diff --git a/tests/data_files/Makefile b/tests/data_files/Makefile
index d6df19c..01d2379 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -1765,6 +1765,22 @@
 	$(MBEDTLS_CERT_WRITE) request_file=server2.req.sha256 serial=2 issuer_crt=$(test_ca_crt) issuer_key=$(test_ca_key_file_rsa) issuer_pwd=$(test_ca_pwd_rsa) not_before=20190210144406 not_after=20290210144406 md=SHA256 version=3 output_file=$@
 all_final += server2-sha256.crt
 
+server2-sha256.ku-ka.crt: SERVER2_CRT_SERIAL=22
+server2-sha256.ku-ka.crt: SERVER2_KEY_USAGE=key_agreement
+server2-sha256.ku-ke.crt: SERVER2_CRT_SERIAL=23
+server2-sha256.ku-ke.crt: SERVER2_KEY_USAGE=key_encipherment
+server2-sha256.ku-ds.crt: SERVER2_CRT_SERIAL=24
+server2-sha256.ku-ds.crt: SERVER2_KEY_USAGE=digital_signature
+server2-sha256.ku-ds_ke.crt: SERVER2_CRT_SERIAL=28
+server2-sha256.ku-ds_ke.crt: SERVER2_KEY_USAGE=digital_signature,key_encipherment
+server2-sha256.ku-%.crt: server2.req.sha256
+	$(MBEDTLS_CERT_WRITE) request_file=server2.req.sha256 serial=$(SERVER2_CRT_SERIAL) \
+		issuer_crt=$(test_ca_crt) issuer_key=$(test_ca_key_file_rsa) issuer_pwd=$(test_ca_pwd_rsa) \
+		key_usage="$(SERVER2_KEY_USAGE)" \
+		not_before=20190210144406 not_after=20290210144406 md=SHA256 version=3 output_file=$@
+all_final += server2-sha256.ku-ka.crt server2-sha256.ku-ke.crt server2-sha256.ku-ds.crt server2-sha256.ku-ds_ke.crt
+
+all_final += server2.ku-ka.crt server2.ku-ke.crt server2.ku-ds.crt server2.ku-ds_ke.crt
 server2.ku-ka.crt: SERVER2_CRT_SERIAL=42
 server2.ku-ka.crt: SERVER2_KEY_USAGE=key_agreement
 server2.ku-ke.crt: SERVER2_CRT_SERIAL=43
diff --git a/tests/data_files/server2-sha256.ku-ds.crt b/tests/data_files/server2-sha256.ku-ds.crt
new file mode 100644
index 0000000..0d4866c
--- /dev/null
+++ b/tests/data_files/server2-sha256.ku-ds.crt
@@ -0,0 +1,20 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----
diff --git a/tests/data_files/server2-sha256.ku-ds_ke.crt b/tests/data_files/server2-sha256.ku-ds_ke.crt
new file mode 100644
index 0000000..e89e17d
--- /dev/null
+++ b/tests/data_files/server2-sha256.ku-ds_ke.crt
@@ -0,0 +1,20 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----
diff --git a/tests/data_files/server2-sha256.ku-ka.crt b/tests/data_files/server2-sha256.ku-ka.crt
new file mode 100644
index 0000000..326876b
--- /dev/null
+++ b/tests/data_files/server2-sha256.ku-ka.crt
@@ -0,0 +1,20 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----
diff --git a/tests/data_files/server2-sha256.ku-ke.crt b/tests/data_files/server2-sha256.ku-ke.crt
new file mode 100644
index 0000000..ca5c3c7
--- /dev/null
+++ b/tests/data_files/server2-sha256.ku-ke.crt
@@ -0,0 +1,20 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----
diff --git a/tests/opt-testcases/tls13-kex-modes.sh b/tests/opt-testcases/tls13-kex-modes.sh
index 49f06e0..bd4f877 100755
--- a/tests/opt-testcases/tls13-kex-modes.sh
+++ b/tests/opt-testcases/tls13-kex-modes.sh
@@ -1460,8 +1460,10 @@
             -S "key exchange mode: ephemeral"
 
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_SECP_R1_256
 run_test    "TLS 1.3: O->m: psk_ephemeral group(secp256r1) check, good" \
             "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_identity=Client_identity psk=6162636465666768696a6b6c6d6e6f70" \
             "$O_NEXT_CLI -tls1_3 -msg  -allow_no_dhe_kex -groups P-256 \
@@ -1473,8 +1475,10 @@
             -S "key exchange mode: ephemeral"
 
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_SECP_R1_384
 run_test    "TLS 1.3: O->m: psk_ephemeral group(secp384r1) check, good" \
             "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_identity=Client_identity psk=6162636465666768696a6b6c6d6e6f70" \
             "$O_NEXT_CLI -tls1_3 -msg  -allow_no_dhe_kex -groups secp384r1 \
@@ -1486,8 +1490,10 @@
             -S "key exchange mode: ephemeral"
 
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_SECP_R1_521
 run_test    "TLS 1.3: O->m: psk_ephemeral group(secp521r1) check, good" \
             "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_identity=Client_identity psk=6162636465666768696a6b6c6d6e6f70" \
             "$O_NEXT_CLI -tls1_3 -msg  -allow_no_dhe_kex -groups secp521r1 \
@@ -1499,8 +1505,10 @@
             -S "key exchange mode: ephemeral"
 
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_MONTGOMERY_255
 run_test    "TLS 1.3: O->m: psk_ephemeral group(x25519) check, good" \
             "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_identity=Client_identity psk=6162636465666768696a6b6c6d6e6f70" \
             "$O_NEXT_CLI -tls1_3 -msg  -allow_no_dhe_kex -groups X25519 \
@@ -1512,8 +1520,10 @@
             -S "key exchange mode: ephemeral"
 
