diff --git a/include/gmssl/sm2.h b/include/gmssl/sm2.h
index 5c4964cf..f14b583e 100644
--- a/include/gmssl/sm2.h
+++ b/include/gmssl/sm2.h
@@ -128,8 +128,16 @@ int sm2_do_sign(const SM2_KEY *key, const uint8_t dgst[32], SM2_SIGNATURE *sig);
 int sm2_do_verify(const SM2_KEY *key, const uint8_t dgst[32], const SM2_SIGNATURE *sig);
 
 int sm2_fast_sign_compute_key(const SM2_KEY *key, sm2_z256_t fast_private);
-int sm2_fast_sign_pre_compute(sm2_z256_t k, sm2_z256_t x1_modn);
-int sm2_fast_sign(const sm2_z256_t fast_private, const sm2_z256_t k, const sm2_z256_t x1_modn,
+
+typedef struct {
+	sm2_z256_t k;
+	sm2_z256_t x1_modn;
+} SM2_SIGN_PRE_COMP;
+
+#define SM2_SIGN_PRE_COMP_COUNT 32
+
+int sm2_fast_sign_pre_compute(SM2_SIGN_PRE_COMP pre_comp[32]);
+int sm2_fast_sign(const sm2_z256_t fast_private, SM2_SIGN_PRE_COMP *pre_comp,
 	const uint8_t dgst[32], SM2_SIGNATURE *sig);
 
 
@@ -159,12 +167,6 @@ int sm2_sign_fixlen(const SM2_KEY *key, const uint8_t dgst[32], size_t siglen, u
 int sm2_compute_z(uint8_t z[32], const SM2_Z256_POINT *pub, const char *id, size_t idlen);
 
 
-typedef struct {
-	sm2_z256_t k;
-	sm2_z256_t x1; // x1 (mod n)
-} SM2_SIGN_PRE_COMP;
-
-#define SM2_SIGN_PRE_COMP_COUNT 32
 
 typedef struct {
 	SM3_CTX sm3_ctx;
diff --git a/src/sm2_sign.c b/src/sm2_sign.c
index 15e90061..fbcbf721 100644
--- a/src/sm2_sign.c
+++ b/src/sm2_sign.c
@@ -101,35 +101,81 @@ int sm2_fast_sign_compute_key(const SM2_KEY *key, sm2_z256_t fast_private)
 	return 1;
 }
 
-// (x1, y1) = [k]G
-int sm2_fast_sign_pre_compute(sm2_z256_t k, sm2_z256_t x1_modn)
+// use Montgomery's Trick to inverse Z coordinates on multiple (x1, y1) = [k]G
+int sm2_fast_sign_pre_compute(SM2_SIGN_PRE_COMP pre_comp[32])
 {
-	SM2_Z256_POINT P;
+	SM2_Z256_POINT P[32];
+	sm2_z256_t f[32];
+	sm2_z256_t g[32];
+	int i;
 
-	// rand k in [1, n - 1]
-	do {
-		if (sm2_z256_rand_range(k, sm2_z256_order()) != 1) {
-			error_print();
-			return -1;
-		}
-	} while (sm2_z256_is_zero(k));
+	for (i = 0; i < 32; i++) {
 
-	// (x1, y1) = kG
-	sm2_z256_point_mul_generator(&P, k);
-	sm2_z256_point_get_xy(&P, x1_modn, NULL);
+		// rand k in [1, n - 1]
+		do {
+			if (sm2_z256_rand_range(pre_comp[i].k, sm2_z256_order()) != 1) {
+				error_print();
+				return -1;
+			}
+		} while (sm2_z256_is_zero(pre_comp[i].k));
 
