diff --git a/crypto/ec/ec_asn1.c b/crypto/ec/ec_asn1.c
index c7ed01ef..33c4c230 100644
--- a/crypto/ec/ec_asn1.c
+++ b/crypto/ec/ec_asn1.c
@@ -367,10 +367,8 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve)
 {
     int ok = 0, nid;
     BIGNUM *tmp_1 = NULL, *tmp_2 = NULL;
-    unsigned char *buffer_1 = NULL, *buffer_2 = NULL,
-        *a_buf = NULL, *b_buf = NULL;
-    size_t len_1, len_2;
-    unsigned char char_zero = 0;
+    unsigned char *a_buf = NULL, *b_buf = NULL;
+    size_t len;
 
     if (!group || !curve || !curve->a || !curve->b)
         return 0;
@@ -398,44 +396,26 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve)
         }
     }
 #endif
-    len_1 = (size_t)BN_num_bytes(tmp_1);
-    len_2 = (size_t)BN_num_bytes(tmp_2);
-
-    if (len_1 == 0) {
-        /* len_1 == 0 => a == 0 */
-        a_buf = &char_zero;
-        len_1 = 1;
-    } else {
-        if ((buffer_1 = OPENSSL_malloc(len_1)) == NULL) {
-            ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE);
-            goto err;
-        }
-        if ((len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) {
-            ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB);
-            goto err;
-        }
-        a_buf = buffer_1;
+    /*
+     * Per SEC 1, the curve coefficients must be padded up to size. See C.2's
+     * definition of Curve, C.1's definition of FieldElement, and 2.3.5's
+     * definition of how to encode the field elements.
+     */
+    len = ((size_t)EC_GROUP_get_degree(group) + 7) / 8;
+    if ((a_buf = OPENSSL_malloc(len)) == NULL
+        || (b_buf = OPENSSL_malloc(len)) == NULL) {
+        ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE);
+        goto err;
     }
-
-    if (len_2 == 0) {
-        /* len_2 == 0 => b == 0 */
-        b_buf = &char_zero;
-        len_2 = 1;
-    } else {
-        if ((buffer_2 = OPENSSL_malloc(len_2)) == NULL) {
-            ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE);
-            goto err;
-        }
-        if ((len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) {
-            ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB);
-            goto err;
-        }
-        b_buf = buffer_2;
+    if (BN_bn2binpad(tmp_1, a_buf, len) < 0
+        || BN_bn2binpad(tmp_2, b_buf, len) < 0) {
+        ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB);
+        goto err;
     }
 
     /* set a and b */
-    if (!ASN1_OCTET_STRING_set(curve->a, a_buf, len_1) ||
-        !ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) {
+    if (!ASN1_OCTET_STRING_set(curve->a, a_buf, len)
+        || !ASN1_OCTET_STRING_set(curve->b, b_buf, len)) {
         ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB);
         goto err;
     }
@@ -462,8 +442,8 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve)
     ok = 1;
 
  err:
-    OPENSSL_free(buffer_1);
-    OPENSSL_free(buffer_2);
+    OPENSSL_free(a_buf);
+    OPENSSL_free(b_buf);
     BN_free(tmp_1);
     BN_free(tmp_2);
     return ok;
@@ -611,7 +591,12 @@ EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params)
         goto err;
     }
 
-    /* now extract the curve parameters a and b */
+    /*
+     * Now extract the curve parameters a and b. Note that, although SEC 1
+     * specifies the length of their encodings, historical versions of OpenSSL
+     * encoded them incorrectly, so we must accept any length for backwards
+     * compatibility.
+     */
     if (!params->curve || !params->curve->a ||
         !params->curve->a->data || !params->curve->b ||
         !params->curve->b->data) {
@@ -856,7 +841,7 @@ EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params)
             ECerr(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS, ERR_R_EC_LIB);
             return NULL;
         }
-        EC_GROUP_set_asn1_flag(ret, 0x0);
+        EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_EXPLICIT_CURVE);
     } else if (params->type == 2) { /* implicitlyCA */
         return NULL;
     } else {
diff --git a/crypto/threads_win.c b/crypto/threads_win.c
index 1e5cf820..7fdbc1f6 100644
--- a/crypto/threads_win.c
+++ b/crypto/threads_win.c
@@ -101,7 +101,26 @@ int CRYPTO_THREAD_init_local(CRYPTO_THREAD_LOCAL *key, void (*cleanup)(void *))
 
