diff --git a/ChangeLog.d/ecp_max_bits.txt b/ChangeLog.d/ecp_max_bits.txt
new file mode 100644
index 0000000..bfbe11f
--- /dev/null
+++ b/ChangeLog.d/ecp_max_bits.txt
@@ -0,0 +1,4 @@
+Security
+   * It was possible to configure MBEDTLS_ECP_MAX_BITS to a value that is
+     too small, leading to buffer overflows in ECC operations. Fail the build
+     in such a case.
diff --git a/include/mbedtls/ecp.h b/include/mbedtls/ecp.h
index bdc750e..e4a1ed8 100644
--- a/include/mbedtls/ecp.h
+++ b/include/mbedtls/ecp.h
@@ -154,6 +154,40 @@
 }
 mbedtls_ecp_point;
 
+/* Determine the minimum safe value of MBEDTLS_ECP_MAX_BITS. */
+#if !defined(MBEDTLS_ECP_C)
+#define MBEDTLS_ECP_MAX_BITS_MIN 0
+/* Note: the curves must be listed in DECREASING size! */
+#elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 521
+#elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 512
+#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 448
+#elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 384
+#elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 384
+#elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 256
+#elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 256
+#elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 256
+#elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 255
+#elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 225 // n is slightly above 2^224
+#elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 224
+#elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 192
+#elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS_MIN 192
+#else
+#error "MBEDTLS_ECP_C enabled, but no curve?"
+#endif
+
 #if !defined(MBEDTLS_ECP_ALT)
 /*
  * default mbed TLS elliptic curve arithmetic implementation
@@ -228,7 +262,13 @@
  * \{
  */
 
-#if !defined(MBEDTLS_ECP_MAX_BITS)
+#if defined(MBEDTLS_ECP_MAX_BITS)
+
+#if MBEDTLS_ECP_MAX_BITS < MBEDTLS_ECP_MAX_BITS_MIN
+#error "MBEDTLS_ECP_MAX_BITS is smaller than the largest supported curve"
+#endif
+
+#else
 /**
  * The maximum size of the groups, that is, of \c N and \c P.
  */
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index 3e901f7..9ae84ed 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -393,6 +393,8 @@
     TEST_ASSERT( by_id == by_name );
 
     TEST_ASSERT( by_id->bit_size == size );
+    TEST_ASSERT( size <= MBEDTLS_ECP_MAX_BITS );
+    TEST_ASSERT( size <= MBEDTLS_ECP_MAX_BYTES * 8 );
 }
 /* END_CASE */
 
@@ -750,6 +752,7 @@
     TEST_EQUAL( 0, mbedtls_ecp_point_write_binary(
                     &grp, &R, MBEDTLS_ECP_PF_UNCOMPRESSED,
                     &len, actual_result, sizeof( actual_result ) ) );
+    TEST_ASSERT( len <= MBEDTLS_ECP_MAX_PT_LEN );
 
     ASSERT_COMPARE( expected_result->x, expected_result->len,
                     actual_result, len );
@@ -821,6 +824,7 @@
 
     if( ret == 0 )
     {
+        TEST_ASSERT( olen <= MBEDTLS_ECP_MAX_PT_LEN );
         TEST_ASSERT( mbedtls_test_hexcmp( buf, out->x, olen, out->len ) == 0 );
     }