-	// x1 mod n
-	if (sm2_z256_cmp(x1_modn, sm2_z256_order()) >= 0) {
-		sm2_z256_sub(x1_modn, x1_modn, sm2_z256_order());
+		// (x1, y1) = kG
+		sm2_z256_point_mul_generator(&P[i], pre_comp[i].k);
 	}
+
+	// f[0] = Z[0]
+	// f[1] = Z[0] * Z[1]
+	// ...
+	// f[31] = Z[0] * Z[1] * ... * Z[31]
+	sm2_z256_copy(f[0], P[0].Z);
+	for (i = 1; i < 32; i++) {
+		sm2_z256_modp_mont_mul(f[i], f[i - 1], P[i].Z);
+	}
+
+	// f[31]^-1 = (Z[0] * ... * Z[31])^-1
+	sm2_z256_modp_mont_inv(f[31], f[31]);
+
+	// g[31] = Z[31]
+	// g[30] = Z[30] * Z[31]
+	// ...
+	// g[1] = Z[1] * Z[2] * ... * Z[31]
+	//
+	sm2_z256_copy(g[31], P[31].Z);
+	for (i = 30; i >= 1; i--) {
+		sm2_z256_modp_mont_mul(g[i], g[i + 1], P[i].Z);
+	}
+
+	// Z[0]^-1 = g[1] * f[31]^-1
+	// Z[1]^-1 = g[2] * f[0] * f[31]^-1
+	// Z[2]^-1 = g[3] * f[1] * f[31]^-1
+	// ...
+	// Z[30]^-1 = g[31] * f[29] * f[31]^-1
+	// Z[31]^-1 = f[30] * f[31]^-1
+	sm2_z256_modp_mont_mul(P[0].Z, g[1], f[31]);
+	for (i = 1; i <= 30; i++) {
+		sm2_z256_modp_mont_mul(P[i].Z, g[i + 1], f[i - 1]);
+		sm2_z256_modp_mont_mul(P[i].Z, P[i].Z, f[31]);
+	}
+	sm2_z256_modp_mont_mul(P[31].Z, f[30], f[31]);
+
+	// x[i] = X[i] * Z[i]^-2 (mod n)
+	for (i = 0; i < 32; i++) {
+		sm2_z256_modp_mont_sqr(P[i].Z, P[i].Z);
+		sm2_z256_modp_mont_mul(pre_comp[i].x1_modn, P[i].X, P[i].Z);
+		sm2_z256_modp_from_mont(pre_comp[i].x1_modn, pre_comp[i].x1_modn);
+		if (sm2_z256_cmp(pre_comp[i].x1_modn, sm2_z256_order()) >= 0) {
+			sm2_z256_sub(pre_comp[i].x1_modn, pre_comp[i].x1_modn, sm2_z256_order());
+		}
+	}
+
 	return 1;
 }
 
+
 // s = (k - r * d)/(1 + d)
 //	= -r + (k + r)*(1 + d)^-1
 //	= -r + (k + r) * d'
-int sm2_fast_sign(const sm2_z256_t fast_private,
-	const sm2_z256_t k, const sm2_z256_t x1_modn,
+int sm2_fast_sign(const sm2_z256_t fast_private, SM2_SIGN_PRE_COMP *pre_comp,
 	const uint8_t dgst[32], SM2_SIGNATURE *sig)
 {
 	SM2_Z256_POINT R;
@@ -144,10 +190,10 @@ int sm2_fast_sign(const sm2_z256_t fast_private,
 	}
 
 	// r = e + x1 (mod n)
-	sm2_z256_modn_add(r, e, x1_modn);
+	sm2_z256_modn_add(r, e, pre_comp->x1_modn);
 
 	// s = (k + r) * d' - r
-	sm2_z256_modn_add(s, k, r);
+	sm2_z256_modn_add(s, pre_comp->k, r);
 	sm2_z256_modn_mul(s, s, fast_private);
 	sm2_z256_modn_sub(s, s, r);
 
@@ -412,11 +458,9 @@ int sm2_sign_init(SM2_SIGN_CTX *ctx, const SM2_KEY *key, const char *id, size_t
 	}
 	ctx->saved_sm3_ctx = ctx->sm3_ctx;
 
-	for (i = 0; i < SM2_SIGN_PRE_COMP_COUNT; i++) {
-		if (sm2_fast_sign_pre_compute(ctx->pre_comp[i].k, ctx->pre_comp[i].x1) != 1) {
-			error_print();
-			return -1;
-		}
+	if (sm2_fast_sign_pre_compute(ctx->pre_comp) != 1) {
+		error_print();
+		return -1;
 	}
 	ctx->num_pre_comp = SM2_SIGN_PRE_COMP_COUNT;
 
