diff --git a/test/build.info b/test/build.info
index ecfcace3c1..af8429b7f7 100644
--- a/test/build.info
+++ b/test/build.info
@@ -459,7 +459,7 @@ IF[{- !$disabled{tests} -}]
       PROGRAMS{noinst}=sm4_internal_test
     ENDIF
     IF[{- !$disabled{ec} -}]
-      PROGRAMS{noinst}=curve448_internal_test
+      PROGRAMS{noinst}=ec_internal_test curve448_internal_test
     ENDIF
 
     SOURCE[poly1305_internal_test]=poly1305_internal_test.c
@@ -510,6 +510,10 @@ IF[{- !$disabled{tests} -}]
     INCLUDE[sm4_internal_test]=.. ../include ../apps/include ../crypto/include
     DEPEND[sm4_internal_test]=../libcrypto.a libtestutil.a
 
+    SOURCE[ec_internal_test]=ec_internal_test.c
+    INCLUDE[ec_internal_test]=../include ../crypto/ec ../apps/include ../crypto/include
+    DEPEND[ec_internal_test]=../libcrypto.a libtestutil.a
+
     SOURCE[curve448_internal_test]=curve448_internal_test.c
     INCLUDE[curve448_internal_test]=.. ../include ../apps/include ../crypto/ec/curve448
     DEPEND[curve448_internal_test]=../libcrypto.a libtestutil.a
diff --git a/test/ec_internal_test.c b/test/ec_internal_test.c
new file mode 100644
index 0000000000..8d3a4fdd67
--- /dev/null
+++ b/test/ec_internal_test.c
@@ -0,0 +1,205 @@
+/*
+ * Copyright 2019 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the Apache License 2.0 (the "License").  You may not use
+ * this file except in compliance with the License.  You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+#include "internal/nelem.h"
+#include "testutil.h"
+#include <openssl/ec.h>
+#include "ec_lcl.h"
+#include <openssl/objects.h>
+
+static size_t crv_len = 0;
+static EC_builtin_curve *curves = NULL;
+
+/* sanity checks field_inv function pointer in EC_METHOD */
+static int group_field_tests(const EC_GROUP *group, BN_CTX *ctx)
+{
+    BIGNUM *a = NULL, *b = NULL, *c = NULL;
+    int ret = 0;
+
+    if (group->meth->field_inv == NULL || group->meth->field_mul == NULL)
+        return 1;
+
+    BN_CTX_start(ctx);
+    a = BN_CTX_get(ctx);
+    b = BN_CTX_get(ctx);
+    if (!TEST_ptr(c = BN_CTX_get(ctx))
+        /* 1/1 = 1 */
+        || !TEST_true(group->meth->field_inv(group, b, BN_value_one(), ctx))
+        || !TEST_true(BN_is_one(b))
+        /* (1/a)*a = 1 */
+        || !TEST_true(BN_pseudo_rand(a, BN_num_bits(group->field) - 1,
+                                     BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
+        || !TEST_true(group->meth->field_inv(group, b, a, ctx))
+        || (group->meth->field_encode &&
+            !TEST_true(group->meth->field_encode(group, a, a, ctx)))
+        || (group->meth->field_encode &&
+            !TEST_true(group->meth->field_encode(group, b, b, ctx)))
+        || !TEST_true(group->meth->field_mul(group, c, a, b, ctx))
+        || (group->meth->field_decode &&
+            !TEST_true(group->meth->field_decode(group, c, c, ctx)))
+        || !TEST_true(BN_is_one(c)))
+        goto err;
+
+    /* 1/0 = error */
+    BN_zero(a);
+    if (!TEST_false(group->meth->field_inv(group, b, a, ctx))
+        || !TEST_true(ERR_GET_LIB(ERR_peek_last_error()) == ERR_LIB_EC)
+        || !TEST_true(ERR_GET_REASON(ERR_peek_last_error()) ==
+                      EC_R_CANNOT_INVERT)
+        /* 1/p = error */
+        || !TEST_false(group->meth->field_inv(group, b, group->field, ctx))
+        || !TEST_true(ERR_GET_LIB(ERR_peek_last_error()) == ERR_LIB_EC)
+        || !TEST_true(ERR_GET_REASON(ERR_peek_last_error()) ==
+                      EC_R_CANNOT_INVERT))
+        goto err;
+
+    ERR_clear_error();
+    ret = 1;
+ err:
+    BN_CTX_end(ctx);
+    return ret;
+}
+
+/* wrapper for group_field_tests for explicit curve params and EC_METHOD */
+static int field_tests(const EC_METHOD *meth, const unsigned char *params,
+                       int len)
+{
+    BN_CTX *ctx = NULL;
+    BIGNUM *p = NULL, *a = NULL, *b = NULL;
+    EC_GROUP *group = NULL;
+    int ret = 0;
+
+    if (!TEST_ptr(ctx = BN_CTX_new()))
+        return 0;
+
+    BN_CTX_start(ctx);
+    p = BN_CTX_get(ctx);
+    a = BN_CTX_get(ctx);
+    if (!TEST_ptr(b = BN_CTX_get(ctx))
+        || !TEST_ptr(group = EC_GROUP_new(meth))
