diff --git a/src/bench.c b/src/bench.c
index eeee710..be5f40a 100644
--- a/src/bench.c
+++ b/src/bench.c
@@ -5,9 +5,22 @@
 #include "impl/group.h"
 #include "impl/ecmult.h"
 #include "impl/ecdsa.h"
+#include "impl/util.h"
+
+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);
+}
 
 int main() {
-    secp256k1_num_start();
     secp256k1_fe_start();
     secp256k1_ge_start();
     secp256k1_ecmult_start();
@@ -24,9 +37,9 @@ int main() {
     int cnt = 0;
     int good = 0;
     for (int i=0; i<1000000; i++) {
-        secp256k1_num_set_rand(&r, order);
-        secp256k1_num_set_rand(&s, order);
-        secp256k1_num_set_rand(&m, order);
+        random_num_order(&r);
+        random_num_order(&s);
+        random_num_order(&m);
         secp256k1_ecdsa_sig_set_rs(&sig, &r, &s);
         secp256k1_gej_t pubkey; secp256k1_gej_set_xo(&pubkey, &x, 1);
         if (secp256k1_gej_is_valid(&pubkey)) {
@@ -43,6 +56,5 @@ int main() {
     secp256k1_ecmult_stop();
     secp256k1_ge_stop();
     secp256k1_fe_stop();
-    secp256k1_num_stop();
     return 0;
 }
diff --git a/src/impl/num_gmp.h b/src/impl/num_gmp.h
index a43be1f..0d6353d 100644
--- a/src/impl/num_gmp.h
+++ b/src/impl/num_gmp.h
@@ -16,12 +16,6 @@ void static secp256k1_num_sanity(const secp256k1_num_t *a) {
 #define secp256k1_num_sanity(a) do { } while(0)
 #endif
 
-void static secp256k1_num_start(void) {
-}
-
-void static secp256k1_num_stop(void) {
-}
-
 void static secp256k1_num_init(secp256k1_num_t *r) {
     r->neg = 0;
     r->limbs = 1;
@@ -385,11 +379,4 @@ void static secp256k1_num_negate(secp256k1_num_t *r) {
     r->neg ^= 1;
 }
 
-void static secp256k1_num_set_rand(secp256k1_num_t *r, const secp256k1_num_t *a) {
-    mpn_random(r->data, a->limbs);
-    r->limbs = a->limbs;
-    r->neg = 0;
-    secp256k1_num_mod(r, a);
-}
-
 #endif
diff --git a/src/impl/num_openssl.h b/src/impl/num_openssl.h
index cb3f951..9153252 100644
--- a/src/impl/num_openssl.h
+++ b/src/impl/num_openssl.h
@@ -9,13 +9,6 @@
 
 #include "../num.h"
 
-void static secp256k1_num_start() {
-}
-
-void static secp256k1_num_stop() {
-}
-
-
 void static secp256k1_num_init(secp256k1_num_t *r) {
     BN_init(&r->bn);
 }
@@ -145,8 +138,4 @@ void static secp256k1_num_negate(secp256k1_num_t *r) {
     BN_set_negative(&r->bn, !BN_is_negative(&r->bn));
 }
 
-void static secp256k1_num_set_rand(secp256k1_num_t *r, const secp256k1_num_t *a) {
-    BN_pseudo_rand_range(&r->bn, &a->bn);
-}
-
 #endif
diff --git a/src/impl/util.h b/src/impl/util.h
new file mode 100644
index 0000000..a031ed6
--- /dev/null
+++ b/src/impl/util.h
@@ -0,0 +1,48 @@
+#ifndef _SECP256K1_UTIL_IMPL_H_
+#define _SECP256K1_UTIL_IMPL_H_
+
+#include <stdint.h>
+#include <string.h>
+
+#include "../util.h"
+
+static inline uint32_t secp256k1_rand32(void) {
+    static uint32_t Rz = 11, Rw = 11;
+    Rz = 36969 * (Rz & 0xFFFF) + (Rz >> 16);
+    Rw = 18000 * (Rw & 0xFFFF) + (Rw >> 16);
+    return (Rw << 16) + Rz;
+}
+
+static void secp256k1_rand256(unsigned char *b32) {
+    for (int i=0; i<8; i++) {
+        uint32_t r = secp256k1_rand32();
+        b32[i*4 + 0] = (r >>  0) & 0xFF;
+        b32[i*4 + 1] = (r >>  8) & 0xFF;
+        b32[i*4 + 2] = (r >> 16) & 0xFF;
+        b32[i*4 + 3] = (r >> 24) & 0xFF;
+    }
+}
+
+static void secp256k1_rand256_test(unsigned char *b32) {
+    int bits=0;
+    uint32_t ent;
+    int entbits = 0;
+    memset(b32, 0, 32);
+    while (bits < 256) {
+        if (entbits < 15) {
+            ent = secp256k1_rand32();
+            entbits = 32;
+        }
+        int now = 1 + ((ent % 64)*((ent >> 6) % 32)+16)/31;
+        uint32_t val = 1 & (ent >> 11);
+        ent -= 12;
+        entbits >>= 12;
+        while (now > 0 && bits < 256) {
+            b32[bits / 8] |= val << (bits % 8);
+            now--;
+            bits++;
+        }
+    }
+}
+
+#endif
diff --git a/src/num.h b/src/num.h
index 060ea64..633200c 100644
--- a/src/num.h
+++ b/src/num.h
@@ -11,12 +11,6 @@
 #error "Please select num implementation"
 #endif
 
