diff --git a/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am
index e5657f7f31..c071fbe275 100644
--- a/src/secp256k1/Makefile.am
+++ b/src/secp256k1/Makefile.am
@@ -93,7 +93,10 @@ TESTS =
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
-tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+if !ENABLE_COVERAGE
+tests_CPPFLAGS += -DVERIFY
+endif
 tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 tests_LDFLAGS = -static
 TESTS += tests
@@ -102,7 +105,10 @@ endif
 if USE_EXHAUSTIVE_TESTS
 noinst_PROGRAMS += exhaustive_tests
 exhaustive_tests_SOURCES = src/tests_exhaustive.c
-exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES)
+exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src $(SECP_INCLUDES)
+if !ENABLE_COVERAGE
+exhaustive_tests_CPPFLAGS += -DVERIFY
+endif
 exhaustive_tests_LDADD = $(SECP_LIBS)
 exhaustive_tests_LDFLAGS = -static
 TESTS += exhaustive_tests
diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index ec50ffe3a2..e5fcbcb4ed 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/configure.ac
@@ -20,7 +20,7 @@ AC_PATH_TOOL(STRIP, strip)
 AX_PROG_CC_FOR_BUILD
 
 if test "x$CFLAGS" = "x"; then
-  CFLAGS="-O3 -g"
+  CFLAGS="-g"
 fi
 
 AM_PROG_CC_C_O
@@ -89,6 +89,11 @@ AC_ARG_ENABLE(benchmark,
     [use_benchmark=$enableval],
     [use_benchmark=no])
 
+AC_ARG_ENABLE(coverage,
+    AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis]),
+    [enable_coverage=$enableval],
+    [enable_coverage=no])
+
 AC_ARG_ENABLE(tests,
     AS_HELP_STRING([--enable-tests],[compile tests (default is yes)]),
     [use_tests=$enableval],
@@ -154,6 +159,14 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])],
     [ AC_MSG_RESULT([no])
     ])
 
+if test x"$enable_coverage" = x"yes"; then
+    AC_DEFINE(COVERAGE, 1, [Define this symbol to compile out all VERIFY code])
+    CFLAGS="$CFLAGS -O0 --coverage"
+    LDFLAGS="--coverage"
+else
+    CFLAGS="$CFLAGS -O3"
+fi
+
 if test x"$use_ecmult_static_precomputation" != x"no"; then
   save_cross_compiling=$cross_compiling
   cross_compiling=no
@@ -434,6 +447,7 @@ AC_MSG_NOTICE([Using field implementation: $set_field])
 AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
 AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
 AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
+AC_MSG_NOTICE([Building for coverage analysis: $enable_coverage])
 AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
 AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
 AC_MSG_NOTICE([Using jni: $use_jni])
@@ -460,6 +474,7 @@ AC_SUBST(SECP_INCLUDES)
 AC_SUBST(SECP_LIBS)
 AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
+AM_CONDITIONAL([ENABLE_COVERAGE], [test x"$enable_coverage" = x"yes"])
 AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
 AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
 AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
index f268e309d0..fc4c5cefbb 100644
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/include/secp256k1.h
@@ -163,6 +163,8 @@ typedef int (*secp256k1_nonce_function)(
  *
  *  Returns: a newly created context object.
  *  In:      flags: which parts of the context to initialize.
+ *
+ *  See also secp256k1_context_randomize.
  */
 SECP256K1_API secp256k1_context* secp256k1_context_create(
     unsigned int flags
@@ -485,6 +487,28 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
     const unsigned char *seckey
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
+/** Negates a private key in place.
+ *
+ *  Returns: 1 always
+ *  Args:   ctx:        pointer to a context object
+ *  In/Out: pubkey:     pointer to the public key to be negated (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate(
+    const secp256k1_context* ctx,
+    unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Negates a public key in place.
+ *
+ *  Returns: 1 always
+ *  Args:   ctx:        pointer to a context object
+ *  In/Out: pubkey:     pointer to the public key to be negated (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
 /** Tweak a private key by adding tweak to it.
  * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
  *          uniformly random 32-byte arrays, or if the resulting private key
@@ -543,11 +567,24 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
     const unsigned char *tweak
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Updates the context randomization.
+/** Updates the context randomization to protect against side-channel leakage.
  *  Returns: 1: randomization successfully updated
  *           0: error
  *  Args:    ctx:       pointer to a context object (cannot be NULL)
  *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
+ *
+ * While secp256k1 code is written to be constant-time no matter what secret
+ * values are, it's possible that a future compiler may output code which isn't,
+ * and also that the CPU may not emit the same radio frequencies or draw the same
+ * amount power for all values.
+ *
+ * This function provides a seed which is combined into the blinding value: that
+ * blinding value is added before each multiplication (and removed afterwards) so
+ * that it does not affect function results, but shields against attacks which
+ * rely on any input-dependent behaviour.
+ *
+ * You should call this after secp256k1_context_create or
+ * secp256k1_context_clone, and may call this repeatedly afterwards.
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
     secp256k1_context* ctx,
diff --git a/src/secp256k1/src/bench.h b/src/secp256k1/src/bench.h
index 3a71b4aafa..d67f08a426 100644
--- a/src/secp256k1/src/bench.h
+++ b/src/secp256k1/src/bench.h
@@ -23,7 +23,7 @@ void print_number(double x) {
     if (y < 0.0) {
         y = -y;
     }
-    while (y < 100.0) {
+    while (y > 0 && y < 100.0) {
         y *= 10.0;
         c++;
     }
diff --git a/src/secp256k1/src/bench_schnorr_verify.c b/src/secp256k1/src/bench_schnorr_verify.c
deleted file mode 100644
index 5f137dda23..0000000000
--- a/src/secp256k1/src/bench_schnorr_verify.c
+++ /dev/null
@@ -1,73 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                   *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#include <stdio.h>
-#include <string.h>
-
-#include "include/secp256k1.h"
-#include "include/secp256k1_schnorr.h"
-#include "util.h"
-#include "bench.h"
-
-typedef struct {
-    unsigned char key[32];
-    unsigned char sig[64];
-    unsigned char pubkey[33];
-    size_t pubkeylen;
-} benchmark_schnorr_sig_t;
-
-typedef struct {
-    secp256k1_context *ctx;
-    unsigned char msg[32];
-    benchmark_schnorr_sig_t sigs[64];
-    int numsigs;
-} benchmark_schnorr_verify_t;
-
-static void benchmark_schnorr_init(void* arg) {
-    int i, k;
-    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
-
-    for (i = 0; i < 32; i++) {
-        data->msg[i] = 1 + i;
-    }
-    for (k = 0; k < data->numsigs; k++) {
-        secp256k1_pubkey pubkey;
-        for (i = 0; i < 32; i++) {
-            data->sigs[k].key[i] = 33 + i + k;
-        }
-        secp256k1_schnorr_sign(data->ctx, data->sigs[k].sig, data->msg, data->sigs[k].key, NULL, NULL);
-        data->sigs[k].pubkeylen = 33;
-        CHECK(secp256k1_ec_pubkey_create(data->ctx, &pubkey, data->sigs[k].key));
-        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
-    }
-}
-
-static void benchmark_schnorr_verify(void* arg) {
-    int i;
-    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
-
-    for (i = 0; i < 20000 / data->numsigs; i++) {
-        secp256k1_pubkey pubkey;
-        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
-        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->sigs[0].pubkey, data->sigs[0].pubkeylen));
-        CHECK(secp256k1_schnorr_verify(data->ctx, data->sigs[0].sig, data->msg, &pubkey) == ((i & 0xFF) == 0));
-        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
-    }
-}
-
-
-
-int main(void) {
-    benchmark_schnorr_verify_t data;
-
-    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-
-    data.numsigs = 1;
-    run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
-
-    secp256k1_context_destroy(data.ctx);
-    return 0;
-}
diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h
index 9a42e519bd..453bb11880 100644
--- a/src/secp256k1/src/ecdsa_impl.h
+++ b/src/secp256k1/src/ecdsa_impl.h
@@ -225,14 +225,12 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
 #if defined(EXHAUSTIVE_TEST_ORDER)
 {
     secp256k1_scalar computed_r;
-    int overflow = 0;
     secp256k1_ge pr_ge;
     secp256k1_ge_set_gej(&pr_ge, &pr);
     secp256k1_fe_normalize(&pr_ge.x);
 
