diff --git a/openssl-sys/src/lib.rs b/openssl-sys/src/lib.rs
index fda47fd0..e7bd046e 100644
--- a/openssl-sys/src/lib.rs
+++ b/openssl-sys/src/lib.rs
@@ -1453,6 +1453,10 @@ pub unsafe fn BIO_set_retry_write(b: *mut BIO) {
     BIO_set_flags(b, BIO_FLAGS_WRITE | BIO_FLAGS_SHOULD_RETRY)
 }
 
+pub unsafe fn EVP_get_digestbynid(type_: c_int) -> *const EVP_MD {
+    EVP_get_digestbyname(OBJ_nid2sn(type_))
+}
+
 // EVP_PKEY_CTX_ctrl macros
 pub unsafe fn EVP_PKEY_CTX_set_rsa_padding(ctx: *mut EVP_PKEY_CTX, pad: c_int) -> c_int {
     EVP_PKEY_CTX_ctrl(
@@ -2103,6 +2107,8 @@ extern "C" {
         no_name: c_int,
     ) -> c_int;
     pub fn OBJ_nid2sn(nid: c_int) -> *const c_char;
+    pub fn OBJ_find_sigid_algs(signid: c_int, pdig_nid: *mut c_int, ppkey_nid: *mut c_int)
+        -> c_int;
 
     pub fn OCSP_BASICRESP_new() -> *mut OCSP_BASICRESP;
     pub fn OCSP_BASICRESP_free(r: *mut OCSP_BASICRESP);
@@ -2840,6 +2846,7 @@ extern "C" {
     );
 
     pub fn EVP_MD_size(md: *const EVP_MD) -> c_int;
+    pub fn EVP_get_digestbyname(name: *const c_char) -> *const EVP_MD;
     pub fn EVP_get_cipherbyname(name: *const c_char) -> *const EVP_CIPHER;
 
     pub fn SSL_set_connect_state(s: *mut SSL);
diff --git a/openssl/src/hash.rs b/openssl/src/hash.rs
index 582a2ada..49797df8 100644
--- a/openssl/src/hash.rs
+++ b/openssl/src/hash.rs
@@ -4,6 +4,10 @@ use std::io;
 use std::io::prelude::*;
 use std::ops::{Deref, DerefMut};
 
+use error::ErrorStack;
+use nid::Nid;
+use {cvt, cvt_p};
+
 cfg_if! {
     if #[cfg(ossl110)] {
         use ffi::{EVP_MD_CTX_free, EVP_MD_CTX_new};
@@ -12,9 +16,6 @@ cfg_if! {
     }
 }
 
-use error::ErrorStack;
-use {cvt, cvt_p};
-
 #[derive(Copy, Clone)]
 pub struct MessageDigest(*const ffi::EVP_MD);
 
@@ -23,6 +24,22 @@ impl MessageDigest {
         MessageDigest(x)
     }
 
+    /// Returns the `MessageDigest` corresponding to an `Nid`.
+    ///
+    /// This corresponds to [`EVP_get_digestbynid`].
+    ///
+    /// [`EVP_get_digestbynid`]: https://www.openssl.org/docs/man1.1.0/crypto/EVP_DigestInit.html
+    pub fn from_nid(type_: Nid) -> Option<MessageDigest> {
+        unsafe {
+            let ptr = ffi::EVP_get_digestbynid(type_.as_raw());
+            if ptr.is_null() {
+                None
+            } else {
+                Some(MessageDigest(ptr))
+            }
+        }
+    }
+
     pub fn md5() -> MessageDigest {
         unsafe { MessageDigest(ffi::EVP_md5()) }
     }
@@ -405,4 +422,12 @@ mod tests {
             hash_test(MessageDigest::ripemd160(), test);
         }
     }
+
+    #[test]
+    fn from_nid() {
+        assert_eq!(
+            MessageDigest::from_nid(Nid::SHA256).unwrap().as_ptr(),
+            MessageDigest::sha256().as_ptr()
+        );
+    }
 }
diff --git a/openssl/src/nid.rs b/openssl/src/nid.rs
index 7c041236..78ffac96 100644
--- a/openssl/src/nid.rs
+++ b/openssl/src/nid.rs
@@ -1,6 +1,7 @@
 //! A collection of numerical identifiers for OpenSSL objects.
 use ffi;
 use libc::c_int;
+use std::ptr;
 
 /// A numerical identifier for an OpenSSL object.
 ///
@@ -42,6 +43,20 @@ impl Nid {
         self.0
     }
 
+    /// Returns the `Nid` of the digest algorithm associated with a signature ID.
+    ///
+    /// This corresponds to `OBJ_find_sigid_algs`.
+    pub fn digest_algorithm(&self) -> Option<Nid> {
+        unsafe {
+            let mut digest = 0;
+            if ffi::OBJ_find_sigid_algs(self.0, &mut digest, ptr::null_mut()) == 1 {
+                Some(Nid(digest))
+            } else {
+                None
+            }
+        }
+    }
+
     pub const UNDEF: Nid = Nid(ffi::NID_undef);
     pub const ITU_T: Nid = Nid(ffi::NID_itu_t);
     pub const CCITT: Nid = Nid(ffi::NID_ccitt);
@@ -991,3 +1006,16 @@ impl Nid {
     pub const AES_192_CBC_HMAC_SHA1: Nid = Nid(ffi::NID_aes_192_cbc_hmac_sha1);
     pub const AES_256_CBC_HMAC_SHA1: Nid = Nid(ffi::NID_aes_256_cbc_hmac_sha1);
 }
+
+#[cfg(test)]
+mod test {
+    use super::Nid;
+
+    #[test]
+    fn signature_digest() {
+        assert_eq!(
+            Nid::SHA256WITHRSAENCRYPTION.digest_algorithm(),
+            Some(Nid::SHA256)
+        );
+    }
+}