diff --git a/library/asn1parse.c b/library/asn1parse.c
index 4764ca4cb..412259e35 100644
--- a/library/asn1parse.c
+++ b/library/asn1parse.c
@@ -149,16 +149,26 @@ int mbedtls_asn1_get_int( unsigned char **p,
     if( ( ret = mbedtls_asn1_get_tag( p, end, &len, MBEDTLS_ASN1_INTEGER ) ) != 0 )
         return( ret );
 
-    if( len == 0 || ( **p & 0x80 ) != 0 )
+    /* len==0 is malformed (0 must be represented as 020100). */
+    if( len == 0 )
+        return( MBEDTLS_ERR_ASN1_INVALID_LENGTH );
+    /* This is a cryptography library. Reject negative integers. */
+    if( ( **p & 0x80 ) != 0 )
         return( MBEDTLS_ERR_ASN1_INVALID_LENGTH );
 
+    /* Skip leading zeros. */
     while( len > 0 && **p == 0 )
     {
         ++( *p );
         --len;
     }
+
+    /* Reject integers that don't fit in an int. This code assumes that
+     * the int type has no padding bit. */
     if( len > sizeof( int ) )
         return( MBEDTLS_ERR_ASN1_INVALID_LENGTH );
+    if( len == sizeof( int ) && ( **p & 0x80 ) != 0 )
+        return( MBEDTLS_ERR_ASN1_INVALID_LENGTH );
 
     *val = 0;
     while( len-- > 0 )
diff --git a/tests/suites/test_suite_asn1parse.data b/tests/suites/test_suite_asn1parse.data
index c5d9136b7..4abae0bb4 100644
--- a/tests/suites/test_suite_asn1parse.data
+++ b/tests/suites/test_suite_asn1parse.data
@@ -164,8 +164,7 @@ Not BOOLEAN
 get_boolean:"020101":0:MBEDTLS_ERR_ASN1_UNEXPECTED_TAG
 
 Empty INTEGER
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"0200":"":MBEDTLS_ERR_ASN1_INVALID_LENGTH
+empty_integer:"0200"
 
 INTEGER 0
 get_integer:"020100":"0":0
@@ -173,27 +172,15 @@ get_integer:"020100":"0":0
 INTEGER 0, extra leading 0
 get_integer:"02020000":"0":0
 
-INTEGER -0
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"020180":"0":0
-
 INTEGER 1
 get_integer:"020101":"1":0:
 
 INTEGER 1, extra leading 0
 get_integer:"02020001":"1":0:
 
-INTEGER -1
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"020181":"-1":0
-
 INTEGER 0x7f
 get_integer:"02017f":"7f":0
 
-INTEGER -0x7f
-depends_on:SUPPORT_NEGATIVE_INTEGERS
-get_integer:"0201ff":"-7f":0
-
 INTEGER 0x80
 get_integer:"02020080":"80":0
 
@@ -212,9 +199,30 @@ get_integer:"020412345678":"12345678":0
 INTEGER 0x12345678, extra leading 0
 get_integer:"02050012345678":"12345678":0
 
+INTEGER 0x7fffffff
+get_integer:"02047fffffff":"7fffffff":0
+
+INTEGER 0x7fffffff, extra leading 0
+get_integer:"0205007fffffff":"7fffffff":0
+
+INTEGER 0x80000000
+get_integer:"02050080000000":"80000000":0
+
+INTEGER 0xffffffff
+get_integer:"020500ffffffff":"ffffffff":0
+
+INTEGER 0x100000000
+get_integer:"02050100000000":"0100000000":0
+
 INTEGER 0x123456789abcdef0
 get_integer:"0208123456789abcdef0":"123456789abcdef0":0
 
+INTEGER 0xfedcab9876543210
+get_integer:"020900fedcab9876543210":"fedcab9876543210":0
+
+INTEGER 0x1fedcab9876543210
+get_integer:"020901fedcab9876543210":"1fedcab9876543210":0
+
 INTEGER with 127 value octets
 get_integer:"027f0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcd":"0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcd":0
 
@@ -227,6 +235,51 @@ get_integer:"0281800123456789abcdef0123456789abcdef0123456789abcdef0123456789abc
 INTEGER with 128 value octets (leading 0 in length)
 get_integer:"028200800123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef":"0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef":0
 
+INTEGER -1
+get_integer:"0201ff":"-1":0
+
+INTEGER -1, extra leading ff
+get_integer:"0202ffff":"-1":0
+
+INTEGER -0x7f
+get_integer:"020181":"-7f":0
+
+INTEGER -0x80
+get_integer:"020180":"-80":0
+
+INTEGER -0x81
+get_integer:"0202ff7f":"-81":0
+
+INTEGER -0xff
+get_integer:"0202ff01":"-ff":0
+
+INTEGER -0x100
+get_integer:"0202ff00":"-100":0
+
+INTEGER -0x7fffffff
+get_integer:"020480000001":"-7fffffff":0
+
+INTEGER -0x80000000
+get_integer:"020480000000":"-80000000":0
+
+INTEGER -0x80000001
+get_integer:"0205ff7fffffff":"-80000001":0
+
+INTEGER -0xffffffff
+get_integer:"0205ff00000001":"-ffffffff":0
+
+INTEGER -0x100000000
+get_integer:"0205ff00000000":"-100000000":0
+
+INTEGER -0x123456789abcdef0
+get_integer:"0208edcba98765432110":"-123456789abcdef0":0
+
+INTEGER -0xfedcba9876543210
+get_integer:"0209ff0123456789abcdf0":"-fedcba9876543210":0
+
+INTEGER -0x1fedcab9876543210
+get_integer:"0209fe0123546789abcdf0":"-1fedcab9876543210":0
+
 Not INTEGER
 get_integer:"010101":"":MBEDTLS_ERR_ASN1_UNEXPECTED_TAG
 
