacMarker;
+#[cfg(feature = "oid")]
+use const_oid::{AssociatedOid, ObjectIdentifier};
 use core::{fmt, marker::PhantomData};
 use crypto_common::{
     generic_array::{ArrayLength, GenericArray},
@@ -12,10 +14,15 @@ use crypto_common::{
     Block, BlockSizeUser, OutputSizeUser,
 };
 
+/// Dummy type used with [`CtVariableCoreWrapper`] in cases when
+/// resulting hash does not have a known OID.
+#[derive(Copy, Clone, Debug, Eq, PartialEq, Hash)]
+pub struct NoOid;
+
 /// Wrapper around [`VariableOutputCore`] which selects output size
 /// at compile time.
 #[derive(Clone)]
-pub struct CtVariableCoreWrapper<T, OutSize>
+pub struct CtVariableCoreWrapper<T, OutSize, O = NoOid>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -24,10 +31,10 @@ where
     Le<T::BlockSize, U256>: NonZero,
 {
     inner: T,
-    _out: PhantomData<OutSize>,
+    _out: PhantomData<(OutSize, O)>,
 }
 
-impl<T, OutSize> HashMarker for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> HashMarker for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore + HashMarker,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -38,7 +45,7 @@ where
 }
 
 #[cfg(feature = "mac")]
-impl<T, OutSize> MacMarker for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> MacMarker for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore + MacMarker,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -48,7 +55,7 @@ where
 {
 }
 
-impl<T, OutSize> BlockSizeUser for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> BlockSizeUser for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -59,7 +66,7 @@ where
     type BlockSize = T::BlockSize;
 }
 
-impl<T, OutSize> UpdateCore for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> UpdateCore for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -73,7 +80,7 @@ where
     }
 }
 
-impl<T, OutSize> OutputSizeUser for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> OutputSizeUser for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize> + 'static,
@@ -84,7 +91,7 @@ where
     type OutputSize = OutSize;
 }
 
-impl<T, OutSize> BufferKindUser for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> BufferKindUser for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -95,7 +102,7 @@ where
     type BufferKind = T::BufferKind;
 }
 
-impl<T, OutSize> FixedOutputCore for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> FixedOutputCore for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize> + 'static,
@@ -120,7 +127,7 @@ where
     }
 }
 
-impl<T, OutSize> Default for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> Default for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -137,7 +144,7 @@ where
     }
 }
 
-impl<T, OutSize> Reset for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> Reset for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -151,7 +158,7 @@ where
     }
 }
 
-impl<T, OutSize> AlgorithmName for CtVariableCoreWrapper<T, OutSize>
+impl<T, OutSize, O> AlgorithmName for CtVariableCoreWrapper<T, OutSize, O>
 where
     T: VariableOutputCore + AlgorithmName,
     OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
@@ -165,3 +172,33 @@ where
         write!(f, "{}", OutSize::USIZE)
     }
 }
+
+#[cfg(feature = "oid")]
+#[cfg_attr(docsrs, doc(cfg(feature = "oid")))]
+impl<T, OutSize, O> AssociatedOid for CtVariableCoreWrapper<T, OutSize, O>
+where
+    T: VariableOutputCore,
+    O: AssociatedOid,
+    OutSize: ArrayLength<u8> + IsLessOrEqual<T::OutputSize>,
+    LeEq<OutSize, T::OutputSize>: NonZero,
+    T::BlockSize: IsLess<U256>,
+    Le<T::BlockSize, U256>: NonZero,
+{
+    const OID: ObjectIdentifier = O::OID;
+}
+
+/// Implement dummy type with hidden docs which is used to "carry" hasher
+/// OID for [`CtVariableCoreWrapper`].
+#[macro_export]
+macro_rules! impl_oid_carrier {
+    ($name:ident, $oid:literal) => {
+        #[doc(hidden)]
+        #[derive(Copy, Clone, Debug, Eq, PartialEq, Hash)]
+        pub struct $name;
+
+        #[cfg(feature = "oid")]
+        impl AssociatedOid for $name {
+            const OID: ObjectIdentifier = ObjectIdentifier::new_unwrap($oid);
+        }
+    };
+}
diff --git a/digest/src/core_api/wrapper.rs b/digest/src/core_api/wrapper.rs
index 4ad0f7eea..ca977381e 100644
--- a/digest/src/core_api/wrapper.rs
+++ b/digest/src/core_api/wrapper.rs
@@ -14,6 +14,8 @@ use crypto_common::{
 
 #[cfg(feature = "mac")]
 use crate::MacMarker;
+#[cfg(feature = "oid")]
+use const_oid::{AssociatedOid, ObjectIdentifier};
 
 /// Wrapper around [`BufferKindUser`].
 ///
@@ -227,6 +229,17 @@ where
     }
 }
 
+#[cfg(feature = "oid")]
+#[cfg_attr(docsrs, doc(cfg(feature = "oid")))]
+impl<T> AssociatedOid for CoreWrapper<T>
+where
+    T: BufferKindUser + AssociatedOid,
+    T::BlockSize: IsLess<U256>,
+    Le<T::BlockSize, U256>: NonZero,
+{
+    const OID: ObjectIdentifier = T::OID;
+}
+
 #[cfg(feature = "std")]
 #[cfg_attr(docsrs, doc(cfg(feature = "std")))]
 impl<T> std::io::Write for CoreWrapper<T>
diff --git a/digest/src/lib.rs b/digest/src/lib.rs
index c2edb40ee..fc82e2e3a 100644
--- a/digest/src/lib.rs
+++ b/digest/src/lib.rs
@@ -27,8 +27,7 @@
 #![forbid(unsafe_code)]
 #![doc(
     html_logo_url = "https://raw.githubusercontent.com/RustCrypto/media/6ee8e381/logo.svg",
-    html_favicon_url = "https://raw.githubusercontent.com/RustCrypto/media/6ee8e381/logo.svg",
-    html_root_url = "https://docs.rs/digest/0.10.3"
+    html_favicon_url = "https://raw.githubusercontent.com/RustCrypto/media/6ee8e381/logo.svg"
 )]
 #![warn(missing_docs, rust_2018_idioms)]
 
@@ -60,6 +59,9 @@ mod mac;
 #[cfg(feature = "core-api")]
 #[cfg_attr(docsrs, doc(cfg(feature = "core-api")))]
 pub use block_buffer;
+#[cfg(feature = "oid")]
+#[cfg_attr(docsrs, doc(cfg(feature = "oid")))]
+pub use const_oid;
 pub use crypto_common;
 
 pub use crate::digest::{Digest, DynDigest, HashMarker};