diff --git a/.travis.yml b/.travis.yml
index 24a86b561b..12692deafa 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -18,6 +18,7 @@ env:
     - FIELD=64bit     ENDOMORPHISM=yes
     - FIELD=32bit
     - FIELD=32bit     ENDOMORPHISM=yes
+    - BIGNUM=none
     - BUILD=distcheck
     - EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
 before_script: ./autogen.sh
diff --git a/configure.ac b/configure.ac
index 88ca8dfa58..f0d69f93de 100644
--- a/configure.ac
+++ b/configure.ac
@@ -95,7 +95,7 @@ AC_ARG_ENABLE(endomorphism,
 AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=gmp|64bit|64bit_asm|32bit|auto],
 [Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
 
-AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|auto],
+AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|none|auto],
 [Specify Bignum Implementation. Default is auto])],[req_bignum=$withval], [req_bignum=auto])
 
 AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
@@ -179,7 +179,7 @@ if test x"$req_bignum" = x"auto"; then
   fi
 
   if test x"$set_bignum" = x; then
-    AC_MSG_ERROR([no working bignum implementation found])
+    set_bignum=none
   fi
 else
   set_bignum=$req_bignum
@@ -187,8 +187,7 @@ else
   gmp)
     SECP_GMP_CHECK
     ;;
-  openssl)
-    SECP_OPENSSL_CHECK
+  none)
     ;;
   *)
     AC_MSG_ERROR([invalid bignum implementation selection])
@@ -221,11 +220,16 @@ esac
 # select bignum implementation
 case $set_bignum in
 gmp)
-  AC_DEFINE(HAVE_LIBGMP,1,[Define this symbol if libgmp is installed])
-  AC_DEFINE(USE_NUM_GMP, 1, [Define this symbol to use the gmp implementation])
+  AC_DEFINE(HAVE_LIBGMP, 1, [Define this symbol if libgmp is installed])
+  AC_DEFINE(USE_NUM_GMP, 1, [Define this symbol to use the gmp implementation for num])
   AC_DEFINE(USE_FIELD_INV_NUM, 1, [Define this symbol to use the num-based field inverse implementation])
   AC_DEFINE(USE_SCALAR_INV_NUM, 1, [Define this symbol to use the num-based scalar inverse implementation])
   ;;
+none)
+  AC_DEFINE(USE_NUM_NONE, 1, [Define this symbol to use no num implementation])
+  AC_DEFINE(USE_FIELD_INV_BUILTIN, 1, [Define this symbol to use the native field inverse implementation])
+  AC_DEFINE(USE_SCALAR_INV_BUILTIN, 1, [Define this symbol to use the native scalar inverse implementation])
+  ;;
 *)
   AC_MSG_ERROR([invalid bignum implementation])
   ;;
@@ -266,6 +270,9 @@ if test x"$set_field" = x"gmp" || test x"$set_bignum" = x"gmp"; then
 fi
 
 if test x"$use_endomorphism" = x"yes"; then
+  if test x"$set_bignum" = x"none"; then
+    AC_MSG_ERROR([Cannot use endomorphism optimization without a bignum implementation])
+  fi
   AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism])
 fi
 
diff --git a/src/ecdsa_impl.h b/src/ecdsa_impl.h
index 525516e7bf..81b67e825d 100644
--- a/src/ecdsa_impl.h
+++ b/src/ecdsa_impl.h
@@ -29,10 +29,14 @@ static void secp256k1_ecdsa_start(void) {
     /* Allocate. */
     secp256k1_ecdsa_consts_t *ret = (secp256k1_ecdsa_consts_t*)malloc(sizeof(secp256k1_ecdsa_consts_t));
 
-    unsigned char p[32];
-    secp256k1_num_get_bin(p, 32, &secp256k1_ge_consts->order);
-    secp256k1_fe_set_b32(&ret->order_as_fe, p);
+    static const unsigned char order[] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+    };
 