 void *CRYPTO_THREAD_get_local(CRYPTO_THREAD_LOCAL *key)
 {
-    return TlsGetValue(*key);
+    DWORD last_error;
+    void *ret;
+
+    /*
+     * TlsGetValue clears the last error even on success, so that callers may
+     * distinguish it successfully returning NULL or failing. It is documented
+     * to never fail if the argument is a valid index from TlsAlloc, so we do
+     * not need to handle this.
+     *
+     * However, this error-mangling behavior interferes with the caller's use of
+     * GetLastError. In particular SSL_get_error queries the error queue to
+     * determine whether the caller should look at the OS's errors. To avoid
+     * destroying state, save and restore the Windows error.
+     *
+     * https://msdn.microsoft.com/en-us/library/windows/desktop/ms686812(v=vs.85).aspx
+     */
+    last_error = GetLastError();
+    ret = TlsGetValue(*key);
+    SetLastError(last_error);
+    return ret;
 }
 
 int CRYPTO_THREAD_set_local(CRYPTO_THREAD_LOCAL *key, void *val)
diff --git a/test/build.info b/test/build.info
index c3a09048..000153d5 100644
--- a/test/build.info
+++ b/test/build.info
@@ -51,7 +51,7 @@ INCLUDE_MAIN___test_libtestutil_OLB = /INCLUDE=MAIN
           recordlentest drbgtest drbg_cavs_test sslbuffertest \
           time_offset_test pemtest ssl_cert_table_internal_test ciphername_test \
           servername_test ocspapitest rsa_mp_test fatalerrtest tls13ccstest \
-          sysdefaulttest
+          sysdefaulttest errtest
 
   SOURCE[versions]=versions.c
   INCLUDE[versions]=../include
@@ -535,6 +535,10 @@ INCLUDE_MAIN___test_libtestutil_OLB = /INCLUDE=MAIN
   SOURCE[sysdefaulttest]=sysdefaulttest.c
   INCLUDE[sysdefaulttest]=../include
   DEPEND[sysdefaulttest]=../libcrypto ../libssl libtestutil.a
+
+  SOURCE[errtest]=errtest.c
+  INCLUDE[errtest]=../include
+  DEPEND[errtest]=../libcrypto libtestutil.a
 ENDIF
 
 {-
diff --git a/test/ectest.c b/test/ectest.c
index 1c31cce8..73e8aa87 100644
--- a/test/ectest.c
+++ b/test/ectest.c
@@ -1407,20 +1407,91 @@ err:
 }
 # endif
 