     secp256k1_fe_get_b32(c, &pr_ge.x);
-    secp256k1_scalar_set_b32(&computed_r, c, &overflow);
-    /* we fully expect overflow */
+    secp256k1_scalar_set_b32(&computed_r, c, NULL);
     return secp256k1_scalar_eq(sigr, &computed_r);
 }
 #else
@@ -285,14 +283,10 @@ static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, sec
     secp256k1_fe_normalize(&r.y);
     secp256k1_fe_get_b32(b, &r.x);
     secp256k1_scalar_set_b32(sigr, b, &overflow);
-    if (secp256k1_scalar_is_zero(sigr)) {
-        /* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature.
-         * This branch is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N.
-         */
-        secp256k1_gej_clear(&rp);
-        secp256k1_ge_clear(&r);
-        return 0;
-    }
+    /* These two conditions should be checked before calling */
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr));
+    VERIFY_CHECK(overflow == 0);
+
     if (recid) {
         /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
          * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h
index 7b8c079608..234c13a644 100644
--- a/src/secp256k1/src/field_10x26_impl.h
+++ b/src/secp256k1/src/field_10x26_impl.h
@@ -38,10 +38,6 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
-#else
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
-    (void)a;
-}
 #endif
 
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
@@ -325,17 +321,17 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
 }
 
 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
-    int i;
-    r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
-    r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
-    for (i=0; i<32; i++) {
-        int j;
-        for (j=0; j<4; j++) {
-            int limb = (8*i+2*j)/26;
-            int shift = (8*i+2*j)%26;
-            r->n[limb] |= (uint32_t)((a[31-i] >> (2*j)) & 0x3) << shift;
-        }
-    }
+    r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
+    r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22);
+    r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20);
+    r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
+    r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
+    r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22);
+    r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20);
+    r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
+    r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
+    r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
+
     if (r->n[9] == 0x3FFFFFUL && (r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL && (r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL) {
         return 0;
     }
@@ -349,21 +345,42 @@ static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
-    int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
 #endif
-    for (i=0; i<32; i++) {
-        int j;
-        int c = 0;
-        for (j=0; j<4; j++) {
-            int limb = (8*i+2*j)/26;
-            int shift = (8*i+2*j)%26;
-            c |= ((a->n[limb] >> shift) & 0x3) << (2 * j);
-        }
-        r[31-i] = c;
-    }
+    r[0] = (a->n[9] >> 14) & 0xff;
+    r[1] = (a->n[9] >> 6) & 0xff;
+    r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
+    r[3] = (a->n[8] >> 16) & 0xff;
+    r[4] = (a->n[8] >> 8) & 0xff;
+    r[5] = a->n[8] & 0xff;
+    r[6] = (a->n[7] >> 18) & 0xff;
+    r[7] = (a->n[7] >> 10) & 0xff;
+    r[8] = (a->n[7] >> 2) & 0xff;
+    r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
+    r[10] = (a->n[6] >> 12) & 0xff;
+    r[11] = (a->n[6] >> 4) & 0xff;
+    r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
+    r[13] = (a->n[5] >> 14) & 0xff;
+    r[14] = (a->n[5] >> 6) & 0xff;
+    r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
+    r[16] = (a->n[4] >> 16) & 0xff;
+    r[17] = (a->n[4] >> 8) & 0xff;
+    r[18] = a->n[4] & 0xff;
+    r[19] = (a->n[3] >> 18) & 0xff;
+    r[20] = (a->n[3] >> 10) & 0xff;
+    r[21] = (a->n[3] >> 2) & 0xff;
+    r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
+    r[23] = (a->n[2] >> 12) & 0xff;
+    r[24] = (a->n[2] >> 4) & 0xff;
+    r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
+    r[26] = (a->n[1] >> 14) & 0xff;
+    r[27] = (a->n[1] >> 6) & 0xff;
+    r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
+    r[29] = (a->n[0] >> 16) & 0xff;
+    r[30] = (a->n[0] >> 8) & 0xff;
+    r[31] = a->n[0] & 0xff;
 }
 
