diff --git a/evp.go b/evp.go
index ef68bbfb..f6a2d3ed 100644
--- a/evp.go
+++ b/evp.go
@@ -89,78 +89,78 @@ func hashFuncToMD(fn func() hash.Hash) (C.GO_EVP_MD_PTR, error) {
 	return md, nil
 }
 
-// cryptoHashToMD converts a crypto.Hash to a GO_EVP_MD_PTR.
-func cryptoHashToMD(ch crypto.Hash) (md C.GO_EVP_MD_PTR) {
+// cryptoHashToMD converts a crypto.Hash to a EVP_MD.
+func cryptoHashToMD(ch crypto.Hash) C.GO_EVP_MD_PTR {
 	if v, ok := cacheMD.Load(ch); ok {
 		return v.(C.GO_EVP_MD_PTR)
 	}
-	defer func() {
-		if md != nil {
-			switch vMajor {
-			case 1:
-				// On OpenSSL 1 EVP_MD objects can be not-nil even
-				// when they are not supported. We need to pass the md
-				// to a EVP_MD_CTX to really know if they can be used.
-				ctx := C.go_openssl_EVP_MD_CTX_new()
-				if C.go_openssl_EVP_DigestInit_ex(ctx, md, nil) != 1 {
-					md = nil
-				}
-				C.go_openssl_EVP_MD_CTX_free(ctx)
-			case 3:
-				// On OpenSSL 3, directly operating on a EVP_MD object
-				// not created by EVP_MD_fetch has negative performance
-				// implications, as digest operations will have
-				// to fetch it on every call. Better to just fetch it once here.
-				md = C.go_openssl_EVP_MD_fetch(nil, C.go_openssl_EVP_MD_get0_name(md), nil)
-			default:
-				panic(errUnsupportedVersion())
-			}
-		}
-		cacheMD.Store(ch, md)
-	}()
-	// SupportsHash returns false for MD5SHA1 because we don't
-	// provide a hash.Hash implementation for it. Yet, it can
-	// still be used when signing/verifying with an RSA key.
-	if ch == crypto.MD5SHA1 {
-		if vMajor == 1 && vMinor == 0 {
-			return C.go_openssl_EVP_md5_sha1_backport()
-		} else {
-			return C.go_openssl_EVP_md5_sha1()
-		}
-	}
+	var md C.GO_EVP_MD_PTR
 	switch ch {
+	case crypto.RIPEMD160:
+		md = C.go_openssl_EVP_ripemd160()
 	case crypto.MD4:
-		return C.go_openssl_EVP_md4()
+		md = C.go_openssl_EVP_md4()
 	case crypto.MD5:
-		return C.go_openssl_EVP_md5()
+		md = C.go_openssl_EVP_md5()
+	case crypto.MD5SHA1:
+		if vMajor == 1 && vMinor == 0 {
+			md = C.go_openssl_EVP_md5_sha1_backport()
+		} else {
+			md = C.go_openssl_EVP_md5_sha1()
+		}
 	case crypto.SHA1:
-		return C.go_openssl_EVP_sha1()
+		md = C.go_openssl_EVP_sha1()
 	case crypto.SHA224:
-		return C.go_openssl_EVP_sha224()
+		md = C.go_openssl_EVP_sha224()
 	case crypto.SHA256:
-		return C.go_openssl_EVP_sha256()
+		md = C.go_openssl_EVP_sha256()
 	case crypto.SHA384:
-		return C.go_openssl_EVP_sha384()
+		md = C.go_openssl_EVP_sha384()
 	case crypto.SHA512:
-		return C.go_openssl_EVP_sha512()
+		md = C.go_openssl_EVP_sha512()
+	case crypto.SHA512_224:
+		if versionAtOrAbove(1, 1, 1) {
+			md = C.go_openssl_EVP_sha512_224()
+		}
+	case crypto.SHA512_256:
+		if versionAtOrAbove(1, 1, 1) {
+			md = C.go_openssl_EVP_sha512_256()
+		}
 	case crypto.SHA3_224:
 		if versionAtOrAbove(1, 1, 1) {
-			return C.go_openssl_EVP_sha3_224()
+			md = C.go_openssl_EVP_sha3_224()
 		}
 	case crypto.SHA3_256:
 		if versionAtOrAbove(1, 1, 1) {
-			return C.go_openssl_EVP_sha3_256()
+			md = C.go_openssl_EVP_sha3_256()
 		}
 	case crypto.SHA3_384:
 		if versionAtOrAbove(1, 1, 1) {
-			return C.go_openssl_EVP_sha3_384()
+			md = C.go_openssl_EVP_sha3_384()
 		}
 	case crypto.SHA3_512:
 		if versionAtOrAbove(1, 1, 1) {
-			return C.go_openssl_EVP_sha3_512()
+			md = C.go_openssl_EVP_sha3_512()
 		}
 	}
-	return nil
+	if md == nil {
+		cacheMD.Store(ch, nil)
+		return nil
+	}
+	if vMajor == 3 {
+		// On OpenSSL 3, directly operating on a EVP_MD object
+		// not created by EVP_MD_fetch has negative performance
+		// implications, as digest operations will have
+		// to fetch it on every call. Better to just fetch it once here.
+		md1 := C.go_openssl_EVP_MD_fetch(nil, C.go_openssl_EVP_MD_get0_name(md), nil)
+		// Don't overwrite md in case it can't be fetched, as the md may still be used
+		// outside of EVP_MD_CTX, for example to sign and verify RSA signatures.
+		if md1 != nil {
+			md = md1
+		}
+	}
+	cacheMD.Store(ch, md)
+	return md
 }
 