+        || !TEST_true(BN_bin2bn(params, len, p))
+        || !TEST_true(BN_bin2bn(params + len, len, a))
+        || !TEST_true(BN_bin2bn(params + 2 * len, len, b))
+        || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
+        || !group_field_tests(group, ctx))
+        goto err;
+    ret = 1;
+
+ err:
+    BN_CTX_end(ctx);
+    BN_CTX_free(ctx);
+    if (group != NULL)
+        EC_GROUP_free(group);
+    return ret;
+}
+
+/* NIST prime curve P-256 */
+static const unsigned char params_p256[] = {
+    /* p */
+    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
+    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+    /* a */
+    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
+    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC,
+    /* b */
+    0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55,
+    0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6,
+    0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B
+};
+
+#ifndef OPENSSL_NO_EC2M
+/* NIST binary curve B-283 */
+static const unsigned char params_b283[] = {
+    /* p */
+    0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1,
+    /* a */
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+    /* b */
+    0x02, 0x7B, 0x68, 0x0A, 0xC8, 0xB8, 0x59, 0x6D, 0xA5, 0xA4, 0xAF, 0x8A,
+    0x19, 0xA0, 0x30, 0x3F, 0xCA, 0x97, 0xFD, 0x76, 0x45, 0x30, 0x9F, 0xA2,
+    0xA5, 0x81, 0x48, 0x5A, 0xF6, 0x26, 0x3E, 0x31, 0x3B, 0x79, 0xA2, 0xF5
+};
+#endif
+
+/* test EC_GFp_simple_method directly */
+static int field_tests_ecp_simple(void)
+{
+    TEST_info("Testing EC_GFp_simple_method()\n");
+    return field_tests(EC_GFp_simple_method(), params_p256,
+                       sizeof(params_p256) / 3);
+}
+
+/* test EC_GFp_mont_method directly */
+static int field_tests_ecp_mont(void)
+{
+    TEST_info("Testing EC_GFp_mont_method()\n");
+    return field_tests(EC_GFp_mont_method(), params_p256,
+                       sizeof(params_p256) / 3);
+}
+
+#ifndef OPENSSL_NO_EC2M
+/* test EC_GF2m_simple_method directly */
+static int field_tests_ec2_simple(void)
+{
+    TEST_info("Testing EC_GF2m_simple_method()\n");
+    return field_tests(EC_GF2m_simple_method(), params_b283,
+                       sizeof(params_b283) / 3);
+}
+#endif
+
+/* test default method for a named curve */
+static int field_tests_default(int n)
+{
+    BN_CTX *ctx = NULL;
+    EC_GROUP *group = NULL;
+    int nid = curves[n].nid;
+    int ret = 0;
+
+    TEST_info("Testing curve %s\n", OBJ_nid2sn(nid));
+
+    if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))
+        || !TEST_ptr(ctx = BN_CTX_new())
+        || !group_field_tests(group, ctx))
+        goto err;
+
+    ret = 1;
+ err:
+    if (group != NULL)
+        EC_GROUP_free(group);
+    if (ctx != NULL)
+        BN_CTX_free(ctx);
+    return ret;
+}
+
+int setup_tests(void)
+{
+    crv_len = EC_get_builtin_curves(NULL, 0);
+    if (!TEST_ptr(curves = OPENSSL_malloc(sizeof(*curves) * crv_len))
+        || !TEST_true(EC_get_builtin_curves(curves, crv_len)))
+        return 0;
+
+    ADD_TEST(field_tests_ecp_simple);
+    ADD_TEST(field_tests_ecp_mont);
+#ifndef OPENSSL_NO_EC2M
+    ADD_TEST(field_tests_ec2_simple);
+#endif
+    ADD_ALL_TESTS(field_tests_default, crv_len);
+    return 1;
+}
+
+void cleanup_tests(void)
+{
+    OPENSSL_free(curves);
+}
diff --git a/test/recipes/03-test_internal_ec.t b/test/recipes/03-test_internal_ec.t
new file mode 100644
index 0000000000..0d31d0ac07
--- /dev/null
+++ b/test/recipes/03-test_internal_ec.t
@@ -0,0 +1,19 @@
+#! /usr/bin/env perl
+# Copyright 2019 The OpenSSL Project Authors. All Rights Reserved.
+#
+# Licensed under the Apache License 2.0 (the "License").  You may not use
+# this file except in compliance with the License.  You can obtain a copy
+# in the file LICENSE in the source distribution or at
+# https://www.openssl.org/source/license.html
+
+use strict;
+use OpenSSL::Test;              # get 'plan'
+use OpenSSL::Test::Simple;
+use OpenSSL::Test::Utils;
+
+setup("test_internal_ec");
+
+plan skip_all => "This test is unsupported in a no-ec build"
+    if disabled("ec");
+
+simple_test("test_internal_ec", "ec_internal_test");