@@ -458,19 +502,15 @@ int sm2_sign_finish(SM2_SIGN_CTX *ctx, uint8_t *sig, size_t *siglen)
 	sm3_finish(&ctx->sm3_ctx, dgst);
 
 	if (ctx->num_pre_comp == 0) {
-		size_t i;
-		for (i = 0; i < SM2_SIGN_PRE_COMP_COUNT; i++) {
-			if (sm2_fast_sign_pre_compute(ctx->pre_comp[i].k, ctx->pre_comp[i].x1) != 1) {
-				error_print();
-				return -1;
-			}
+		if (sm2_fast_sign_pre_compute(ctx->pre_comp) != 1) {
+			error_print();
+			return -1;
 		}
 		ctx->num_pre_comp = SM2_SIGN_PRE_COMP_COUNT;
 	}
 
 	ctx->num_pre_comp--;
-	if (sm2_fast_sign(ctx->fast_sign_private,
-		ctx->pre_comp[ctx->num_pre_comp].k, ctx->pre_comp[ctx->num_pre_comp].x1,
+	if (sm2_fast_sign(ctx->fast_sign_private, &ctx->pre_comp[ctx->num_pre_comp],
 		dgst, &signature) != 1) {
 		error_print();
 		return -1;
diff --git a/tests/sm2_signtest.c b/tests/sm2_signtest.c
index f14523d4..3a1d163d 100644
--- a/tests/sm2_signtest.c
+++ b/tests/sm2_signtest.c
@@ -106,6 +106,7 @@ static int test_sm2_fast_sign(void)
 {
 	SM2_KEY sm2_key;
 	sm2_z256_t fast_private;
+	SM2_SIGN_PRE_COMP pre_comp[32];
 	uint8_t dgst[32];
 	SM2_SIGNATURE sig;
 	size_t i;
@@ -118,17 +119,15 @@ static int test_sm2_fast_sign(void)
 		error_print();
 		return -1;
 	}
+	if (sm2_fast_sign_pre_compute(pre_comp) != 1) {
+		error_print();
+		return -1;
+	}
 	rand_bytes(dgst, sizeof(dgst));
 
-	for (i = 0; i < TEST_COUNT; i++) {
-		sm2_z256_t k;
-		sm2_z256_t x1_modn;
+	for (i = 0; i < TEST_COUNT && i < sizeof(pre_comp)/sizeof(pre_comp[0]); i++) {
 
-		if (sm2_fast_sign_pre_compute(k, x1_modn) != 1) {
-			error_print();
-			return -1;
-		}
-		if (sm2_fast_sign(fast_private, k, x1_modn, dgst, &sig) != 1) {
+		if (sm2_fast_sign(fast_private, &pre_comp[i], dgst, &sig) != 1) {
 			error_print();
 			return -1;
 		}
@@ -143,45 +142,6 @@ static int test_sm2_fast_sign(void)
 	return 1;
 }
 
-static int test_sm2_do_sign_pre_compute(void)
-{
-	SM2_KEY sm2_key;
-	uint64_t d[4];
-
-	uint64_t k[4];
-	uint64_t x1[4];
-	uint8_t dgst[32];
-	SM2_SIGNATURE sig;
-
-
-	sm2_key_generate(&sm2_key);
-
-		const uint64_t *one = sm2_z256_one();
-		sm2_z256_copy(d, sm2_key.private_key);
-		sm2_z256_modn_add(d, d, one);
-		sm2_z256_modn_inv(d, d);
-
-	if (sm2_fast_sign_pre_compute(k, x1) != 1) {
-		error_print();
-		return -1;
-	}
-
-	rand_bytes(dgst, sizeof(dgst));
-
-	if (sm2_fast_sign(d, k, x1, dgst, &sig) != 1) {
-		error_print();
-		return -1;
-	}
-
-	if (sm2_do_verify(&sm2_key, dgst, &sig) != 1) {
-		error_print();
-		return -1;
-	}
-
-	printf("%s() ok\n", __FUNCTION__);
-	return 1;
-}
-
 static int test_sm2_sign(void)
 {
 	SM2_KEY sm2_key;
@@ -334,7 +294,6 @@ int main(void)
 {
 	if (test_sm2_signature() != 1) goto err;
 	if (test_sm2_do_sign() != 1) goto err;
-	if (test_sm2_do_sign_pre_compute() != 1) goto err;
 	if (test_sm2_fast_sign() != 1) goto err;
 	if (test_sm2_sign() != 1) goto err;
 	if (test_sm2_sign_ctx() != 1) goto err;