diff --git a/include/gmssl/sm9_z256.h b/include/gmssl/sm9_z256.h
index 4490984b8..1e7a640c4 100644
--- a/include/gmssl/sm9_z256.h
+++ b/include/gmssl/sm9_z256.h
@@ -39,6 +39,7 @@ void sm9_z256_copy_conditional(sm9_z256_t dst, const sm9_z256_t src, uint64_t mo
 void sm9_z256_set_zero(sm9_z256_t r);
 int  sm9_z256_cmp(const sm9_z256_t a, const sm9_z256_t b);
 void sm9_z256_mul(uint64_t r[8], const sm9_z256_t a, const sm9_z256_t b);
+void sm9_z256_mul_low(uint64_t r[4], const sm9_z256_t a, const sm9_z256_t b);
 int  sm9_z256_from_hex(sm9_z256_t r, const char *hex);
 void sm9_z256_to_hex(const sm9_z256_t r, char hex[64]);
 int  sm9_z256_equ_hex(const sm9_z256_t a, const char *hex);
diff --git a/src/sm9_z256_alg.c b/src/sm9_z256_alg.c
index 5fed72986..1059eff67 100644
--- a/src/sm9_z256_alg.c
+++ b/src/sm9_z256_alg.c
@@ -268,6 +268,17 @@ uint64_t sm9_z256_sub(sm9_z256_t r, const sm9_z256_t a, const sm9_z256_t b)
 	return c;
 }
 
+#ifndef ENABLE_SM9_Z256_ARMV8
+void sm9_z256_mul_low(uint64_t r[4], const sm9_z256_t a, const sm9_z256_t b)
+{
+	uint64_t t[8];
+	sm9_z256_mul(t, a, b);
+	r[0] = t[0];
+	r[1] = t[1];
+	r[2] = t[2];
+	r[3] = t[3];
+}
+
 void sm9_z256_mul(uint64_t r[8], const sm9_z256_t a, const sm9_z256_t b)
 {
 	uint64_t a_[8];
@@ -297,6 +308,7 @@ void sm9_z256_mul(uint64_t r[8], const sm9_z256_t a, const sm9_z256_t b)
 		r[i] = (s[2 * i + 1] << 32) | s[2 * i];
 	}
 }
+#endif
 
 uint64_t sm9_z512_add(uint64_t r[8], const uint64_t a[8], const uint64_t b[8])
 {
@@ -380,7 +392,7 @@ void sm9_z256_to_hex(const sm9_z256_t r, char hex[64])
 {
 	int i;
 	for (i = 3; i >= 0; i--) {
-		(void)sprintf(hex + 16*(3-i), "%016lx", r[i]);
+		(void)sprintf(hex + 16*(3-i), "%016llx", r[i]);
 	}
 }
 
@@ -521,8 +533,47 @@ void sm9_u64_mul_add(uint64_t *w0, uint64_t *w1,
 	*w1 = r[1];
 }
 
-#ifndef ENABLE_SM9_Z256_ARMV8
-void sm9_z256_fp_mont_mul(sm9_z256_t r, const sm9_z256_t a, const sm9_z256_t b)
+													
+// p = b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457d
+// p' = -p^(-1) mod 2^256 = afd2bac5558a13b3966a4b291522b137181ae39613c8dbaf892bc42c2f2ee42b
+// sage: -(IntegerModRing(2^256)(p))^-1
+const uint64_t SM9_Z256_P_PRIME[4] = {
+	0x892bc42c2f2ee42b, 0x181ae39613c8dbaf, 0x966a4b291522b137, 0xafd2bac5558a13b3,
+};
+
+
+// z = a*b
+// c = (z + (z * p' mod 2^256) * p)/2^256
+void sm9_z256_fp_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
+{
+	uint64_t z[8];
+	uint64_t t[8];
+	uint64_t c;
+
+	// z = a * b
+	sm9_z256_mul(z, a, b);
+
+	// t = low(z) * p'
+	sm9_z256_mul_low(t, z, SM9_Z256_P_PRIME);
+
+	// t = low(t) * p
+	sm9_z256_mul(t, t, SM9_Z256_P);
+
+	// z = z + t
+	c = sm9_z512_add(z, z, t);
+
+	// r = high(r)
+	sm9_z256_copy(r, z + 4);
+
+	if (c) {
+		sm9_z256_add(r, r, SM9_Z256_MODP_MONT_ONE);
+
+	} else if (sm9_z256_cmp(r, SM9_Z256_P) >= 0) {
+		(void)sm9_z256_sub(r, r, SM9_Z256_P);
+	}
+}
+
+void sm9_z256_fp_mont_mul_2way(sm9_z256_t r, const sm9_z256_t a, const sm9_z256_t b)
 {
 	sm9_z256_t d = {0}, e = {0};
 	uint64_t q, t0, t1, p0, p1, tmp;
@@ -562,7 +613,6 @@ void sm9_z256_fp_mont_sqr(sm9_z256_t r, const sm9_z256_t a)
 {
 	sm9_z256_fp_mont_mul(r, a, a);
 }
-#endif
 
 void sm9_z256_fp_pow(sm9_z256_t r, const sm9_z256_t a, const sm9_z256_t e)
 {
@@ -633,7 +683,7 @@ void sm9_z256_fp_to_hex(const sm9_z256_t r, char hex[64])
 	sm9_z256_fp_from_mont(t, r);
 	int i;
 	for (i = 3; i >= 0; i--) {
-		(void)sprintf(hex + 16*(3-i), "%016lx", t[i]);
+		(void)sprintf(hex + 16*(3-i), "%016llx", t[i]);
 	}
 }