 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h
index 7a99eb21ec..8e8b286baf 100644
--- a/src/secp256k1/src/field_5x52_impl.h
+++ b/src/secp256k1/src/field_5x52_impl.h
@@ -49,10 +49,6 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
-#else
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
-    (void)a;
-}
 #endif
 
 static void secp256k1_fe_normalize(secp256k1_fe *r) {
@@ -288,16 +284,40 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
 }
 
 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
-    int i;
-    r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
-    for (i=0; i<32; i++) {
-        int j;
-        for (j=0; j<2; j++) {
-            int limb = (8*i+4*j)/52;
-            int shift = (8*i+4*j)%52;
-            r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
-        }
-    }
+    r->n[0] = (uint64_t)a[31]
+            | ((uint64_t)a[30] << 8)
+            | ((uint64_t)a[29] << 16)
+            | ((uint64_t)a[28] << 24)
+            | ((uint64_t)a[27] << 32)
+            | ((uint64_t)a[26] << 40)
+            | ((uint64_t)(a[25] & 0xF)  << 48);
+    r->n[1] = (uint64_t)((a[25] >> 4) & 0xF)
+            | ((uint64_t)a[24] << 4)
+            | ((uint64_t)a[23] << 12)
+            | ((uint64_t)a[22] << 20)
+            | ((uint64_t)a[21] << 28)
+            | ((uint64_t)a[20] << 36)
+            | ((uint64_t)a[19] << 44);
+    r->n[2] = (uint64_t)a[18]
+            | ((uint64_t)a[17] << 8)
+            | ((uint64_t)a[16] << 16)
+            | ((uint64_t)a[15] << 24)
+            | ((uint64_t)a[14] << 32)
+            | ((uint64_t)a[13] << 40)
+            | ((uint64_t)(a[12] & 0xF) << 48);
+    r->n[3] = (uint64_t)((a[12] >> 4) & 0xF)
+            | ((uint64_t)a[11] << 4)
+            | ((uint64_t)a[10] << 12)
+            | ((uint64_t)a[9]  << 20)
+            | ((uint64_t)a[8]  << 28)
+            | ((uint64_t)a[7]  << 36)
+            | ((uint64_t)a[6]  << 44);
+    r->n[4] = (uint64_t)a[5]
+            | ((uint64_t)a[4] << 8)
+            | ((uint64_t)a[3] << 16)
+            | ((uint64_t)a[2] << 24)
+            | ((uint64_t)a[1] << 32)
+            | ((uint64_t)a[0] << 40);
     if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
         return 0;
     }
@@ -311,21 +331,42 @@ static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
-    int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
 #endif
-    for (i=0; i<32; i++) {
-        int j;
-        int c = 0;
-        for (j=0; j<2; j++) {
-            int limb = (8*i+4*j)/52;
-            int shift = (8*i+4*j)%52;
-            c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
-        }
-        r[31-i] = c;
-    }
+    r[0] = (a->n[4] >> 40) & 0xFF;
+    r[1] = (a->n[4] >> 32) & 0xFF;
+    r[2] = (a->n[4] >> 24) & 0xFF;
+    r[3] = (a->n[4] >> 16) & 0xFF;
+    r[4] = (a->n[4] >> 8) & 0xFF;
+    r[5] = a->n[4] & 0xFF;
+    r[6] = (a->n[3] >> 44) & 0xFF;
+    r[7] = (a->n[3] >> 36) & 0xFF;
+    r[8] = (a->n[3] >> 28) & 0xFF;
+    r[9] = (a->n[3] >> 20) & 0xFF;
+    r[10] = (a->n[3] >> 12) & 0xFF;
+    r[11] = (a->n[3] >> 4) & 0xFF;
+    r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4);
+    r[13] = (a->n[2] >> 40) & 0xFF;
+    r[14] = (a->n[2] >> 32) & 0xFF;
+    r[15] = (a->n[2] >> 24) & 0xFF;
+    r[16] = (a->n[2] >> 16) & 0xFF;
+    r[17] = (a->n[2] >> 8) & 0xFF;
+    r[18] = a->n[2] & 0xFF;
+    r[19] = (a->n[1] >> 44) & 0xFF;
+    r[20] = (a->n[1] >> 36) & 0xFF;
+    r[21] = (a->n[1] >> 28) & 0xFF;
+    r[22] = (a->n[1] >> 20) & 0xFF;
+    r[23] = (a->n[1] >> 12) & 0xFF;
+    r[24] = (a->n[1] >> 4) & 0xFF;
+    r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4);
+    r[26] = (a->n[0] >> 40) & 0xFF;
+    r[27] = (a->n[0] >> 32) & 0xFF;
+    r[28] = (a->n[0] >> 24) & 0xFF;
+    r[29] = (a->n[0] >> 16) & 0xFF;
+    r[30] = (a->n[0] >> 8) & 0xFF;
+    r[31] = a->n[0] & 0xFF;
 }
 