+    secp256k1_fe_set_b32(&ret->order_as_fe, order);
     secp256k1_fe_negate(&ret->p_minus_order, &ret->order_as_fe, 1);
     secp256k1_fe_normalize(&ret->p_minus_order);
 
diff --git a/src/field.h b/src/field.h
index 99a049ffc9..86aee41b18 100644
--- a/src/field.h
+++ b/src/field.h
@@ -33,7 +33,9 @@
 #endif
 
 typedef struct {
+#ifndef USE_NUM_NONE
     secp256k1_num_t p;
+#endif
     secp256k1_fe_t order;
 } secp256k1_fe_consts_t;
 
diff --git a/src/field_impl.h b/src/field_impl.h
index 4aac6ebc67..4d25e53715 100644
--- a/src/field_impl.h
+++ b/src/field_impl.h
@@ -267,16 +267,20 @@ static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t r[len], const se
 }
 
 static void secp256k1_fe_start(void) {
+#ifndef USE_NUM_NONE
     static const unsigned char secp256k1_fe_consts_p[] = {
         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,0xFE,0xFF,0xFF,0xFC,0x2F
     };
+#endif
     if (secp256k1_fe_consts == NULL) {
         secp256k1_fe_inner_start();
         secp256k1_fe_consts_t *ret = (secp256k1_fe_consts_t*)malloc(sizeof(secp256k1_fe_consts_t));
+#ifndef USE_NUM_NONE
         secp256k1_num_set_bin(&ret->p, secp256k1_fe_consts_p, sizeof(secp256k1_fe_consts_p));
+#endif
         secp256k1_fe_consts = ret;
     }
 }
diff --git a/src/group.h b/src/group.h
index 1600e96a27..b0d42721da 100644
--- a/src/group.h
+++ b/src/group.h
@@ -27,8 +27,6 @@ typedef struct {
 
 /** Global constants related to the group */
 typedef struct {
-    secp256k1_num_t order; /* the order of the curve (= order of its generator) */
-    secp256k1_num_t half_order; /* half the order of the curve (= order of its generator) */
     secp256k1_ge_t g; /* the generator point */
 
 #ifdef USE_ENDOMORPHISM
diff --git a/src/group_impl.h b/src/group_impl.h
index d11ca4e366..237cc157bd 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -413,12 +413,6 @@ static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *
 
 
 static void secp256k1_ge_start(void) {
-    static const unsigned char secp256k1_ge_consts_order[] = {
-        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
-        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
-        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
-    };
     static const unsigned char secp256k1_ge_consts_g_x[] = {
         0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,
         0x55,0xA0,0x62,0x95,0xCE,0x87,0x0B,0x07,
@@ -442,9 +436,6 @@ static void secp256k1_ge_start(void) {
 #endif
     if (secp256k1_ge_consts == NULL) {
         secp256k1_ge_consts_t *ret = (secp256k1_ge_consts_t*)malloc(sizeof(secp256k1_ge_consts_t));
-        secp256k1_num_set_bin(&ret->order,  secp256k1_ge_consts_order,  sizeof(secp256k1_ge_consts_order));
-        secp256k1_num_copy(&ret->half_order, &ret->order);
-        secp256k1_num_shift(&ret->half_order, 1);
 #ifdef USE_ENDOMORPHISM
         VERIFY_CHECK(secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta));
 #endif
diff --git a/src/num.h b/src/num.h
index 7beaf1d897..9e073b4a59 100644
--- a/src/num.h
+++ b/src/num.h
@@ -7,6 +7,8 @@
 #ifndef _SECP256K1_NUM_
 #define _SECP256K1_NUM_
 
+#ifndef USE_NUM_NONE
+
 #if defined HAVE_CONFIG_H
 #include "libsecp256k1-config.h"
 #endif
@@ -65,3 +67,5 @@ static int secp256k1_num_is_neg(const secp256k1_num_t *a);
 static void secp256k1_num_negate(secp256k1_num_t *r);
 
 #endif
+
+#endif
diff --git a/src/num_impl.h b/src/num_impl.h
index f73d3ceea8..0b0e3a072a 100644
--- a/src/num_impl.h
+++ b/src/num_impl.h
@@ -15,6 +15,8 @@
 
 #if defined(USE_NUM_GMP)
 #include "num_gmp_impl.h"
+#elif defined(USE_NUM_NONE)
+/* Nothing. */
 #else
 #error "Please select num implementation"
 #endif
diff --git a/src/scalar.h b/src/scalar.h
index 4b5d73fdeb..b5c43b45bf 100644
--- a/src/scalar.h
+++ b/src/scalar.h
@@ -72,9 +72,14 @@ static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a);
 /** Check whether a scalar is higher than the group order divided by 2. */
 static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a);
 
+#ifndef USE_NUM_NONE
 /** Convert a scalar to a number. */
 static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a);
 
