diff --git a/ChangeLog.d/x509-add-tag-check-to-algorithm-params b/ChangeLog.d/x509-add-tag-check-to-algorithm-params
new file mode 100644
index 000000000..f2c72b0ec
--- /dev/null
+++ b/ChangeLog.d/x509-add-tag-check-to-algorithm-params
@@ -0,0 +1,11 @@
+Security
+   * Fix a compliance issue whereby we were not checking the tag on the
+     algorithm parameters (only the size) when comparing the signature in the
+     description part of the cert to the real signature. This meant that a
+     NULL algorithm parameters entry would look identical to an array of REAL
+     (size zero) to the library and thus the certificate would be considered
+     valid. However, if the parameters do not match in *any* way then the
+     certificate should be considered invalid, and indeed OpenSSL marks these
+     certs as invalid when mbedtls did not.
+     Many thanks to guidovranken who found this issue via differential fuzzing
+     and reported it in #3629.
diff --git a/library/x509_crt.c b/library/x509_crt.c
index d519a3fa1..fd89135b9 100644
--- a/library/x509_crt.c
+++ b/library/x509_crt.c
@@ -1088,6 +1088,7 @@ static int x509_crt_parse_der_core( mbedtls_x509_crt *crt, const unsigned char *
 
     if( crt->sig_oid.len != sig_oid2.len ||
         memcmp( crt->sig_oid.p, sig_oid2.p, crt->sig_oid.len ) != 0 ||
+        sig_params1.tag != sig_params2.tag ||
         sig_params1.len != sig_params2.len ||
         ( sig_params1.len != 0 &&
           memcmp( sig_params1.p, sig_params2.p, sig_params1.len ) != 0 ) )
diff --git a/tests/data_files/Makefile b/tests/data_files/Makefile
index 0429bddd1..6c9e24513 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -155,7 +155,11 @@ cli-rsa-sha256.crt.der: cli-rsa-sha256.crt
 	$(OPENSSL) x509 -in $< -out $@ -inform PEM -outform DER
 all_final += cli-rsa-sha256.crt.der
 
- cli-rsa.key.der: $(cli_crt_key_file_rsa)
+cli-rsa-sha256-badalg.crt.der: cli-rsa-sha256.crt.der
+	hexdump -ve '1/1 "%.2X"' $< | sed "s/06092A864886F70D01010B0500/06092A864886F70D01010B0900/2" | xxd -r -p > $@
+all_final += cli-rsa-sha256-badalg.crt.der
+
+cli-rsa.key.der: $(cli_crt_key_file_rsa)
 	$(OPENSSL) pkey -in $< -out $@ -inform PEM -outform DER
 all_final += cli-rsa.key.der
 
diff --git a/tests/data_files/cli-rsa-sha256-badalg.crt.der b/tests/data_files/cli-rsa-sha256-badalg.crt.der
new file mode 100644
index 000000000..c40ba2a44
Binary files /dev/null and b/tests/data_files/cli-rsa-sha256-badalg.crt.der differ
diff --git a/tests/suites/test_suite_x509parse.data b/tests/suites/test_suite_x509parse.data
index 28ba79bff..14ba0ded1 100644
--- a/tests/suites/test_suite_x509parse.data
+++ b/tests/suites/test_suite_x509parse.data
@@ -1876,6 +1876,10 @@ X509 File parse (trailing spaces, OK)
 depends_on:MBEDTLS_ECDSA_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED:MBEDTLS_SHA256_C:MBEDTLS_RSA_C
 x509parse_crt_file:"data_files/server7_trailing_space.crt":0
 
+X509 File parse (Algorithm Params Tag mismatch)
+depends_on:MBEDTLS_SHA256_C:MBEDTLS_RSA_C
+x509parse_crt_file:"data_files/cli-rsa-sha256-badalg.crt.der":MBEDTLS_ERR_X509_SIG_MISMATCH
+
 X509 Get time (UTC no issues)
 depends_on:MBEDTLS_X509_USE_C
 x509_get_time:MBEDTLS_ASN1_UTC_TIME:"500101000000Z":0:1950:1:1:0:0:0