 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index 2e192b62fd..7d723532ff 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -200,12 +200,6 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
     secp256k1_fe_clear(&r->z);
 }
 
-static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
-    r->infinity = 1;
-    secp256k1_fe_clear(&r->x);
-    secp256k1_fe_clear(&r->y);
-}
-
 static void secp256k1_gej_clear(secp256k1_gej *r) {
     r->infinity = 0;
     secp256k1_fe_clear(&r->x);
diff --git a/src/secp256k1/src/modules/ecdh/main_impl.h b/src/secp256k1/src/modules/ecdh/main_impl.h
index c23e4f82f7..9e30fb73dd 100644
--- a/src/secp256k1/src/modules/ecdh/main_impl.h
+++ b/src/secp256k1/src/modules/ecdh/main_impl.h
@@ -16,10 +16,10 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const se
     secp256k1_gej res;
     secp256k1_ge pt;
     secp256k1_scalar s;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(result != NULL);
     ARG_CHECK(point != NULL);
     ARG_CHECK(scalar != NULL);
-    (void)ctx;
 
     secp256k1_pubkey_load(ctx, &pt, point);
     secp256k1_scalar_set_b32(&s, scalar, &overflow);
diff --git a/src/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h
index 7badc9033f..85a5d0a9a6 100644
--- a/src/secp256k1/src/modules/ecdh/tests_impl.h
+++ b/src/secp256k1/src/modules/ecdh/tests_impl.h
@@ -7,6 +7,35 @@
 #ifndef _SECP256K1_MODULE_ECDH_TESTS_
 #define _SECP256K1_MODULE_ECDH_TESTS_
 
+void test_ecdh_api(void) {
+    /* Setup context that just counts errors */
+    secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_pubkey point;
+    unsigned char res[32];
+    unsigned char s_one[32] = { 0 };
+    int32_t ecount = 0;
+    s_one[31] = 1;
+
+    secp256k1_context_set_error_callback(tctx, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(tctx, counting_illegal_callback_fn, &ecount);
+    CHECK(secp256k1_ec_pubkey_create(tctx, &point, s_one) == 1);
+
+    /* Check all NULLs are detected */
+    CHECK(secp256k1_ecdh(tctx, res, &point, s_one) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ecdh(tctx, NULL, &point, s_one) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdh(tctx, res, NULL, s_one) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdh(tctx, res, &point, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdh(tctx, res, &point, s_one) == 1);
+    CHECK(ecount == 3);
+
+    /* Cleanup */
+    secp256k1_context_destroy(tctx);
+}
+
 void test_ecdh_generator_basepoint(void) {
     unsigned char s_one[32] = { 0 };
     secp256k1_pubkey point[2];
@@ -68,6 +97,7 @@ void test_bad_scalar(void) {
 }
 
 void run_ecdh_tests(void) {
+    test_ecdh_api();
     test_ecdh_generator_basepoint();
     test_bad_scalar();
 }
diff --git a/src/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h
index 86f2f0cb2b..c6fbe23981 100755
--- a/src/secp256k1/src/modules/recovery/main_impl.h
+++ b/src/secp256k1/src/modules/recovery/main_impl.h
@@ -179,7 +179,7 @@ int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubk
     ARG_CHECK(pubkey != NULL);
 
     secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
-    ARG_CHECK(recid >= 0 && recid < 4);
+    VERIFY_CHECK(recid >= 0 && recid < 4);  /* should have been caught in parse_compact */
     secp256k1_scalar_set_b32(&m, msg32, NULL);
     if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
         secp256k1_pubkey_save(pubkey, &q);
diff --git a/src/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h
index 8932d5f0af..765c7dd81e 100644
--- a/src/secp256k1/src/modules/recovery/tests_impl.h
+++ b/src/secp256k1/src/modules/recovery/tests_impl.h
@@ -7,6 +7,146 @@
 #ifndef _SECP256K1_MODULE_RECOVERY_TESTS_
 #define _SECP256K1_MODULE_RECOVERY_TESTS_
 