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_MONTGOMERY_448
 run_test    "TLS 1.3: O->m: psk_ephemeral group(x448) check, good" \
             "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_identity=Client_identity psk=6162636465666768696a6b6c6d6e6f70" \
             "$O_NEXT_CLI -tls1_3 -msg  -allow_no_dhe_kex -groups X448 \
@@ -1524,9 +1534,11 @@
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
 
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
 requires_openssl_tls1_3_with_compatible_ephemeral
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_SECP_R1_384
 run_test "TLS 1.3 O->m: psk_ephemeral group(secp256r1->secp384r1) check, good" \
          "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_list=Client_identity,6162636465666768696a6b6c6d6e6f70,abc,dead,def,beef groups=secp384r1" \
          "$O_NEXT_CLI_NO_CERT -tls1_3 -msg -allow_no_dhe_kex -psk_identity Client_identity -psk 6162636465666768696a6b6c6d6e6f70 -groups P-256:P-384" \
@@ -1537,12 +1549,13 @@
          -s "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: ephemeral"
 
-requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C
 requires_gnutls_tls1_3
 requires_gnutls_next_no_ticket
 requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
-requires_config_enabled PSA_WANT_ALG_ECDH
+requires_all_configs_enabled MBEDTLS_SSL_PROTO_TLS1_3 MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             PSA_WANT_ALG_ECDH PSA_WANT_ECC_SECP_R1_384
 run_test "TLS 1.3 G->m: psk_ephemeral group(secp256r1->secp384r1) check, good" \
          "$P_SRV tls13_kex_modes=psk_ephemeral debug_level=5 psk_list=Client_identity,6162636465666768696a6b6c6d6e6f70,abc,dead,def,beef groups=secp384r1" \
          "$G_NEXT_CLI_NO_CERT --debug=4 --single-key-share --priority NORMAL:-VERS-ALL:-KX-ALL:+ECDHE-PSK:+DHE-PSK:+PSK:+VERS-TLS1.3:-GROUP-ALL:+GROUP-SECP256R1:+GROUP-SECP384R1 --pskusername Client_identity --pskkey 6162636465666768696a6b6c6d6e6f70 localhost" \
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 3aabec4..b12a86f 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -44,7 +44,7 @@
 #     * GNUTLS_{CLI,SERV} = 3.4.10
 #     * GNUTLS_NEXT_{CLI,SERV} = 3.7.2
 #     * OPENSSL = 1.0.2g (without Debian/Ubuntu patches)
-#     * OPENSSL_NEXT = 1.1.1a
+#     * OPENSSL_NEXT = 3.1.2
 # See the invocation of check_tools below for details.
 #
 # This script must be invoked from the toplevel directory of a git
@@ -195,6 +195,10 @@
         export CC="clang"
     fi
 
+    if [ -n "${OPENSSL_3+set}" ]; then
+        export OPENSSL_NEXT="$OPENSSL_3"
+    fi
+
     # Include more verbose output for failing tests run by CMake or make
     export CTEST_OUTPUT_ON_FAILURE=1
 
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 76be941..3549a7b 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -7716,7 +7716,7 @@
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED
 run_test    "keyUsage cli 1.3: DigitalSignature+KeyEncipherment, RSA: OK" \
             "$O_NEXT_SRV_NO_CERT -tls1_3 -num_tickets=0 -key data_files/server2.key \
-             -cert data_files/server2.ku-ds_ke.crt" \
+             -cert data_files/server2-sha256.ku-ds_ke.crt" \
             "$P_CLI debug_level=3" \
             0 \
             -C "bad certificate (usage extensions)" \
@@ -7728,7 +7728,7 @@
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED
 run_test    "keyUsage cli 1.3: KeyEncipherment, RSA: fail" \
             "$O_NEXT_SRV_NO_CERT -tls1_3 -num_tickets=0 -key data_files/server2.key \
-             -cert data_files/server2.ku-ke.crt" \
+             -cert data_files/server2-sha256.ku-ke.crt" \
             "$P_CLI debug_level=1" \
             1 \
             -c "bad certificate (usage extensions)" \
@@ -7740,7 +7740,7 @@
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED
 run_test    "keyUsage cli 1.3: KeyAgreement, RSA: fail" \
             "$O_NEXT_SRV_NO_CERT -tls1_3 -num_tickets=0 -key data_files/server2.key \
-             -cert data_files/server2.ku-ka.crt" \
+             -cert data_files/server2-sha256.ku-ka.crt" \
             "$P_CLI debug_level=1" \
             1 \
             -c "bad certificate (usage extensions)" \
@@ -7839,7 +7839,7 @@
 run_test    "keyUsage cli-auth 1.3: RSA, DigitalSignature: OK" \
             "$P_SRV debug_level=1 force_version=tls13 auth_mode=optional" \
             "$O_NEXT_CLI_NO_CERT -key data_files/server2.key \
-             -cert data_files/server2.ku-ds.crt" \
+             -cert data_files/server2-sha256.ku-ds.crt" \
             0 \
             -s "Verifying peer X.509 certificate... ok" \
             -S "bad certificate (usage extensions)" \
@@ -7851,7 +7851,7 @@
 run_test    "keyUsage cli-auth 1.3: RSA, KeyEncipherment: fail (soft)" \
             "$P_SRV debug_level=1 force_version=tls13 auth_mode=optional" \
             "$O_NEXT_CLI_NO_CERT -key data_files/server2.key \
-             -cert data_files/server2.ku-ke.crt" \
+             -cert data_files/server2-sha256.ku-ke.crt" \
             0 \
             -s "bad certificate (usage extensions)" \
             -S "Processing of the Certificate handshake message failed"