diff --git a/tests/suites/test_suite_x509parse.data b/tests/suites/test_suite_x509parse.data
index ce49ff0fc1..6f4b4c9872 100644
--- a/tests/suites/test_suite_x509parse.data
+++ b/tests/suites/test_suite_x509parse.data
@@ -1058,7 +1058,8 @@ x509parse_crt:"30193004a0020285300d06092a864886f70d01010b0500030200ff":"":MBEDTL
 
 X509 CRT ASN1 (TBS, valid inner version tag, inner length too large for int)
 depends_on:MBEDTLS_SHA256_C:MBEDTLS_RSA_C
-x509parse_crt:"30293014a012021000000000000000000000000000000000300d06092a864886f70d01010b0500030200ff":"":MBEDTLS_ERR_X509_INVALID_VERSION + MBEDTLS_ERR_ASN1_INVALID_LENGTH
+# tbsCertificate.version = 0x01000000000000000000000000000000 rejected by mbedtls_asn1_get_int
+x509parse_crt:"30293014a012021001000000000000000000000000000000300d06092a864886f70d01010b0500030200ff":"":MBEDTLS_ERR_X509_INVALID_VERSION + MBEDTLS_ERR_ASN1_INVALID_LENGTH
 
 X509 CRT ASN1 (TBS, valid inner version tag, inner vs. outer length mismatch)
 depends_on:MBEDTLS_SHA256_C:MBEDTLS_RSA_C
@@ -1825,13 +1826,36 @@ X509 CRT ASN1 (inv Signature, length out of bounds)
 depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
 x509parse_crt:"3081bb3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b05000301":"":MBEDTLS_ERR_X509_INVALID_SIGNATURE + MBEDTLS_ERR_ASN1_OUT_OF_DATA
 
-X509 CRT ASN1 (inv Signature, empty)
+X509 CRT ASN1 (inv Signature, inv data #1)
 depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
+# signature = bit string with invalid encoding (missing number of unused bits)
 x509parse_crt:"3081bb3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b05000300":"":MBEDTLS_ERR_X509_INVALID_SIGNATURE + MBEDTLS_ERR_ASN1_INVALID_DATA
 
-X509 CRT ASN1 (inv Signature, inv data)
+X509 CRT ASN1 (inv Signature, inv data #2)
 depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
-x509parse_crt:"3081bc3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b0500030100":"":MBEDTLS_ERR_X509_INVALID_SIGNATURE + MBEDTLS_ERR_ASN1_INVALID_DATA
+# signature = bit string with invalid encoding (number of unused bits too large)
+x509parse_crt:"3081bc3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b0500030108":"":MBEDTLS_ERR_X509_INVALID_SIGNATURE + MBEDTLS_ERR_ASN1_INVALID_DATA
+
+## This edge case currently fails to parse due to an ASN.1 bug.
+## It doesn't matter as far as X.509 is concerned since the signature would
+## not be valid anyway.
+## https://github.com/ARMmbed/mbed-crypto/pull/75 will fix this bug and make
+## this test case pass.
+# X509 CRT ASN1 (empty Signature)
+# depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
+# # signature = empty bit string in DER encoding
+# x509parse_crt:"3081bc3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b0500030100":"cert. version     \: 3\nserial number     \: DE\:AD\:BE\:EF\nissuer name       \: ??=Test\nsubject name      \: ??=Test\nissued  on        \: 2009-01-01 00\:00\:00\nexpires on        \: 2009-12-31 23\:59\:59\nsigned using      \: RSA with SHA-256\nRSA key size      \: 128 bits\nsubject alt name  \:\n    dNSName \: foo.test\n    dNSName \: bar.test\n":0
+
+X509 CRT ASN1 (dummy 24-bit Signature)
+depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
+# signature = bit string "011001100110111101101111"
+x509parse_crt:"3081bf3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b0500030400666f6f":"cert. version     \: 3\nserial number     \: DE\:AD\:BE\:EF\nissuer name       \: ??=Test\nsubject name      \: ??=Test\nissued  on        \: 2009-01-01 00\:00\:00\nexpires on        \: 2009-12-31 23\:59\:59\nsigned using      \: RSA with SHA-256\nRSA key size      \: 128 bits\nsubject alt name  \:\n    dNSName \: foo.test\n    dNSName \: bar.test\n":0
+
+# The ASN.1 module rejects non-octet-aligned bit strings.
+X509 CRT ASN1 (inv Signature: not octet-aligned)
+depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C
+# signature = bit string "01100110011011110110111"
+x509parse_crt:"3081bf3081a7a0030201028204deadbeef300d06092a864886f70d01010b0500300c310a30080600130454657374301c170c303930313031303030303030170c303931323331323335393539300c310a30080600130454657374302a300d06092A864886F70D010101050003190030160210ffffffffffffffffffffffffffffffff0202ffffa100a200a321301f301d0603551d11041630148208666f6f2e7465737482086261722e74657374300d06092a864886f70d01010b0500030401666f6e":"":MBEDTLS_ERR_X509_INVALID_SIGNATURE + MBEDTLS_ERR_ASN1_INVALID_DATA
 
 X509 CRT ASN1 (inv Signature, length mismatch)
 depends_on:MBEDTLS_RSA_C:MBEDTLS_SHA256_C