+static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    (void) msg32;
+    (void) key32;
+    (void) algo16;
+    (void) data;
+
+    /* On the first run, return 0 to force a second run */
+    if (counter == 0) {
+        memset(nonce32, 0, 32);
+        return 1;
+    }
+    /* On the second run, return an overflow to force a third run */
+    if (counter == 1) {
+        memset(nonce32, 0xff, 32);
+        return 1;
+    }
+    /* On the next run, return a valid nonce, but flip a coin as to whether or not to fail signing. */
+    memset(nonce32, 1, 32);
+    return secp256k1_rand_bits(1);
+}
+
+void test_ecdsa_recovery_api(void) {
+    /* Setup contexts that just count errors */
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey recpubkey;
+    secp256k1_ecdsa_signature normal_sig;
+    secp256k1_ecdsa_recoverable_signature recsig;
+    unsigned char privkey[32] = { 1 };
+    unsigned char message[32] = { 2 };
+    int32_t ecount = 0;
+    int recid = 0;
+    unsigned char sig[74];
+    unsigned char zero_privkey[32] = { 0 };
+    unsigned char over_privkey[32] = { 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 };
+
+    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Check bad contexts and NULLs for signing */
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_sign_recoverable(none, &recsig, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(sign, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(vrfy, &recsig, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, NULL, message, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, NULL, privkey, NULL, NULL) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, NULL, NULL, NULL) == 0);
+    CHECK(ecount == 5);
+    /* This will fail or succeed randomly, and in either case will not ARG_CHECK failure */
+    secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, recovery_test_nonce_function, NULL);
+    CHECK(ecount == 5);
+    /* These will all fail, but not in ARG_CHECK way */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, zero_privkey, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, over_privkey, NULL, NULL) == 0);
+    /* This one will succeed. */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    CHECK(ecount == 5);
+
+    /* Check signing with a goofy nonce function */
+
+    /* Check bad contexts and NULLs for recovery */
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recover(none, &recpubkey, &recsig, message) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recover(sign, &recpubkey, &recsig, message) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(vrfy, &recpubkey, &recsig, message) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, message) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recover(both, NULL, &recsig, message) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, NULL, message) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, NULL) == 0);
+    CHECK(ecount == 5);
+
+    /* Check NULLs for conversion */
+    CHECK(secp256k1_ecdsa_sign(both, &normal_sig, message, privkey, NULL, NULL) == 1);
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, NULL, &recsig) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, &recsig) == 1);
+
+    /* Check NULLs for de/serialization */
+    CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1);
+    ecount = 0;
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, NULL, &recid, &recsig) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, NULL, &recsig) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, &recsig) == 1);
+
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, NULL, sig, recid) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, NULL, recid) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, -1) == 0);
+    CHECK(ecount == 6);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, 5) == 0);
+    CHECK(ecount == 7);
+    /* overflow in signature will fail but not affect ecount */
+    memcpy(sig, over_privkey, 32);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, recid) == 0);
+    CHECK(ecount == 7);
+
+    /* cleanup */
+    secp256k1_context_destroy(none);
+    secp256k1_context_destroy(sign);
+    secp256k1_context_destroy(vrfy);
+    secp256k1_context_destroy(both);
+}
+
 void test_ecdsa_recovery_end_to_end(void) {
     unsigned char extra[32] = {0x00};
     unsigned char privkey[32];
@@ -241,6 +381,9 @@ void test_ecdsa_recovery_edge_cases(void) {
 
 void run_recovery_tests(void) {
     int i;
+    for (i = 0; i < count; i++) {
+        test_ecdsa_recovery_api();
+    }
     for (i = 0; i < 64*count; i++) {
         test_ecdsa_recovery_end_to_end();
     }
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index f5b2376407..2690d86558 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/src/scalar_impl.h
@@ -66,88 +66,79 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
 #else
     secp256k1_scalar *t;
     int i;
-    /* First compute x ^ (2^N - 1) for some values of N. */
-    secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
+    /* First compute xN as x ^ (2^N - 1) for some values of N,
+     * and uM as x ^ M for some values of M. */
+    secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126;
+    secp256k1_scalar u2, u5, u9, u11, u13;
 
-    secp256k1_scalar_sqr(&x2,  x);
-    secp256k1_scalar_mul(&x2, &x2,  x);
+    secp256k1_scalar_sqr(&u2, x);
+    secp256k1_scalar_mul(&x2, &u2,  x);
+    secp256k1_scalar_mul(&u5, &u2, &x2);
+    secp256k1_scalar_mul(&x3, &u5,  &u2);
+    secp256k1_scalar_mul(&u9, &x3, &u2);
+    secp256k1_scalar_mul(&u11, &u9, &u2);
+    secp256k1_scalar_mul(&u13, &u11, &u2);
 
-    secp256k1_scalar_sqr(&x3, &x2);
-    secp256k1_scalar_mul(&x3, &x3,  x);
-
-    secp256k1_scalar_sqr(&x4, &x3);
-    secp256k1_scalar_mul(&x4, &x4,  x);
-
-    secp256k1_scalar_sqr(&x6, &x4);
+    secp256k1_scalar_sqr(&x6, &u13);
     secp256k1_scalar_sqr(&x6, &x6);
-    secp256k1_scalar_mul(&x6, &x6, &x2);
+    secp256k1_scalar_mul(&x6, &x6, &u11);
 
-    secp256k1_scalar_sqr(&x7, &x6);
-    secp256k1_scalar_mul(&x7, &x7,  x);
+    secp256k1_scalar_sqr(&x8, &x6);
+    secp256k1_scalar_sqr(&x8, &x8);
+    secp256k1_scalar_mul(&x8, &x8,  &x2);
 
-    secp256k1_scalar_sqr(&x8, &x7);
-    secp256k1_scalar_mul(&x8, &x8,  x);
-
-    secp256k1_scalar_sqr(&x15, &x8);
-    for (i = 0; i < 6; i++) {
-        secp256k1_scalar_sqr(&x15, &x15);
+    secp256k1_scalar_sqr(&x14, &x8);
+    for (i = 0; i < 5; i++) {
+        secp256k1_scalar_sqr(&x14, &x14);
     }
-    secp256k1_scalar_mul(&x15, &x15, &x7);
+    secp256k1_scalar_mul(&x14, &x14, &x6);
 
-    secp256k1_scalar_sqr(&x30, &x15);
-    for (i = 0; i < 14; i++) {
-        secp256k1_scalar_sqr(&x30, &x30);
+    secp256k1_scalar_sqr(&x28, &x14);
+    for (i = 0; i < 13; i++) {
+        secp256k1_scalar_sqr(&x28, &x28);
     }
-    secp256k1_scalar_mul(&x30, &x30, &x15);
+    secp256k1_scalar_mul(&x28, &x28, &x14);
 
-    secp256k1_scalar_sqr(&x60, &x30);
-    for (i = 0; i < 29; i++) {
-        secp256k1_scalar_sqr(&x60, &x60);
+    secp256k1_scalar_sqr(&x56, &x28);
+    for (i = 0; i < 27; i++) {
+        secp256k1_scalar_sqr(&x56, &x56);
     }
-    secp256k1_scalar_mul(&x60, &x60, &x30);
+    secp256k1_scalar_mul(&x56, &x56, &x28);
 