+/** Get the order of the group as a number. */
+static void secp256k1_scalar_order_get_num(secp256k1_num_t *r);
+#endif
+
 /** Compare two scalars. */
 static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
 
diff --git a/src/scalar_impl.h b/src/scalar_impl.h
index dcddf3b413..3e8d8b8c56 100644
--- a/src/scalar_impl.h
+++ b/src/scalar_impl.h
@@ -25,6 +25,9 @@
 #endif
 
 typedef struct {
+#ifndef USE_NUM_NONE
+    secp256k1_num_t order;
+#endif
 #ifdef USE_ENDOMORPHISM
     secp256k1_num_t a1b2, b1, a2;
 #endif
@@ -39,6 +42,15 @@ static void secp256k1_scalar_start(void) {
     /* Allocate. */
     secp256k1_scalar_consts_t *ret = (secp256k1_scalar_consts_t*)malloc(sizeof(secp256k1_scalar_consts_t));
 
+#ifndef USE_NUM_NONE
+    static const unsigned char secp256k1_scalar_consts_order[] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+    };
+    secp256k1_num_set_bin(&ret->order, secp256k1_scalar_consts_order, sizeof(secp256k1_scalar_consts_order));
+#endif
 #ifdef USE_ENDOMORPHISM
     static const unsigned char secp256k1_scalar_consts_a1b2[] = {
         0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
@@ -72,12 +84,17 @@ static void secp256k1_scalar_stop(void) {
     free(c);
 }
 
+#ifndef USE_NUM_NONE
 static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) {
     unsigned char c[32];
     secp256k1_scalar_get_b32(c, a);
     secp256k1_num_set_bin(r, c, 32);
 }
 
+static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
+    *r = secp256k1_scalar_consts->order;
+}
+#endif
 
 static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
     /* First compute x ^ (2^N - 1) for some values of N. */
@@ -238,7 +255,7 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
     secp256k1_scalar_get_b32(b, x);
     secp256k1_num_t n;
     secp256k1_num_set_bin(&n, b, 32);
-    secp256k1_num_mod_inverse(&n, &n, &secp256k1_ge_consts->order);
+    secp256k1_num_mod_inverse(&n, &n, &secp256k1_scalar_consts->order);
     secp256k1_num_get_bin(b, 32, &n);
     secp256k1_scalar_set_b32(r, b, NULL);
 #else
@@ -256,19 +273,18 @@ static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_
     secp256k1_num_t rn1, rn2;
 
     const secp256k1_scalar_consts_t *c = secp256k1_scalar_consts;
-    const secp256k1_num_t *order = &secp256k1_ge_consts->order;
     secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2;
 
-    secp256k1_num_copy(&bnn2, order);
+    secp256k1_num_copy(&bnn2, &c->order);
     secp256k1_num_shift(&bnn2, 1);
 
     secp256k1_num_mul(&bnc1, &na, &c->a1b2);
     secp256k1_num_add(&bnc1, &bnc1, &bnn2);
-    secp256k1_num_div(&bnc1, &bnc1, order);
+    secp256k1_num_div(&bnc1, &bnc1, &c->order);
 
     secp256k1_num_mul(&bnc2, &na, &c->b1);
     secp256k1_num_add(&bnc2, &bnc2, &bnn2);
-    secp256k1_num_div(&bnc2, &bnc2, order);
+    secp256k1_num_div(&bnc2, &bnc2, &c->order);
 
     secp256k1_num_mul(&bnt1, &bnc1, &c->a1b2);
     secp256k1_num_mul(&bnt2, &bnc2, &c->a2);
diff --git a/src/tests.c b/src/tests.c
index 5e594e9249..dc0fce2fc6 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -23,23 +23,13 @@
 
 static int count = 64;
 
-/***** NUM TESTS *****/
-
-void random_num_negate(secp256k1_num_t *num) {
-    if (secp256k1_rand32() & 1)
-        secp256k1_num_negate(num);
-}
-
 void random_field_element_test(secp256k1_fe_t *fe) {
     do {
         unsigned char b32[32];
         secp256k1_rand256_test(b32);
-        secp256k1_num_t num;
-        secp256k1_num_set_bin(&num, b32, 32);
-        if (secp256k1_num_cmp(&num, &secp256k1_fe_consts->p) >= 0)
-            continue;
-        VERIFY_CHECK(secp256k1_fe_set_b32(fe, b32));
-        break;
+        if (secp256k1_fe_set_b32(fe, b32)) {
+            break;
+        }
     } while(1);
 }
 
@@ -75,19 +65,6 @@ void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge
     gej->infinity = ge->infinity;
 }
 
