diff --git a/Cargo.lock b/Cargo.lock
index 33f6853d..7f92bb31 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -101,9 +101,9 @@ dependencies = [
 
 [[package]]
 name = "der"
-version = "0.7.0"
+version = "0.7.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bc302fd9b18d66834a6f092d10ea85489c0ca8ad6b7304092135fab171d853cd"
+checksum = "19c5cb402c5c958281c7c0702edea7b780d03b86b606497ca3a10fcd3fc393ac"
 dependencies = [
  "const-oid",
  "pem-rfc7468",
@@ -268,9 +268,9 @@ dependencies = [
 
 [[package]]
 name = "pkcs1"
-version = "0.7.1"
+version = "0.7.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "178ba28ece1961eafdff1991bd1744c29564cbab5d803f3ccb4a4895a6c550a7"
+checksum = "575fd6eebed721a2929faa1ee1383a49788378083bbbd7f299af75dd84195cee"
 dependencies = [
  "der",
  "pkcs8",
@@ -295,9 +295,9 @@ dependencies = [
 
 [[package]]
 name = "pkcs8"
-version = "0.10.1"
+version = "0.10.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3d2820d87d2b008616e5c27212dd9e0e694fb4c6b522de06094106813328cb49"
+checksum = "f950b2377845cebe5cf8b5165cb3cc1a5e0fa5cfa3e1f7f55707d8fd82e0a7b7"
 dependencies = [
  "der",
  "pkcs5",
@@ -374,6 +374,7 @@ version = "0.9.0-pre.0"
 dependencies = [
  "base64ct",
  "byteorder",
+ "const-oid",
  "digest",
  "hex-literal",
  "num-bigint-dig",
@@ -501,9 +502,9 @@ checksum = "6e63cff320ae2c57904679ba7cb63280a3dc4613885beafb148ee7bf9aa9042d"
 
 [[package]]
 name = "spki"
-version = "0.7.0"
+version = "0.7.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c0445c905640145c7ea8c1993555957f65e7c46d0535b91ba501bc9bfc85522f"
+checksum = "37a5be806ab6f127c3da44b7378837ebf01dadca8510a0e572460216b228bd0e"
 dependencies = [
  "base64ct",
  "der",
diff --git a/Cargo.toml b/Cargo.toml
index e8a05d9e..51fefdf5 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -19,15 +19,19 @@ num-integer = { version = "0.1.39", default-features = false }
 num-iter = { version = "0.1.37", default-features = false }
 rand_core = { version = "0.6.4", default-features = false }
 byteorder = { version = "1.3.1", default-features = false }
+const-oid = { version = "0.9", default-features = false }
 subtle = { version = "2.1.1", default-features = false }
 digest = { version = "0.10.5", default-features = false, features = ["alloc", "oid"] }
-pkcs1 = { version = "0.7.1", default-features = false, features = ["alloc", "pkcs8"] }
-pkcs8 = { version = "0.10", default-features = false, features = ["alloc"] }
-serde = { version = "1.0.103", optional = true, default-features = false, features = ["derive"] }
-sha2 = { version = "0.10.6", optional = true, default-features = false, features = ["oid"] }
+pkcs1 = { version = "0.7.2", default-features = false, features = ["alloc", "pkcs8"] }
+pkcs8 = { version = "0.10.2", default-features = false, features = ["alloc"] }
 signature = { version = "2", default-features = false , features = ["digest", "rand_core"] }
 zeroize = { version = "1", features = ["alloc"] }
 