-    secp256k1_scalar_sqr(&x120, &x60);
-    for (i = 0; i < 59; i++) {
-        secp256k1_scalar_sqr(&x120, &x120);
+    secp256k1_scalar_sqr(&x112, &x56);
+    for (i = 0; i < 55; i++) {
+        secp256k1_scalar_sqr(&x112, &x112);
     }
-    secp256k1_scalar_mul(&x120, &x120, &x60);
+    secp256k1_scalar_mul(&x112, &x112, &x56);
 
-    secp256k1_scalar_sqr(&x127, &x120);
-    for (i = 0; i < 6; i++) {
-        secp256k1_scalar_sqr(&x127, &x127);
+    secp256k1_scalar_sqr(&x126, &x112);
+    for (i = 0; i < 13; i++) {
+        secp256k1_scalar_sqr(&x126, &x126);
     }
-    secp256k1_scalar_mul(&x127, &x127, &x7);
+    secp256k1_scalar_mul(&x126, &x126, &x14);
 
-    /* Then accumulate the final result (t starts at x127). */
-    t = &x127;
-    for (i = 0; i < 2; i++) { /* 0 */
+    /* Then accumulate the final result (t starts at x126). */
+    t = &x126;
+    for (i = 0; i < 3; i++) {
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
     for (i = 0; i < 4; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
     secp256k1_scalar_mul(t, t, &x3); /* 111 */
-    for (i = 0; i < 2; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 2; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 2; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
     for (i = 0; i < 4; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x3); /* 111 */
-    for (i = 0; i < 3; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 5; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x2); /* 11 */
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+    for (i = 0; i < 4; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
     for (i = 0; i < 4; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
@@ -156,38 +147,26 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
         secp256k1_scalar_sqr(t, t);
     }
     secp256k1_scalar_mul(t, t, &x3); /* 111 */
-    for (i = 0; i < 4; i++) { /* 00 */
+    for (i = 0; i < 6; i++) { /* 00 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x2); /* 11 */
-    for (i = 0; i < 2; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 4; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 2; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
+    for (i = 0; i < 3; i++) {
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
+    secp256k1_scalar_mul(t, t, &x3); /* 111 */
     for (i = 0; i < 5; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x4); /* 1111 */
-    for (i = 0; i < 2; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+    for (i = 0; i < 6; i++) { /* 000 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 3; i++) { /* 00 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 4; i++) { /* 000 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 2; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
+    secp256k1_scalar_mul(t, t, &u5); /* 101 */
     for (i = 0; i < 10; i++) { /* 0000000 */
         secp256k1_scalar_sqr(t, t);
     }
@@ -200,50 +179,34 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
         secp256k1_scalar_sqr(t, t);
     }
     secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
-    for (i = 0; i < 2; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 3; i++) { /* 00 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 3; i++) { /* 00 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
     for (i = 0; i < 5; i++) { /* 0 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x4); /* 1111 */
-    for (i = 0; i < 2; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+    for (i = 0; i < 6; i++) { /* 00 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 5; i++) { /* 000 */
+    secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+    for (i = 0; i < 4; i++) {
+        secp256k1_scalar_sqr(t, t);
+    }
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 5; i++) {
         secp256k1_scalar_sqr(t, t);
     }
     secp256k1_scalar_mul(t, t, &x2); /* 11 */
-    for (i = 0; i < 4; i++) { /* 00 */
+    for (i = 0; i < 6; i++) { /* 00 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x2); /* 11 */
-    for (i = 0; i < 2; i++) { /* 0 */
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 10; i++) { /* 000000 */
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
-    for (i = 0; i < 8; i++) { /* 000000 */
+    secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+    for (i = 0; i < 4; i++) {
         secp256k1_scalar_sqr(t, t);
     }
-    secp256k1_scalar_mul(t, t, &x2); /* 11 */
-    for (i = 0; i < 3; i++) { /* 0 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, &x2); /* 11 */
-    for (i = 0; i < 3; i++) { /* 00 */
-        secp256k1_scalar_sqr(t, t);
-    }
-    secp256k1_scalar_mul(t, t, x); /* 1 */
+    secp256k1_scalar_mul(t, t, &u9); /* 1001 */
     for (i = 0; i < 6; i++) { /* 00000 */
         secp256k1_scalar_sqr(t, t);
     }
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
old mode 100755
new mode 100644
index fb8b882faa..4f8c01655b
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -424,6 +424,33 @@ int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *p
     return ret;
 }
 
+int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) {
+    secp256k1_scalar sec;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    secp256k1_scalar_negate(&sec, &sec);
+    secp256k1_scalar_get_b32(seckey, &sec);
+
+    return 1;
+}
+
+int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *pubkey) {
+    int ret = 0;
+    secp256k1_ge p;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    ret = secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        secp256k1_ge_neg(&p, &p);
+        secp256k1_pubkey_save(pubkey, &p);
+    }
+    return ret;
+}
+
 int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
     secp256k1_scalar term;
     secp256k1_scalar sec;
@@ -552,10 +579,6 @@ int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *
 # include "modules/ecdh/main_impl.h"
 #endif
 
-#ifdef ENABLE_MODULE_SCHNORR
-# include "modules/schnorr/main_impl.h"
-#endif
-
 #ifdef ENABLE_MODULE_RECOVERY
 # include "modules/recovery/main_impl.h"
 #endif
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 9ae7d30281..3d9bd5ebb4 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -10,6 +10,7 @@
 
 #include <stdio.h>
 #include <stdlib.h>
+#include <string.h>
 
 #include <time.h>
 
@@ -135,6 +136,7 @@ void random_scalar_order(secp256k1_scalar *num) {
 
 void run_context_tests(void) {
     secp256k1_pubkey pubkey;
+    secp256k1_pubkey zero_pubkey;
     secp256k1_ecdsa_signature sig;
     unsigned char ctmp[32];
     int32_t ecount;
@@ -149,6 +151,8 @@ void run_context_tests(void) {
     secp256k1_scalar msg, key, nonce;
     secp256k1_scalar sigr, sigs;
 