-void random_num_order_test(secp256k1_num_t *num) {
-    do {
-        unsigned char b32[32];
-        secp256k1_rand256_test(b32);
-        secp256k1_num_set_bin(num, b32, 32);
-        if (secp256k1_num_is_zero(num))
-            continue;
-        if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0)
-            continue;
-        break;
-    } while(1);
-}
-
 void random_scalar_order_test(secp256k1_scalar_t *num) {
     do {
         unsigned char b32[32];
@@ -112,17 +89,24 @@ void random_scalar_order(secp256k1_scalar_t *num) {
     } while(1);
 }
 
+/***** NUM TESTS *****/
+
+#ifndef USE_NUM_NONE
+void random_num_negate(secp256k1_num_t *num) {
+    if (secp256k1_rand32() & 1)
+        secp256k1_num_negate(num);
+}
+
+void random_num_order_test(secp256k1_num_t *num) {
+    secp256k1_scalar_t sc;
+    random_scalar_order_test(&sc);
+    secp256k1_scalar_get_num(num, &sc);
+}
+
 void random_num_order(secp256k1_num_t *num) {
-    do {
-        unsigned char b32[32];
-        secp256k1_rand256(b32);
-        secp256k1_num_set_bin(num, b32, 32);
-        if (secp256k1_num_is_zero(num))
-            continue;
-        if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0)
-            continue;
-        break;
-    } while(1);
+    secp256k1_scalar_t sc;
+    random_scalar_order(&sc);
+    secp256k1_scalar_get_num(num, &sc);
 }
 
 void test_num_get_set_bin(void) {
@@ -201,6 +185,7 @@ void run_num_smalltests(void) {
         test_num_add_sub();
     }
 }
+#endif
 
 /***** SCALAR TESTS *****/
 
@@ -208,29 +193,29 @@ void scalar_test(void) {
     unsigned char c[32];
 
     /* Set 's' to a random scalar, with value 'snum'. */
-    secp256k1_rand256_test(c);
     secp256k1_scalar_t s;
-    secp256k1_scalar_set_b32(&s, c, NULL);
-    secp256k1_num_t snum;
-    secp256k1_num_set_bin(&snum, c, 32);
-    secp256k1_num_mod(&snum, &secp256k1_ge_consts->order);
+    random_scalar_order_test(&s);
 
     /* Set 's1' to a random scalar, with value 's1num'. */
-    secp256k1_rand256_test(c);
     secp256k1_scalar_t s1;
-    secp256k1_scalar_set_b32(&s1, c, NULL);
-    secp256k1_num_t s1num;
-    secp256k1_num_set_bin(&s1num, c, 32);
-    secp256k1_num_mod(&s1num, &secp256k1_ge_consts->order);
+    random_scalar_order_test(&s1);
 
     /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
-    secp256k1_rand256_test(c);
     secp256k1_scalar_t s2;
-    int overflow = 0;
-    secp256k1_scalar_set_b32(&s2, c, &overflow);
-    secp256k1_num_t s2num;
-    secp256k1_num_set_bin(&s2num, c, 32);
-    secp256k1_num_mod(&s2num, &secp256k1_ge_consts->order);
+    random_scalar_order_test(&s2);
+    secp256k1_scalar_get_b32(c, &s2);
+
+#ifndef USE_NUM_NONE
+    secp256k1_num_t snum, s1num, s2num;
+    secp256k1_scalar_get_num(&snum, &s);
+    secp256k1_scalar_get_num(&s1num, &s1);
+    secp256k1_scalar_get_num(&s2num, &s2);
+
+    secp256k1_num_t order;
+    secp256k1_scalar_order_get_num(&order);
+    secp256k1_num_t half_order = order;
+    secp256k1_num_shift(&half_order, 1);
+#endif
 
     {
         /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
@@ -268,22 +253,12 @@ void scalar_test(void) {
         CHECK(secp256k1_scalar_eq(&n, &s));
     }
 