+# optional dependencies
+serde = { version = "1.0.103", optional = true, default-features = false, features = ["derive"] }
+sha1 = { version = "0.10.5", optional = true, default-features = false, features = ["oid"] }
+sha2 = { version = "0.10.6", optional = true, default-features = false, features = ["oid"] }
+
 [dev-dependencies]
 base64ct = { version = "1", features = ["alloc"] }
 hex-literal = "0.3.3"
diff --git a/src/pkcs1v15.rs b/src/pkcs1v15.rs
index 5d9bac41..30d29df2 100644
--- a/src/pkcs1v15.rs
+++ b/src/pkcs1v15.rs
@@ -11,7 +11,13 @@ use alloc::vec::Vec;
 use core::fmt::{Debug, Display, Formatter, LowerHex, UpperHex};
 use core::marker::PhantomData;
 use digest::Digest;
-use pkcs8::{AssociatedOid, Document, EncodePrivateKey, EncodePublicKey, SecretDocument};
+use pkcs8::{
+    spki::{
+        der::AnyRef, AlgorithmIdentifierRef, AssociatedAlgorithmIdentifier,
+        SignatureAlgorithmIdentifier,
+    },
+    AssociatedOid, Document, EncodePrivateKey, EncodePublicKey, SecretDocument,
+};
 use rand_core::CryptoRngCore;
 use signature::{
     hazmat::{PrehashSigner, PrehashVerifier},
@@ -436,6 +442,28 @@ where
     }
 }
 
+impl<D> AssociatedAlgorithmIdentifier for SigningKey<D>
+where
+    D: Digest,
+{
+    type Params = AnyRef<'static>;
+
+    const ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> = pkcs1::ALGORITHM_ID;
+}
+
+impl<D> SignatureAlgorithmIdentifier for SigningKey<D>
+where
+    D: Digest + oid::RsaSignatureAssociatedOid,
+{
+    type Params = AnyRef<'static>;
+
+    const SIGNATURE_ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> =
+        AlgorithmIdentifierRef {
+            oid: D::OID,
+            parameters: Some(AnyRef::NULL),
+        };
+}
+
 impl<D> From<RsaPrivateKey> for SigningKey<D>
 where
     D: Digest,
@@ -606,6 +634,28 @@ where
     }
 }
 
+impl<D> AssociatedAlgorithmIdentifier for VerifyingKey<D>
+where
+    D: Digest,
+{
+    type Params = AnyRef<'static>;
+
+    const ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> = pkcs1::ALGORITHM_ID;
+}
+
+impl<D> SignatureAlgorithmIdentifier for VerifyingKey<D>
+where
+    D: Digest + oid::RsaSignatureAssociatedOid,
+{
+    type Params = AnyRef<'static>;
+
+    const SIGNATURE_ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> =
+        AlgorithmIdentifierRef {
+            oid: D::OID,
+            parameters: Some(AnyRef::NULL),
+        };
+}
+
 impl<D> From<RsaPublicKey> for VerifyingKey<D>
 where
     D: Digest,
@@ -774,6 +824,46 @@ impl EncryptingKeypair for DecryptingKey {
     }
 }
 
+mod oid {
+    use const_oid::ObjectIdentifier;
+
+    /// A trait which associates an RSA-specific OID with a type.
+    pub(crate) trait RsaSignatureAssociatedOid {
+        /// The OID associated with this type.
+        const OID: ObjectIdentifier;
+    }
+
+    #[cfg(feature = "sha1")]
+    impl RsaSignatureAssociatedOid for sha1::Sha1 {
+        const OID: ObjectIdentifier =
+            const_oid::ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.5");
+    }
+
+    #[cfg(feature = "sha2")]
+    impl RsaSignatureAssociatedOid for sha2::Sha224 {
+        const OID: ObjectIdentifier =
+            const_oid::ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.14");
+    }
+
+    #[cfg(feature = "sha2")]
+    impl RsaSignatureAssociatedOid for sha2::Sha256 {
+        const OID: ObjectIdentifier =
+            const_oid::ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.11");
+    }
+
+    #[cfg(feature = "sha2")]
+    impl RsaSignatureAssociatedOid for sha2::Sha384 {
+        const OID: ObjectIdentifier =
+            const_oid::ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.12");
+    }
+
+    #[cfg(feature = "sha2")]
+    impl RsaSignatureAssociatedOid for sha2::Sha512 {
+        const OID: ObjectIdentifier =
+            const_oid::ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.13");
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/src/pss.rs b/src/pss.rs
index 5111a4a3..5042eda5 100644
--- a/src/pss.rs
+++ b/src/pss.rs
@@ -12,10 +12,19 @@
 use alloc::boxed::Box;
 use alloc::vec::Vec;
 use core::fmt::{self, Debug, Display, Formatter, LowerHex, UpperHex};
-
 use core::marker::PhantomData;
+
+use const_oid::{AssociatedOid, ObjectIdentifier};
 use digest::{Digest, DynDigest, FixedOutputReset};
-use pkcs8::{Document, EncodePrivateKey, EncodePublicKey, SecretDocument};
+use pkcs1::RsaPssParams;
+use pkcs8::{
+    spki::{
+        der::{Any, AnyRef},
+        AlgorithmIdentifier, AlgorithmIdentifierOwned, AlgorithmIdentifierRef,
+        AssociatedAlgorithmIdentifier, DynSignatureAlgorithmIdentifier,
+    },
+    Document, EncodePrivateKey, EncodePublicKey, SecretDocument,
+};
 use rand_core::CryptoRngCore;
 use signature::{
     hazmat::{PrehashVerifier, RandomizedPrehashSigner},
@@ -689,6 +698,57 @@ where
     }
 }
 