+    memset(&zero_pubkey, 0, sizeof(zero_pubkey));
+
     ecount = 0;
     ecount2 = 10;
     secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
@@ -201,12 +205,20 @@ void run_context_tests(void) {
     CHECK(ecount == 2);
     CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
     CHECK(ecount2 == 13);
-    CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+    CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1);
     CHECK(ecount == 2);
-    CHECK(secp256k1_context_randomize(vrfy, ctmp) == 0);
+    CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0);
+    CHECK(ecount2 == 14);
+    CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0);
     CHECK(ecount == 3);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_context_randomize(vrfy, ctmp) == 0);
+    CHECK(ecount == 4);
     CHECK(secp256k1_context_randomize(sign, NULL) == 1);
-    CHECK(ecount2 == 13);
+    CHECK(ecount2 == 14);
     secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
     secp256k1_context_set_illegal_callback(sign, NULL, NULL);
 
@@ -1879,9 +1891,9 @@ void test_ge(void) {
      *
      * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
      */
-    secp256k1_ge *ge = (secp256k1_ge *)malloc(sizeof(secp256k1_ge) * (1 + 4 * runs));
-    secp256k1_gej *gej = (secp256k1_gej *)malloc(sizeof(secp256k1_gej) * (1 + 4 * runs));
-    secp256k1_fe *zinv = (secp256k1_fe *)malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+    secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
+    secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
+    secp256k1_fe *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
     secp256k1_fe zf;
     secp256k1_fe zfi2, zfi3;
 
@@ -1919,7 +1931,7 @@ void test_ge(void) {
 
     /* Compute z inverses. */
     {
-        secp256k1_fe *zs = malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+        secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
         for (i = 0; i < 4 * runs + 1; i++) {
             if (i == 0) {
                 /* The point at infinity does not have a meaningful z inverse. Any should do. */
@@ -2020,7 +2032,7 @@ void test_ge(void) {
     /* Test adding all points together in random order equals infinity. */
     {
         secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
-        secp256k1_gej *gej_shuffled = (secp256k1_gej *)malloc((4 * runs + 1) * sizeof(secp256k1_gej));
+        secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej));
         for (i = 0; i < 4 * runs + 1; i++) {
             gej_shuffled[i] = gej[i];
         }
@@ -2041,9 +2053,9 @@ void test_ge(void) {
 
     /* Test batch gej -> ge conversion with and without known z ratios. */
     {
-        secp256k1_fe *zr = (secp256k1_fe *)malloc((4 * runs + 1) * sizeof(secp256k1_fe));
-        secp256k1_ge *ge_set_table = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
-        secp256k1_ge *ge_set_all = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
+        secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe));
+        secp256k1_ge *ge_set_table = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
+        secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
         for (i = 0; i < 4 * runs + 1; i++) {
             /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
             if (i < 4 * runs) {
@@ -3436,6 +3448,7 @@ void test_ecdsa_end_to_end(void) {
     unsigned char pubkeyc[65];
     size_t pubkeyclen = 65;
     secp256k1_pubkey pubkey;
+    secp256k1_pubkey pubkey_tmp;
     unsigned char seckey[300];
     size_t seckeylen = 300;
 
@@ -3457,6 +3470,13 @@ void test_ecdsa_end_to_end(void) {
     memset(&pubkey, 0, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
 
+    /* Verify negation changes the key and changes it back */
+    memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
+    CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
+    CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
+    CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
+
     /* Verify private key import and export. */
     CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
     CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
@@ -4383,10 +4403,6 @@ void run_ecdsa_openssl(void) {
 # include "modules/ecdh/tests_impl.h"
 #endif
 
-#ifdef ENABLE_MODULE_SCHNORR
-# include "modules/schnorr/tests_impl.h"
-#endif
-
 #ifdef ENABLE_MODULE_RECOVERY
 # include "modules/recovery/tests_impl.h"
 #endif
@@ -4504,11 +4520,6 @@ int main(int argc, char **argv) {
     run_ecdsa_openssl();
 #endif
 
-#ifdef ENABLE_MODULE_SCHNORR
-    /* Schnorr tests */
-    run_schnorr_tests();
-#endif
-
 #ifdef ENABLE_MODULE_RECOVERY
     /* ECDSA pubkey recovery tests */
     run_recovery_tests();
diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
index bda6ee475c..b040bb0733 100644
--- a/src/secp256k1/src/tests_exhaustive.c
+++ b/src/secp256k1/src/tests_exhaustive.c
@@ -26,6 +26,11 @@
 #include "secp256k1.c"
 #include "testrand_impl.h"
 
+#ifdef ENABLE_MODULE_RECOVERY
+#include "src/modules/recovery/main_impl.h"
+#include "include/secp256k1_recovery.h"
+#endif
+
 /** stolen from tests.c */
 void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
     CHECK(a->infinity == b->infinity);
@@ -77,7 +82,7 @@ int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned cha
      * function with an increased `attempt`. So if attempt > 0 this means we
      * need to change the nonce to avoid an infinite loop. */
     if (attempt > 0) {
-        (*idata)++;
+        *idata = (*idata + 1) % EXHAUSTIVE_TEST_ORDER;
     }
     secp256k1_scalar_set_int(&s, *idata);
     secp256k1_scalar_get_b32(nonce32, &s);
@@ -244,6 +249,7 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
     for (i = 1; i < order; i++) {  /* message */
         for (j = 1; j < order; j++) {  /* key */
             for (k = 1; k < order; k++) {  /* nonce */
+                const int starting_k = k;
                 secp256k1_ecdsa_signature sig;
                 secp256k1_scalar sk, msg, r, s, expected_r;
                 unsigned char sk32[32], msg32[32];
@@ -262,6 +268,11 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
                 CHECK(r == expected_r);
                 CHECK((k * s) % order == (i + r * j) % order ||
                       (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+
+                /* Overflow means we've tried every possible nonce */
+                if (k < starting_k) {
+                    break;
+                }
             }
         }
     }
@@ -276,6 +287,130 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
      */
 }
 