-    {
-        /* Test that get_b32 returns the same as get_bin on the number. */
-        unsigned char r1[32];
-        secp256k1_scalar_get_b32(r1, &s2);
-        unsigned char r2[32];
-        secp256k1_num_get_bin(r2, 32, &s2num);
-        CHECK(memcmp(r1, r2, 32) == 0);
-        /* If no overflow occurred when assigning, it should also be equal to the original byte array. */
-        CHECK((memcmp(r1, c, 32) == 0) == (overflow == 0));
-    }
-
+#ifndef USE_NUM_NONE
     {
         /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
         secp256k1_num_t rnum;
         secp256k1_num_add(&rnum, &snum, &s2num);
-        secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
+        secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_t r;
         secp256k1_scalar_add(&r, &s, &s2);
         secp256k1_num_t r2num;
@@ -295,7 +270,7 @@ void scalar_test(void) {
         /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
         secp256k1_num_t rnum;
         secp256k1_num_mul(&rnum, &snum, &s2num);
-        secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
+        secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_t r;
         secp256k1_scalar_mul(&r, &s, &s2);
         secp256k1_num_t r2num;
@@ -312,14 +287,14 @@ void scalar_test(void) {
         /* Check that comparison with zero matches comparison with zero on the number. */
         CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
         /* Check that comparison with the half order is equal to testing for high scalar. */
-        CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &secp256k1_ge_consts->half_order) > 0));
+        CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
         secp256k1_scalar_t neg;
         secp256k1_scalar_negate(&neg, &s);
         secp256k1_num_t negnum;
-        secp256k1_num_sub(&negnum, &secp256k1_ge_consts->order, &snum);
-        secp256k1_num_mod(&negnum, &secp256k1_ge_consts->order);
+        secp256k1_num_sub(&negnum, &order, &snum);
+        secp256k1_num_mod(&negnum, &order);
         /* Check that comparison with the half order is equal to testing for high scalar after negation. */
-        CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &secp256k1_ge_consts->half_order) > 0));
+        CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
         /* Negating should change the high property, unless the value was already zero. */
         CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
         secp256k1_num_t negnum2;
@@ -333,17 +308,20 @@ void scalar_test(void) {
         /* Negating zero should still result in zero. */
         CHECK(secp256k1_scalar_is_zero(&neg));
     }
+#endif
 
     {
         /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
         if (!secp256k1_scalar_is_zero(&s)) {
             secp256k1_scalar_t inv;
             secp256k1_scalar_inverse(&inv, &s);
+#ifndef USE_NUM_NONE
             secp256k1_num_t invnum;
-            secp256k1_num_mod_inverse(&invnum, &snum, &secp256k1_ge_consts->order);
+            secp256k1_num_mod_inverse(&invnum, &snum, &order);
             secp256k1_num_t invnum2;
             secp256k1_scalar_get_num(&invnum2, &inv);
             CHECK(secp256k1_num_eq(&invnum, &invnum2));
+#endif
             secp256k1_scalar_mul(&inv, &inv, &s);
             /* Multiplying a scalar with its inverse must result in one. */
             CHECK(secp256k1_scalar_is_one(&inv));
@@ -431,6 +409,30 @@ void run_scalar_tests(void) {
     for (int i = 0; i < 128 * count; i++) {
         scalar_test();
     }
+
+    {
+        // (-1)+1 should be zero.
+        secp256k1_scalar_t s, o;
+        secp256k1_scalar_set_int(&s, 1);
+        secp256k1_scalar_negate(&o, &s);
+        secp256k1_scalar_add(&o, &o, &s);
+        CHECK(secp256k1_scalar_is_zero(&o));
+    }
+
+#ifndef USE_NUM_NONE
+    {
+        // A scalar with value of the curve order should be 0.
+        secp256k1_num_t order;
+        secp256k1_scalar_order_get_num(&order);
+        unsigned char bin[32];
+        secp256k1_num_get_bin(bin, 32, &order);
+        secp256k1_scalar_t zero;
+        int overflow = 0;
+        secp256k1_scalar_set_b32(&zero, bin, &overflow);
+        CHECK(overflow == 1);
+        CHECK(secp256k1_scalar_is_zero(&zero));
+    }
+#endif
 }
 
 /***** FIELD TESTS *****/
@@ -868,11 +870,11 @@ void test_ecdsa_end_to_end(void) {
 
     /* Generate a random key and message. */
     {
-        secp256k1_num_t msg, key;
-        random_num_order_test(&msg);
-        random_num_order_test(&key);
-        secp256k1_num_get_bin(privkey, 32, &key);
-        secp256k1_num_get_bin(message, 32, &msg);
+        secp256k1_scalar_t msg, key;
+        random_scalar_order_test(&msg);
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_scalar_get_b32(message, &msg);
     }
 
     /* Construct and verify corresponding public key. */
@@ -1119,8 +1121,10 @@ int main(int argc, char **argv) {
     /* initialize */
     secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY);
 
+#ifndef USE_NUM_NONE
     /* num tests */
     run_num_smalltests();
+#endif
 
     /* scalar tests */
     run_scalar_tests();