+fn get_pss_signature_algo_id<D>(
+    salt_len: Option<usize>,
+) -> pkcs8::spki::Result<AlgorithmIdentifierOwned>
+where
+    D: Digest + AssociatedOid,
+{
+    const ID_MGF_1: ObjectIdentifier = ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.8");
+    const ID_RSASSA_PSS: ObjectIdentifier = ObjectIdentifier::new_unwrap("1.2.840.113549.1.1.10");
+
+    let salt_len = salt_len.map_or(RsaPssParams::SALT_LEN_DEFAULT, |l| l as u8);
+
+    let pss_params = RsaPssParams {
+        hash: AlgorithmIdentifierRef {
+            oid: D::OID,
+            parameters: None,
+        },
+        mask_gen: AlgorithmIdentifier {
+            oid: ID_MGF_1,
+            parameters: Some(AlgorithmIdentifierRef {
+                oid: D::OID,
+                parameters: None,
+            }),
+        },
+        salt_len,
+        trailer_field: Default::default(),
+    };
+
+    Ok(AlgorithmIdentifierOwned {
+        oid: ID_RSASSA_PSS,
+        parameters: Some(Any::encode_from(&pss_params)?),
+    })
+}
+
+impl<D> AssociatedAlgorithmIdentifier for SigningKey<D>
+where
+    D: Digest,
+{
+    type Params = AnyRef<'static>;
+
+    const ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> = pkcs1::ALGORITHM_ID;
+}
+
+impl<D> DynSignatureAlgorithmIdentifier for SigningKey<D>
+where
+    D: Digest + AssociatedOid,
+{
+    fn signature_algorithm_identifier(&self) -> pkcs8::spki::Result<AlgorithmIdentifierOwned> {
+        get_pss_signature_algo_id::<D>(self.salt_len)
+    }
+}
+
 impl<D> From<RsaPrivateKey> for SigningKey<D>
 where
     D: Digest,
@@ -825,6 +885,24 @@ where
     }
 }
 
+impl<D> AssociatedAlgorithmIdentifier for BlindedSigningKey<D>
+where
+    D: Digest,
+{
+    type Params = AnyRef<'static>;
+
+    const ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> = pkcs1::ALGORITHM_ID;
+}
+
+impl<D> DynSignatureAlgorithmIdentifier for BlindedSigningKey<D>
+where
+    D: Digest + AssociatedOid,
+{
+    fn signature_algorithm_identifier(&self) -> pkcs8::spki::Result<AlgorithmIdentifierOwned> {
+        get_pss_signature_algo_id::<D>(self.salt_len)
+    }
+}
+
 impl<D> From<RsaPrivateKey> for BlindedSigningKey<D>
 where
     D: Digest,
@@ -958,6 +1036,15 @@ where
     }
 }
 
+impl<D> AssociatedAlgorithmIdentifier for VerifyingKey<D>
+where
+    D: Digest,
+{
+    type Params = AnyRef<'static>;
+
+    const ALGORITHM_IDENTIFIER: AlgorithmIdentifierRef<'static> = pkcs1::ALGORITHM_ID;
+}
+
 impl<D> From<RsaPublicKey> for VerifyingKey<D>
 where
     D: Digest,