+static const unsigned char p521_named[] = {
+    0x06, 0x05, 0x2b, 0x81, 0x04, 0x00, 0x23,
+};
+
+static const unsigned char p521_explicit[] = {
+    0x30, 0x82, 0x01, 0xc3, 0x02, 0x01, 0x01, 0x30, 0x4d, 0x06, 0x07, 0x2a,
+    0x86, 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x42, 0x01, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0x30, 0x81, 0x9f, 0x04, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xfc, 0x04, 0x42, 0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a,
+    0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72,
+    0x5b, 0x99, 0xb3, 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09,
+    0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0,
+    0xbd, 0x3b, 0xb1, 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34,
+    0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00, 0x03, 0x15, 0x00,
+    0xd0, 0x9e, 0x88, 0x00, 0x29, 0x1c, 0xb8, 0x53, 0x96, 0xcc, 0x67, 0x17,
+    0x39, 0x32, 0x84, 0xaa, 0xa0, 0xda, 0x64, 0xba, 0x04, 0x81, 0x85, 0x04,
+    0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e,
+    0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
+    0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b,
+    0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
+    0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e,
+    0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78,
+    0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9,
+    0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17,
+    0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40,
+    0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86,
+    0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50,
+    0x02, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfa,
+    0x51, 0x86, 0x87, 0x83, 0xbf, 0x2f, 0x96, 0x6b, 0x7f, 0xcc, 0x01, 0x48,
+    0xf7, 0x09, 0xa5, 0xd0, 0x3b, 0xb5, 0xc9, 0xb8, 0x89, 0x9c, 0x47, 0xae,
+    0xbb, 0x6f, 0xb7, 0x1e, 0x91, 0x38, 0x64, 0x09, 0x02, 0x01, 0x01,
+};
+
 static int parameter_test(void)
 {
     EC_GROUP *group = NULL, *group2 = NULL;
     ECPARAMETERS *ecparameters = NULL;
-    int r;
+    unsigned char *buf = NULL;
+    int r = 0, len;
 
-    r = TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp112r1))
-        && TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL))
-        && TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters))
-        && TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0);
+    if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp112r1))
+        || !TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL))
+        || !TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters))
+        || !TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0))
+        goto err;
 
+    EC_GROUP_free(group);
+    group = NULL;
+
+    /* Test the named curve encoding, which should be default. */
+    if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp521r1))
+        || !TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
+        || !TEST_mem_eq(buf, len, p521_named, sizeof(p521_named)))
+        goto err;
+
+    OPENSSL_free(buf);
+    buf = NULL;
+
+    /*
+     * Test the explicit encoding. P-521 requires correctly zero-padding the
+     * curve coefficients.
+     */
+    EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE);
+    if (!TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
+        || !TEST_mem_eq(buf, len, p521_explicit, sizeof(p521_explicit)))
+        goto err;
+
+    r = 1;
+err:
     EC_GROUP_free(group);
     EC_GROUP_free(group2);
     ECPARAMETERS_free(ecparameters);
+    OPENSSL_free(buf);
     return r;
 }
 #endif
diff --git a/test/errtest.c b/test/errtest.c
new file mode 100644
index 00000000..e464d08b
--- /dev/null
+++ b/test/errtest.c
@@ -0,0 +1,39 @@
+/*
+ * Copyright 2018 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (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 <openssl/opensslconf.h>
+#include <openssl/err.h>
+
+#include "testutil.h"
+
+#if defined(OPENSSL_SYS_WINDOWS)
+# include <windows.h>
+#else
+# include <errno.h>
+#endif
+
+/* Test that querying the error queue preserves the OS error. */
+static int preserves_system_error(void)
+{
+#if defined(OPENSSL_SYS_WINDOWS)
+    SetLastError(ERROR_INVALID_FUNCTION);
+    ERR_get_error();
+    return TEST_int_eq(GetLastError(), ERROR_INVALID_FUNCTION);
+#else
+    errno = EINVAL;
+    ERR_get_error();
+    return TEST_int_eq(errno, EINVAL);
+#endif
+}
+
+int setup_tests(void)
+{
+    ADD_TEST(preserves_system_error);
+    return 1;
+}
diff --git a/test/recipes/04-test_err.t b/test/recipes/04-test_err.t
new file mode 100644
index 00000000..dd7681af
--- /dev/null
+++ b/test/recipes/04-test_err.t
@@ -0,0 +1,12 @@
+#! /usr/bin/env perl
+# Copyright 2018 The OpenSSL Project Authors. All Rights Reserved.
+#
+# Licensed under the OpenSSL license (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 OpenSSL::Test::Simple;
+
+simple_test("test_err", "errtest");