diff --git a/tests/suites/test_suite_asn1parse.function b/tests/suites/test_suite_asn1parse.function
index 3bfb1c703..defbd01bb 100644
--- a/tests/suites/test_suite_asn1parse.function
+++ b/tests/suites/test_suite_asn1parse.function
@@ -59,6 +59,10 @@ static int nested_parse( unsigned char **const p,
             *p = start;
             ret = mbedtls_asn1_get_mpi( p, end, &mpi );
             mbedtls_mpi_free( &mpi );
+#else
+            *p = start + 1;
+            ret = mbedtls_asn1_get_len( p, end, &len );
+            *p += len;
 #endif
             /* If we're sure that the number fits in an int, also
              * call mbedtls_asn1_get_int(). */
@@ -246,6 +250,41 @@ void get_boolean( const data_t *input,
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void empty_integer( const data_t *input )
+{
+    unsigned char *p;
+#if defined(MBEDTLS_BIGNUM_C)
+    mbedtls_mpi actual_mpi;
+#endif
+    int val;
+
+#if defined(MBEDTLS_BIGNUM_C)
+    mbedtls_mpi_init( & actual_mpi );
+#endif
+
+    /* An INTEGER with no content is not valid. */
+    p = input->x;
+    TEST_EQUAL( mbedtls_asn1_get_int( &p, input->x + input->len, &val ),
+                MBEDTLS_ERR_ASN1_INVALID_LENGTH );
+
+#if defined(MBEDTLS_BIGNUM_C)
+    /* INTEGERs are sometimes abused as bitstrings, so the library accepts
+     * an INTEGER with empty content and gives it the value 0. */
+    p = input->x;
+    TEST_EQUAL( mbedtls_asn1_get_mpi( &p, input->x + input->len, &actual_mpi ),
+                0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &actual_mpi, 0 ), 0 );
+#endif
+
+exit:
+#if defined(MBEDTLS_BIGNUM_C)
+    mbedtls_mpi_free( &actual_mpi );
+#endif
+    /*empty cleanup in some configurations*/ ;
+}
+/* END_CASE */
+
 /* BEGIN_CASE */
 void get_integer( const data_t *input,
                   const char *expected_hex, int expected_result )
@@ -254,16 +293,18 @@ void get_integer( const data_t *input,
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi expected_mpi;
     mbedtls_mpi actual_mpi;
+    mbedtls_mpi complement;
+    int expected_result_for_mpi = expected_result;
 #endif
     long expected_value;
     int expected_result_for_int = expected_result;
-    int expected_result_for_mpi = expected_result;
     int val;
     int ret;
 
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi_init( &expected_mpi );
     mbedtls_mpi_init( &actual_mpi );
+    mbedtls_mpi_init( &complement );
 #endif
 
     errno = 0;
@@ -275,6 +316,16 @@ void get_integer( const data_t *input,
 #endif
             ) )
     {
+        /* The library returns the dubious error code INVALID_LENGTH
+         * for integers that are out of range. */
+        expected_result_for_int = MBEDTLS_ERR_ASN1_INVALID_LENGTH;
+    }
+    if( expected_result == 0 && expected_value < 0 )
+    {
+        /* The library does not support negative INTEGERs and
+         * returns the dubious error code INVALID_LENGTH.
+         * Test that we preserve the historical behavior. If we
+         * decide to change the behavior, we'll also change this test. */
         expected_result_for_int = MBEDTLS_ERR_ASN1_INVALID_LENGTH;
     }
 
@@ -300,7 +351,34 @@ void get_integer( const data_t *input,
     TEST_EQUAL( ret, expected_result_for_mpi );
     if( ret == 0 )
     {
-        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &actual_mpi , &expected_mpi ) == 0 );
+        if( expected_value >= 0 )
+        {
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &actual_mpi,
+                                              &expected_mpi ) == 0 );
+        }
+        else
+        {
+            /* The library ignores the sign bit in ASN.1 INTEGERs
+             * (which makes sense insofar as INTEGERs are sometimes
+             * abused as bit strings), so the result of parsing them
+             * is a positive integer such that expected_mpi +
+             * actual_mpi = 2^n where n is the length of the content
+             * of the INTEGER. (Leading ff octets don't matter for the
+             * expected value, but they matter for the actual value.)
+             * Test that we don't change from this behavior. If we
+             * decide to fix the library to change the behavior on
+             * negative INTEGERs, we'll fix this test code. */
+            unsigned char *q = input->x + 1;
+            size_t len;
+            TEST_ASSERT( mbedtls_asn1_get_len( &q, input->x + input->len,
+                                               &len ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_lset( &complement, 1 ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_shift_l( &complement, len * 8 ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_add_mpi( &complement, &complement,
+                                              &expected_mpi ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &complement,
+                                              &actual_mpi ) == 0 );
+        }
         TEST_ASSERT( p == input->x + input->len );
     }
 #endif
@@ -309,7 +387,9 @@ exit:
 #if defined(MBEDTLS_BIGNUM_C)
     mbedtls_mpi_free( &expected_mpi );
     mbedtls_mpi_free( &actual_mpi );
+    mbedtls_mpi_free( &complement );
 #endif
+    /*empty cleanup in some configurations*/ ;
 }
 /* END_CASE */