 // generateEVPPKey generates a new EVP_PKEY with the given id and properties.
diff --git a/hash.go b/hash.go
index 6fd3a518..379dd1b8 100644
--- a/hash.go
+++ b/hash.go
@@ -78,9 +78,29 @@ func SHA512(p []byte) (sum [64]byte) {
 	return
 }
 
-// SupportsHash returns true if a hash.Hash implementation is supported for h.
+// cacheHashSupported is a cache of crypto.Hash support.
+var cacheHashSupported sync.Map
+
+// SupportsHash reports whether the current OpenSSL version supports the given hash.
 func SupportsHash(h crypto.Hash) bool {
-	return cryptoHashToMD(h) != nil
+	if v, ok := cacheHashSupported.Load(h); ok {
+		return v.(bool)
+	}
+	md := cryptoHashToMD(h)
+	if md == nil {
+		cacheHashSupported.Store(h, false)
+		return false
+	}
+	// EVP_MD objects can be non-nil even when they can't be used
+	// in a EVP_MD_CTX, e.g. MD5 in FIPS mode. We need to prove
+	// if they can be used by passing them to a EVP_MD_CTX.
+	var supported bool
+	if ctx := C.go_openssl_EVP_MD_CTX_new(); ctx != nil {
+		supported = C.go_openssl_EVP_DigestInit_ex(ctx, md, nil) == 1
+		C.go_openssl_EVP_MD_CTX_free(ctx)
+	}
+	cacheHashSupported.Store(h, supported)
+	return supported
 }
 
 func SHA3_224(p []byte) (sum [28]byte) {
diff --git a/rsa_test.go b/rsa_test.go
index 5b92025e..4b383384 100644
--- a/rsa_test.go
+++ b/rsa_test.go
@@ -7,6 +7,7 @@ import (
 	"fmt"
 	"math/big"
 	"strconv"
+	"strings"
 	"testing"
 
 	"github.com/golang-fips/openssl/v2"
@@ -193,7 +194,61 @@ func TestRSAEncryptDecryptOAEP_WrongLabel(t *testing.T) {
 	}
 }
 
+// These are all the hashes supported by Go's crypto/rsa package
+// as of Go 1.24.
+var stdHashes = [...]crypto.Hash{
+	crypto.MD5SHA1,
+	crypto.MD5,
+	crypto.SHA1,
+	crypto.SHA224,
+	crypto.SHA256,
+	crypto.SHA512,
+	crypto.SHA512_224,
+	crypto.SHA512_256,
+	crypto.SHA3_224,
+	crypto.SHA3_256,
+	crypto.SHA3_512,
+	crypto.RIPEMD160,
+}
+
 func TestRSASignVerifyPKCS1v15(t *testing.T) {
+	priv, pub := newRSAKey(t, 2048)
+	for _, hash := range append([]crypto.Hash{0}, stdHashes[:]...) {
+		var name string
+		if hash == 0 {
+			name = "unhashed"
+		} else {
+			name = hash.String()
+		}
+		t.Run(name, func(t *testing.T) {
+			if hash != 0 && !openssl.SupportsHash(hash) {
+				t.Skip("skipping test because hash is not supported")
+			}
+			// Construct a fake hashed data.
+			size := 1
+			if hash != 0 {
+				size = hash.Size()
+			}
+			hashed := make([]byte, size)
+			hashed[0] = 0x30
+			signed, err := openssl.SignRSAPKCS1v15(priv, hash, hashed)
+			if err != nil {
+				if strings.Contains(err.Error(), "invalid digest") || strings.Contains(err.Error(), "digest not allowed") {
+					// Can happen if the hash is supported by EVP_MD_CTX but not by EVP_PKEY_CTX.
+					// There is nothing we can do about it.
+					t.Skip("skipping test because hash is not supported")
+				}
+				t.Fatal(err)
+			}
+			err = openssl.VerifyRSAPKCS1v15(pub, hash, hashed, signed)
+			if err != nil {
+				t.Fatal(err)
+			}
+		})
+	}
+}
+
+func TestRSAHashSignVerifyPKCS1v15(t *testing.T) {
 	sha256 := openssl.NewSHA256()
 	priv, pub := newRSAKey(t, 2048)
 	msg := []byte("hi!")
@@ -220,23 +275,6 @@ func TestRSASignVerifyPKCS1v15(t *testing.T) {
 	}
 }
 
