diff --git a/library/mbedtls_utils.h b/library/mbedtls_utils.h
new file mode 100644
index 0000000000..67f74786b3
--- /dev/null
+++ b/library/mbedtls_utils.h
@@ -0,0 +1,23 @@
+#include "mbedtls/pk.h"
+#include "psa/crypto.h"
+
+#ifndef MBEDTLS_UTILS_H
+#define MBEDTLS_UTILS_H
+
+/* Return the PSA algorithm associated to the given combination of "sigalg" and "hash_alg". */
+static inline psa_algorithm_t mbedtls_psa_alg_from_pk_sigalg(mbedtls_pk_sigalg_t sigalg,
+                                                             psa_algorithm_t hash_alg)
+{
+    switch (sigalg) {
+        case MBEDTLS_PK_SIGALG_RSA_PKCS1V15:
+            return PSA_ALG_RSA_PKCS1V15_SIGN(hash_alg);
+        case MBEDTLS_PK_SIGALG_RSA_PSS:
+            return PSA_ALG_RSA_PSS(hash_alg);
+        case MBEDTLS_PK_SIGALG_ECDSA:
+            return MBEDTLS_PK_ALG_ECDSA(hash_alg);
+        default:
+            return PSA_ALG_NONE;
+    }
+}
+
+#endif /* MBEDTLS_UTILS_H */
diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index 36c6bf9586..be071defac 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -5605,13 +5605,15 @@ void mbedtls_ssl_config_free(mbedtls_ssl_config *conf)
  */
 unsigned char mbedtls_ssl_sig_from_pk(mbedtls_pk_context *pk)
 {
+    psa_key_type_t key_type = mbedtls_pk_get_key_type(pk);
+
 #if defined(MBEDTLS_RSA_C)
-    if (mbedtls_pk_can_do(pk, MBEDTLS_PK_RSA)) {
+    if (PSA_KEY_TYPE_IS_RSA(key_type)) {
         return MBEDTLS_SSL_SIG_RSA;
     }
 #endif
 #if defined(MBEDTLS_KEY_EXCHANGE_ECDSA_CERT_REQ_ANY_ALLOWED_ENABLED)
-    if (mbedtls_pk_can_do(pk, MBEDTLS_PK_ECDSA)) {
+    if (PSA_KEY_TYPE_IS_ECC(key_type)) {
         return MBEDTLS_SSL_SIG_ECDSA;
     }
 #endif
@@ -8780,7 +8782,7 @@ int mbedtls_ssl_verify_certificate(mbedtls_ssl_context *ssl,
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
     defined(PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY)
     if (ssl->tls_version == MBEDTLS_SSL_VERSION_TLS1_2 &&
-        mbedtls_pk_can_do(&chain->pk, MBEDTLS_PK_ECKEY)) {
+        PSA_KEY_TYPE_IS_ECC(mbedtls_pk_get_type(&chain->pk))) {
         if (mbedtls_ssl_check_curve(ssl, mbedtls_pk_get_ec_group_id(&chain->pk)) != 0) {
             MBEDTLS_SSL_DEBUG_MSG(1, ("bad certificate (EC key curve)"));
             ssl->session_negotiate->verify_result |= MBEDTLS_X509_BADCERT_BAD_KEY;
diff --git a/library/ssl_tls12_client.c b/library/ssl_tls12_client.c
index c4f75b63de..ebcc0d56bb 100644
--- a/library/ssl_tls12_client.c
+++ b/library/ssl_tls12_client.c
@@ -16,6 +16,7 @@
 #include "debug_internal.h"
 #include "mbedtls/error.h"
 #include "mbedtls/constant_time.h"
+#include "mbedtls_utils.h"
 
 #include "psa/crypto.h"
 #if defined(MBEDTLS_KEY_EXCHANGE_ECDHE_PSK_ENABLED)
@@ -1883,6 +1884,7 @@ start_processing:
         unsigned char hash[MBEDTLS_MD_MAX_SIZE];
 
         mbedtls_md_type_t md_alg = MBEDTLS_MD_NONE;
+        psa_algorithm_t psa_hash_alg;
         mbedtls_pk_sigalg_t pk_alg = MBEDTLS_PK_SIGALG_NONE;
         unsigned char *params = ssl->in_msg + mbedtls_ssl_hs_hdr_len(ssl);
         size_t params_len = (size_t) (p - params);
@@ -1921,7 +1923,10 @@ start_processing:
         }
         p += 2;
 