-/** Initialize the num module. */
-void static secp256k1_num_start(void);
-
-/** De-initialize the num module. */
-void static secp256k1_num_stop(void);
-
 /** Initialize a number. */
 void static secp256k1_num_init(secp256k1_num_t *r);
 
@@ -93,7 +87,4 @@ void static secp256k1_num_split(secp256k1_num_t *rl, secp256k1_num_t *rh, const
 /** Change a number's sign. */
 void static secp256k1_num_negate(secp256k1_num_t *r);
 
-/** Set a number to an random value below the passed number. */
-void static secp256k1_num_set_rand(secp256k1_num_t *r, const secp256k1_num_t *a);
-
 #endif
diff --git a/src/secp256k1.c b/src/secp256k1.c
index aecdad9..4d7929a 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -5,7 +5,6 @@
 #include "impl/ecdsa.h"
 
 void secp256k1_start(void) {
-    secp256k1_num_start();
     secp256k1_fe_start();
     secp256k1_ge_start();
     secp256k1_ecmult_start();
@@ -15,7 +14,6 @@ void secp256k1_stop(void) {
     secp256k1_ecmult_stop();
     secp256k1_ge_stop();
     secp256k1_fe_stop();
-    secp256k1_num_stop();
 }
 
 int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
diff --git a/src/tests.c b/src/tests.c
index 51f42f6..65f0317 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -5,10 +5,24 @@
 #include "impl/group.h"
 #include "impl/ecmult.h"
 #include "impl/ecdsa.h"
+#include "impl/util.h"
 
 // #define COUNT 2
 #define COUNT 100
 
+void random_num_order(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 test_run_ecmult_chain() {
     // random starting point A (on the curve)
     secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64);
@@ -130,21 +144,14 @@ void test_wnaf(const secp256k1_num_t *number, int w) {
 }
 
 void test_run_wnaf() {
-    secp256k1_num_t range, min, n;
-    secp256k1_num_init(&range);
-    secp256k1_num_init(&min);
+    secp256k1_num_t n;
     secp256k1_num_init(&n);
-    secp256k1_num_set_hex(&range, "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 66);
-    secp256k1_num_copy(&min, &range);
-    secp256k1_num_shift(&min, 1);
-    secp256k1_num_negate(&min);
     for (int i=0; i<COUNT; i++) {
-        secp256k1_num_set_rand(&n, &range);
-        secp256k1_num_add(&n, &n, &min);
+        random_num_order(&n);
+        if (i % 1)
+            secp256k1_num_negate(&n);
         test_wnaf(&n, 4+(i%10));
     }
-    secp256k1_num_free(&range);
-    secp256k1_num_free(&min);
     secp256k1_num_free(&n);
 }
 
@@ -152,15 +159,15 @@ void test_ecdsa_sign_verify() {
     const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
     secp256k1_num_t msg, key, nonce;
     secp256k1_num_init(&msg);
-    secp256k1_num_set_rand(&msg, &c->order);
+    random_num_order(&msg);
     secp256k1_num_init(&key);
-    secp256k1_num_set_rand(&key, &c->order);
+    random_num_order(&key);
     secp256k1_num_init(&nonce);
     secp256k1_gej_t pub; secp256k1_ecmult_gen(&pub, &key);
     secp256k1_ecdsa_sig_t sig;
     secp256k1_ecdsa_sig_init(&sig);
     do {
-        secp256k1_num_set_rand(&nonce, &c->order);
+        random_num_order(&nonce);
     } while(!secp256k1_ecdsa_sig_sign(&sig, &key, &msg, &nonce));
     assert(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
     secp256k1_num_inc(&msg);
@@ -178,7 +185,6 @@ void test_run_ecdsa_sign_verify() {
 }
 
 int main(void) {
-    secp256k1_num_start();
     secp256k1_fe_start();
     secp256k1_ge_start();
     secp256k1_ecmult_start();
@@ -191,6 +197,5 @@ int main(void) {
     secp256k1_ecmult_stop();
     secp256k1_ge_stop();
     secp256k1_fe_stop();
-    secp256k1_num_stop();
     return 0;
 }
diff --git a/src/util.h b/src/util.h
new file mode 100644
index 0000000..3aced7a
--- /dev/null
+++ b/src/util.h
@@ -0,0 +1,15 @@
+#ifndef _SECP256K1_UTIL_H_
+#define _SECP256K1_UTIL_H_
+
+/** Generate a pseudorandom 32-bit number. */
+static uint32_t secp256k1_rand32(void);
+
+/** Generate a pseudorandom 32-byte array. */
+static void secp256k1_rand256(unsigned char *b32);
+
+/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
+static void secp256k1_rand256_test(unsigned char *b32);
+
+#include "impl/util.h"
+
+#endif