-func TestRSASignVerifyPKCS1v15_Unhashed(t *testing.T) {
-	if openssl.SymCryptProviderAvailable() {
-		t.Skip("SymCrypt provider does not support unhashed PKCS1v15")
-	}
-
-	msg := []byte("hi!")
-	priv, pub := newRSAKey(t, 2048)
-	signed, err := openssl.SignRSAPKCS1v15(priv, 0, msg)
-	if err != nil {
-		t.Fatal(err)
-	}
-	err = openssl.VerifyRSAPKCS1v15(pub, 0, msg, signed)
-	if err != nil {
-		t.Fatal(err)
-	}
-}
-
 func TestRSASignVerifyPKCS1v15_Invalid(t *testing.T) {
 	sha256 := openssl.NewSHA256()
 	msg := []byte("hi!")
@@ -254,6 +292,37 @@ func TestRSASignVerifyPKCS1v15_Invalid(t *testing.T) {
 }
 
 func TestRSASignVerifyRSAPSS(t *testing.T) {
+	priv, pub := newRSAKey(t, 2048)
+	for _, hash := range stdHashes {
+		t.Run(hash.String(), func(t *testing.T) {
+			if !openssl.SupportsHash(hash) {
+				t.Skip("skipping test because hash is not supported")
+			}
+			// Construct a fake hashed data.
+			size := 1
+			if hash != 0 {
+				size = hash.Size()
+			}
+			hashed := make([]byte, size)
+			hashed[0] = 0x30
+			signed, err := openssl.SignRSAPSS(priv, hash, hashed, rsa.PSSSaltLengthEqualsHash)
+			if err != nil {
+				if strings.Contains(err.Error(), "invalid digest") || strings.Contains(err.Error(), "digest not allowed") {
+					// Can happen if the hash is supported by EVP_MD_CTX but not by EVP_PKEY_CTX.
+					// There is nothing we can do about it.
+					t.Skip("skipping test because hash is not supported")
+				}
+				t.Fatal(err)
+			}
+			err = openssl.VerifyRSAPSS(pub, hash, hashed, signed, rsa.PSSSaltLengthEqualsHash)
+			if err != nil {
+				t.Fatal(err)
+			}
+		})
+	}
+}
+
+func TestRSASignVerifyRSAPSS_SaltLength(t *testing.T) {
 	// Test cases taken from
 	// https://github.com/golang/go/blob/54182ff54a687272dd7632c3a963e036ce03cb7c/src/crypto/rsa/pss_test.go#L200.
 	const keyBits = 2048
diff --git a/shims.h b/shims.h
index c8f599f7..cfb65ff5 100644
--- a/shims.h
+++ b/shims.h
@@ -237,6 +237,7 @@ DEFINEFUNC_LEGACY_1_0(int, SHA1_Init, (GO_SHA_CTX_PTR c), (c)) \
 DEFINEFUNC_LEGACY_1_0(int, SHA1_Update, (GO_SHA_CTX_PTR c, const void *data, size_t len), (c, data, len)) \
 DEFINEFUNC_LEGACY_1_0(int, SHA1_Final, (unsigned char *md, GO_SHA_CTX_PTR c), (md, c)) \
 DEFINEFUNC_1_1(const GO_EVP_MD_PTR, EVP_md5_sha1, (void), ()) \
+DEFINEFUNC(const GO_EVP_MD_PTR, EVP_ripemd160, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_md4, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_md5, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_sha1, (void), ()) \
@@ -244,6 +245,8 @@ DEFINEFUNC(const GO_EVP_MD_PTR, EVP_sha224, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_sha256, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_sha384, (void), ()) \
 DEFINEFUNC(const GO_EVP_MD_PTR, EVP_sha512, (void), ()) \
+DEFINEFUNC_1_1_1(const GO_EVP_MD_PTR, EVP_sha512_224, (void), ()) \
+DEFINEFUNC_1_1_1(const GO_EVP_MD_PTR, EVP_sha512_256, (void), ()) \
 DEFINEFUNC_1_1_1(const GO_EVP_MD_PTR, EVP_sha3_224, (void), ()) \
 DEFINEFUNC_1_1_1(const GO_EVP_MD_PTR, EVP_sha3_256, (void), ()) \
 DEFINEFUNC_1_1_1(const GO_EVP_MD_PTR, EVP_sha3_384, (void), ()) \