-        if (!mbedtls_pk_can_do(peer_pk, (mbedtls_pk_type_t) pk_alg)) {
+        psa_hash_alg = mbedtls_md_psa_alg_from_type(md_alg);
+        if (!mbedtls_pk_can_do_psa(peer_pk,
+                                   mbedtls_psa_alg_from_pk_sigalg(pk_alg, psa_hash_alg),
+                                   PSA_KEY_USAGE_VERIFY_HASH)) {
             MBEDTLS_SSL_DEBUG_MSG(1,
                                   ("bad server key exchange message"));
             mbedtls_ssl_send_alert_message(
@@ -1977,14 +1982,6 @@ start_processing:
         /*
          * Verify signature
          */
-        if (!mbedtls_pk_can_do(peer_pk, (mbedtls_pk_type_t) pk_alg)) {
-            MBEDTLS_SSL_DEBUG_MSG(1, ("bad server key exchange message"));
-            mbedtls_ssl_send_alert_message(
-                ssl,
-                MBEDTLS_SSL_ALERT_LEVEL_FATAL,
-                MBEDTLS_SSL_ALERT_MSG_HANDSHAKE_FAILURE);
-            return MBEDTLS_ERR_SSL_PK_TYPE_MISMATCH;
-        }
 
 #if defined(MBEDTLS_SSL_ECP_RESTARTABLE_ENABLED)
         if (ssl->handshake->ecrs_enabled) {
diff --git a/library/ssl_tls12_server.c b/library/ssl_tls12_server.c
index 1f4ac3ea79..ec4446c1b4 100644
--- a/library/ssl_tls12_server.c
+++ b/library/ssl_tls12_server.c
@@ -16,6 +16,7 @@
 #include "mbedtls/error.h"
 #include "mbedtls/platform_util.h"
 #include "mbedtls/constant_time.h"
+#include "mbedtls_utils.h"
 
 #include <string.h>
 
@@ -3324,6 +3325,7 @@ static int ssl_parse_certificate_verify(mbedtls_ssl_context *ssl)
     const mbedtls_ssl_ciphersuite_t *ciphersuite_info =
         ssl->handshake->ciphersuite_info;
     mbedtls_pk_context *peer_pk;
+    psa_algorithm_t psa_sig_alg;
 
     MBEDTLS_SSL_DEBUG_MSG(2, ("=> parse certificate verify"));
 
@@ -3421,7 +3423,8 @@ static int ssl_parse_certificate_verify(mbedtls_ssl_context *ssl)
     /*
      * Check the certificate's key type matches the signature alg
      */
-    if (!mbedtls_pk_can_do(peer_pk, (mbedtls_pk_type_t) pk_alg)) {
+    psa_sig_alg = mbedtls_psa_alg_from_pk_sigalg(pk_alg, mbedtls_md_psa_alg_from_type(md_alg));
+    if (!mbedtls_pk_can_do_psa(peer_pk, psa_sig_alg, PSA_KEY_USAGE_VERIFY_HASH)) {
         MBEDTLS_SSL_DEBUG_MSG(1, ("sig_alg doesn't match cert key"));
         return MBEDTLS_ERR_SSL_ILLEGAL_PARAMETER;
     }
diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index c7d3d48561..078daea352 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -18,6 +18,7 @@
 #include "mbedtls/constant_time.h"
 #include "psa/crypto.h"
 #include "mbedtls/psa_util.h"
+#include "mbedtls_utils.h"
 
 #include "ssl_tls13_invasive.h"
 #include "ssl_tls13_keys.h"
@@ -276,7 +277,9 @@ static int ssl_tls13_parse_certificate_verify(mbedtls_ssl_context *ssl,
     /*
      * Check the certificate's key type matches the signature alg
      */
-    if (!mbedtls_pk_can_do(&ssl->session_negotiate->peer_cert->pk, (mbedtls_pk_type_t) sig_alg)) {
+    if (!mbedtls_pk_can_do_psa(&ssl->session_negotiate->peer_cert->pk,
+                               mbedtls_psa_alg_from_pk_sigalg(sig_alg, hash_alg),
+                               PSA_KEY_USAGE_VERIFY_HASH)) {
         MBEDTLS_SSL_DEBUG_MSG(1, ("signature algorithm doesn't match cert key"));
         goto error;
     }
diff --git a/library/x509_crt.c b/library/x509_crt.c
index e18dbe777e..61dca746a3 100644
--- a/library/x509_crt.c
+++ b/library/x509_crt.c
@@ -43,6 +43,8 @@
 #include "mbedtls/threading.h"
 #endif
 