+#ifdef ENABLE_MODULE_RECOVERY
+void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int i, j, k;
+
+    /* Loop */
+    for (i = 1; i < order; i++) {  /* message */
+        for (j = 1; j < order; j++) {  /* key */
+            for (k = 1; k < order; k++) {  /* nonce */
+                const int starting_k = k;
+                secp256k1_fe r_dot_y_normalized;
+                secp256k1_ecdsa_recoverable_signature rsig;
+                secp256k1_ecdsa_signature sig;
+                secp256k1_scalar sk, msg, r, s, expected_r;
+                unsigned char sk32[32], msg32[32];
+                int expected_recid;
+                int recid;
+                secp256k1_scalar_set_int(&msg, i);
+                secp256k1_scalar_set_int(&sk, j);
+                secp256k1_scalar_get_b32(sk32, &sk);
+                secp256k1_scalar_get_b32(msg32, &msg);
+
+                secp256k1_ecdsa_sign_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+                /* Check directly */
+                secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig);
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+                /* In computing the recid, there is an overflow condition that is disabled in
+                 * scalar_low_impl.h `secp256k1_scalar_set_b32` because almost every r.y value
+                 * will exceed the group order, and our signing code always holds out for r
+                 * values that don't overflow, so with a proper overflow check the tests would
+                 * loop indefinitely. */
+                r_dot_y_normalized = group[k].y;
+                secp256k1_fe_normalize(&r_dot_y_normalized);
+                /* Also the recovery id is flipped depending if we hit the low-s branch */
+                if ((k * s) % order == (i + r * j) % order) {
+                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 1 : 0;
+                } else {
+                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 0 : 1;
+                }
+                CHECK(recid == expected_recid);
+
+                /* Convert to a standard sig then check */
+                secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
+                /* Note that we compute expected_r *after* signing -- this is important
+                 * because our nonce-computing function function might change k during
+                 * signing. */
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+
+                /* Overflow means we've tried every possible nonce */
+                if (k < starting_k) {
+                    break;
+                }
+            }
+        }
+    }
+}
+
+void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    /* This is essentially a copy of test_exhaustive_verify, with recovery added */
+    int s, r, msg, key;
+    for (s = 1; s < order; s++) {
+        for (r = 1; r < order; r++) {
+            for (msg = 1; msg < order; msg++) {
+                for (key = 1; key < order; key++) {
+                    secp256k1_ge nonconst_ge;
+                    secp256k1_ecdsa_recoverable_signature rsig;
+                    secp256k1_ecdsa_signature sig;
+                    secp256k1_pubkey pk;
+                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
+                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
+                    int recid = 0;
+                    int k, should_verify;
+                    unsigned char msg32[32];
+
+                    secp256k1_scalar_set_int(&s_s, s);
+                    secp256k1_scalar_set_int(&r_s, r);
+                    secp256k1_scalar_set_int(&msg_s, msg);
+                    secp256k1_scalar_set_int(&sk_s, key);
+                    secp256k1_scalar_get_b32(msg32, &msg_s);
+
+                    /* Verify by hand */
+                    /* Run through every k value that gives us this r and check that *one* works.
+                     * Note there could be none, there could be multiple, ECDSA is weird. */
+                    should_verify = 0;
+                    for (k = 0; k < order; k++) {
+                        secp256k1_scalar check_x_s;
+                        r_from_k(&check_x_s, group, k);
+                        if (r_s == check_x_s) {
+                            secp256k1_scalar_set_int(&s_times_k_s, k);
+                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
+                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
+                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
+                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
+                        }
+                    }
+                    /* nb we have a "high s" rule */
+                    should_verify &= !secp256k1_scalar_is_high(&s_s);
+
+                    /* We would like to try recovering the pubkey and checking that it matches,
+                     * but pubkey recovery is impossible in the exhaustive tests (the reason
+                     * being that there are 12 nonzero r values, 12 nonzero points, and no
+                     * overlap between the sets, so there are no valid signatures). */
+
+                    /* Verify by converting to a standard signature and calling verify */
+                    secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
+                    secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+                    secp256k1_pubkey_save(&pk, &nonconst_ge);
+                    CHECK(should_verify ==
+                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+                }
+            }
+        }
+    }
+}
+#endif
+
 int main(void) {
     int i;
     secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
@@ -324,6 +459,12 @@ int main(void) {
     test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
     test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
 
+#ifdef ENABLE_MODULE_RECOVERY
+    test_exhaustive_recovery_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_recovery_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+#endif
+
+    secp256k1_context_destroy(ctx);
     return 0;
 }
 
diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h
index 4eef4ded47..4092a86c91 100644
--- a/src/secp256k1/src/util.h
+++ b/src/secp256k1/src/util.h
@@ -57,7 +57,10 @@ static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback *
 #endif
 
 /* Like assert(), but when VERIFY is defined, and side-effect safe. */
-#ifdef VERIFY
+#if defined(COVERAGE)
+#define VERIFY_CHECK(check)
+#define VERIFY_SETUP(stmt)
+#elif defined(VERIFY)
 #define VERIFY_CHECK CHECK
 #define VERIFY_SETUP(stmt) do { stmt; } while(0)
 #else