diff --git a/ChangeLog.d/mpi_fill_random-rng_failure.txt b/ChangeLog.d/mpi_fill_random-rng_failure.txt
new file mode 100644
index 0000000..8addf18
--- /dev/null
+++ b/ChangeLog.d/mpi_fill_random-rng_failure.txt
@@ -0,0 +1,8 @@
+Security
+   * A failure of the random generator was ignored in mbedtls_mpi_fill_random(),
+     which is how most uses of randomization in asymmetric cryptography
+     (including key generation, intermediate value randomization and blinding)
+     are implemented. This could cause failures or the silent use of non-random
+     values. A random generator can fail if it needs reseeding and cannot not
+     obtain entropy, or due to an internal failure (which, for Mbed TLS's own
+     CTR_DRBG or HMAC_DRBG, can only happen due to a misconfiguration).
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 0000000..f2c72b0
--- /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/bignum.c b/library/bignum.c
index a9d5194..55d9482 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -2338,7 +2338,7 @@
     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
 
     Xp = (unsigned char*) X->p;
-    f_rng( p_rng, Xp + overhead, size );
+    MBEDTLS_MPI_CHK( f_rng( p_rng, Xp + overhead, size ) );
 
     mpi_bigendian_to_host( X->p, limbs );
 
diff --git a/library/x509_crt.c b/library/x509_crt.c
index d519a3f..fd89135 100644
--- a/library/x509_crt.c
+++ b/library/x509_crt.c
@@ -1088,6 +1088,7 @@
 
     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 0429bdd..6c9e245 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -155,7 +155,11 @@
 	$(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 0000000..c40ba2a
--- /dev/null
+++ b/tests/data_files/cli-rsa-sha256-badalg.crt.der
Binary files differ
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index e5ec777..1298689 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -949,6 +949,48 @@
 Test bit set (Invalid bit value)
 mbedtls_mpi_set_bit:16:"00":5:2:16:"00":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
 
+Fill random: 0 bytes
+mpi_fill_random:0:0:0
+
+Fill random: 1 byte, good
+mpi_fill_random:1:1:0
+
+Fill random: 2 bytes, good, no leading zero
+mpi_fill_random:2:2:0
+
+Fill random: 2 bytes, good, 1 leading zero
+mpi_fill_random:2:256:0
+
+Fill random: MAX_SIZE - 7, good
+mpi_fill_random:MBEDTLS_MPI_MAX_SIZE - 7:MBEDTLS_MPI_MAX_SIZE - 7:0
+
+Fill random: MAX_SIZE, good
+mpi_fill_random:MBEDTLS_MPI_MAX_SIZE:MBEDTLS_MPI_MAX_SIZE:0
+
+Fill random: 1 byte, RNG failure
+mpi_fill_random:1:0:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 2 bytes, RNG failure after 1 byte
+mpi_fill_random:2:1:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 4 bytes, RNG failure after 3 bytes
+mpi_fill_random:4:3:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 8 bytes, RNG failure after 7 bytes
+mpi_fill_random:8:7:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 16 bytes, RNG failure after 1 bytes
+mpi_fill_random:16:1:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 16 bytes, RNG failure after 8 bytes
+mpi_fill_random:16:8:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: 16 bytes, RNG failure after 15 bytes
+mpi_fill_random:16:15:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
+Fill random: MAX_SIZE bytes, RNG failure after MAX_SIZE-1 bytes
+mpi_fill_random:MBEDTLS_MPI_MAX_SIZE:MBEDTLS_MPI_MAX_SIZE-1:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
+
 MPI Selftest
 depends_on:MBEDTLS_SELF_TEST
 mpi_selftest:
diff --git a/tests/suites/test_suite_mpi.function b/tests/suites/test_suite_mpi.function
index 0335538..ffda605 100644
--- a/tests/suites/test_suite_mpi.function
+++ b/tests/suites/test_suite_mpi.function
@@ -1,5 +1,6 @@
 /* BEGIN_HEADER */
 #include "mbedtls/bignum.h"
+#include "mbedtls/entropy.h"
 
 #if MBEDTLS_MPI_MAX_BITS > 792
 #define MPI_MAX_BITS_LARGER_THAN_792
@@ -47,6 +48,22 @@
 
     return( 0 );
 }
+
+/* Random generator that is told how many bytes to return. */
+static int f_rng_bytes_left( void *state, unsigned char *buf, size_t len )
+{
+    size_t *bytes_left = state;
+    size_t i;
+    for( i = 0; i < len; i++ )
+    {
+        if( *bytes_left == 0 )
+            return( MBEDTLS_ERR_ENTROPY_SOURCE_FAILED );
+        buf[i] = *bytes_left & 0xff;
+        --( *bytes_left );
+    }
+    return( 0 );
+}
+
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -1289,6 +1306,37 @@
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void mpi_fill_random( int wanted_bytes, int rng_bytes, int expected_ret )
+{
+    mbedtls_mpi X;
+    int ret;
+    size_t bytes_left = rng_bytes;
+    mbedtls_mpi_init( &X );
+
+    ret = mbedtls_mpi_fill_random( &X, wanted_bytes,
+                                   f_rng_bytes_left, &bytes_left );
+    TEST_ASSERT( ret == expected_ret );
+
+    if( expected_ret == 0 )
+    {
+        /* mbedtls_mpi_fill_random is documented to use bytes from the RNG
+         * as a big-endian representation of the number. We know when
+         * our RNG function returns null bytes, so we know how many
+         * leading zero bytes the number has. */
+        size_t leading_zeros = 0;
+        if( wanted_bytes > 0 && rng_bytes % 256 == 0 )
+            leading_zeros = 1;
+        TEST_ASSERT( mbedtls_mpi_size( &X ) + leading_zeros ==
+                     (size_t) wanted_bytes );
+        TEST_ASSERT( (int) bytes_left == rng_bytes - wanted_bytes );
+    }
+
+exit:
+    mbedtls_mpi_free( &X );
+}
+/* END_CASE */
+
 /* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
 void mpi_selftest(  )
 {
diff --git a/tests/suites/test_suite_x509parse.data b/tests/suites/test_suite_x509parse.data
index 28ba79b..14ba0de 100644
--- a/tests/suites/test_suite_x509parse.data
+++ b/tests/suites/test_suite_x509parse.data
@@ -1876,6 +1876,10 @@
 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