+#include "mbedtls_utils.h"
+
 #if defined(MBEDTLS_HAVE_TIME)
 #if defined(_WIN32) && !defined(EFIX64) && !defined(EFI32)
 #ifndef WIN32_LEAN_AND_MEAN
@@ -2108,6 +2110,13 @@ static int x509_crt_check_signature(const mbedtls_x509_crt *child,
     psa_algorithm_t hash_alg = mbedtls_md_psa_alg_from_type(child->sig_md);
     psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
 
+    /* Skip expensive computation on obvious mismatch */
+    if (!mbedtls_pk_can_do_psa(&parent->pk,
+                               mbedtls_psa_alg_from_pk_sigalg(child->sig_pk, hash_alg),
+                               PSA_KEY_USAGE_VERIFY_HASH)) {
+        return -1;
+    }
+
     status = psa_hash_compute(hash_alg,
                               child->tbs.p,
                               child->tbs.len,
@@ -2118,11 +2127,6 @@ static int x509_crt_check_signature(const mbedtls_x509_crt *child,
         return MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED;
     }
 
-    /* Skip expensive computation on obvious mismatch */
-    if (!mbedtls_pk_can_do(&parent->pk, (mbedtls_pk_type_t) child->sig_pk)) {
-        return -1;
-    }
-
 #if defined(MBEDTLS_ECP_RESTARTABLE)
     if (rs_ctx != NULL && child->sig_pk == MBEDTLS_PK_SIGALG_ECDSA) {
         return mbedtls_pk_verify_restartable(&parent->pk,
diff --git a/library/x509write_crt.c b/library/x509write_crt.c
index 399c923097..8c77f10c34 100644
--- a/library/x509write_crt.c
+++ b/library/x509write_crt.c
@@ -392,6 +392,7 @@ int mbedtls_x509write_crt_der(mbedtls_x509write_cert *ctx,
     unsigned char hash[MBEDTLS_MD_MAX_SIZE];
     psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
     psa_algorithm_t psa_algorithm;
+    psa_key_type_t key_type = mbedtls_pk_get_key_type(ctx->issuer_key);
 
     size_t sub_len = 0, pub_len = 0, sig_and_oid_len = 0, sig_len;
     size_t len = 0;
@@ -407,9 +408,9 @@ int mbedtls_x509write_crt_der(mbedtls_x509write_cert *ctx,
 
     /* There's no direct way of extracting a signature algorithm
      * (represented as an element of mbedtls_pk_type_t) from a PK instance. */
-    if (mbedtls_pk_can_do(ctx->issuer_key, MBEDTLS_PK_RSA)) {
+    if (PSA_KEY_TYPE_IS_RSA(key_type)) {
         pk_alg = MBEDTLS_PK_SIGALG_RSA_PKCS1V15;
-    } else if (mbedtls_pk_can_do(ctx->issuer_key, MBEDTLS_PK_ECDSA)) {
+    } else if (PSA_KEY_TYPE_IS_ECC(key_type)) {
         pk_alg = MBEDTLS_PK_SIGALG_ECDSA;
     } else {
         return MBEDTLS_ERR_X509_INVALID_ALG;
diff --git a/library/x509write_csr.c b/library/x509write_csr.c
index 8a81f7ee56..22651032b1 100644
--- a/library/x509write_csr.c
+++ b/library/x509write_csr.c
@@ -144,6 +144,7 @@ static int x509write_csr_der_internal(mbedtls_x509write_csr *ctx,
     mbedtls_pk_sigalg_t pk_alg;
     size_t hash_len;
     psa_algorithm_t hash_alg = mbedtls_md_psa_alg_from_type(ctx->md_alg);
+    psa_key_type_t key_type = mbedtls_pk_get_key_type(ctx->key);
 
     /* Write the CSR backwards starting from the end of buf */
     c = buf + size;
@@ -217,9 +218,9 @@ static int x509write_csr_der_internal(mbedtls_x509write_csr *ctx,
         return MBEDTLS_ERR_PLATFORM_HW_ACCEL_FAILED;
     }
 
-    if (mbedtls_pk_can_do(ctx->key, MBEDTLS_PK_RSA)) {
+    if (PSA_KEY_TYPE_IS_RSA(key_type)) {
         pk_alg = MBEDTLS_PK_SIGALG_RSA_PKCS1V15;
-    } else if (mbedtls_pk_can_do(ctx->key, MBEDTLS_PK_ECDSA)) {
+    } else if (PSA_KEY_TYPE_IS_ECC(key_type)) {
         pk_alg = MBEDTLS_PK_SIGALG_ECDSA;
     } else {
         return MBEDTLS_ERR_X509_INVALID_ALG;