diff --git a/include/gmssl/sm9.h b/include/gmssl/sm9.h
index c4a3fd2b..7021b186 100644
--- a/include/gmssl/sm9.h
+++ b/include/gmssl/sm9.h
@@ -1,4 +1,4 @@
-/*
+/*
  * Copyright (c) 2016 - 2021 The GmSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
@@ -53,42 +53,220 @@
 extern "C" {
 #endif
 
-
-// set the same value as sm2
-#define SM9_MAX_ID_BITS		65535
-#define SM9_MAX_ID_SIZE		(SM9_MAX_ID_BITS/8)
+typedef uint64_t sm9_bn_t[8];
+typedef sm9_bn_t sm9_fp_t;
+typedef sm9_bn_t sm9_fn_t;
+typedef uint64_t sm9_barrett_bn_t[9];
+typedef sm9_fp_t sm9_fp2_t[2];
+typedef sm9_fp2_t sm9_fp4_t[2];
+typedef sm9_fp4_t sm9_fp12_t[3];
 
 typedef struct {
-	uint8_t x[32];
-	uint8_t y[32];
-} SM9_POINT;
+	sm9_fp_t X;
+	sm9_fp_t Y;
+	sm9_fp_t Z;
+} sm9_point_t;
 
 typedef struct {
-	uint8_t x[64];
-	uint8_t y[64];
-} SM9_TWIST_POINT;
-
-typedef struct {
-	uint8_t ks[32];
-	SM9_TWIST_POINT Ppubs; // Ppubs = ks * P2
-} SM9_SIGN_MASTER_KEY;
-
-typedef struct {
-	SM9_POINT ds;
-} SM9_SIGN_KEY;
-
-typedef struct {
-	uint8_t h[32];
-	SM9_TWIST_POINT S;
-} SM9_SIGNATURE;
-
-int sm9_sign_setup(SM9_SIGN_MASTER_KEY *msk);
-int sm9_sign_keygen(SM9_SIGN_MASTER_KEY *msk, const char *id, size_t idlen, SM9_POINT *ds);
-
-int sm9_do_sign(SM9_SIGN_KEY *key, const uint8_t dgst[32], SM9_SIGNATURE *sig);
-int sm9_do_verify(SM9_SIGN_KEY *key, const uint8_t dgst[32], const SM9_SIGNATURE *sig);
+	sm9_fp2_t X;
+	sm9_fp2_t Y;
+	sm9_fp2_t Z;
+} sm9_twist_point_t;
 
 
+#define sm9_bn_init(r)		memset((r),0,sizeof(sm9_bn_t))
+#define sm9_bn_clean(r)		memset((r),0,sizeof(sm9_bn_t))
+#define sm9_bn_set_zero(r)	memset((r),0,sizeof(sm9_bn_t))
+#define sm9_bn_set_one(r)	memcpy((r),&SM9_ONE,sizeof(sm9_bn_t))
+#define sm9_bn_copy(r,a)	memcpy((r),(a),sizeof(sm9_bn_t))
+#define sm9_bn_is_zero(a)	(memcmp((a),&SM9_ZERO, sizeof(sm9_bn_t)) == 0)
+#define sm9_bn_is_one(a)	(memcmp((a),&SM9_ONE, sizeof(sm9_bn_t)) == 0)
+
+static void sm9_bn_to_bytes(const sm9_bn_t a, uint8_t out[32]);
+static void sm9_bn_from_bytes(sm9_bn_t r, const uint8_t in[32]);
+static int sm9_bn_from_hex(sm9_bn_t r, const char hex[65]);
+static void sm9_bn_to_hex(const sm9_bn_t a, char hex[65]);
+static void sm9_print_bn(const char *prefix, const sm9_bn_t a);
+static void sm9_bn_to_bits(const sm9_bn_t a, char bits[256]);
+
+static int sm9_bn_cmp(const sm9_bn_t a, const sm9_bn_t b);
+static int sm9_bn_equ_hex(const sm9_bn_t a, const char *hex);
+static void sm9_bn_set_word(sm9_bn_t r, uint32_t a);
+static void sm9_bn_add(sm9_bn_t r, const sm9_bn_t a, const sm9_bn_t b);
+static void sm9_bn_sub(sm9_bn_t ret, const sm9_bn_t a, const sm9_bn_t b);
+static void sm9_bn_rand_range(sm9_bn_t r, const sm9_bn_t range);
+
+#define sm9_fp_init(a)		sm9_bn_init(a)
+#define sm9_fp_clean(a)		sm9_bn_clean(a)
+#define sm9_fp_is_zero(a)	sm9_bn_is_zero(a)
+#define sm9_fp_is_one(a)	sm9_bn_is_one(a)
+#define sm9_fp_set_zero(a)	sm9_bn_set_zero(a)
+#define sm9_fp_set_one(a)	sm9_bn_set_one(a)
+#define sm9_fp_from_hex(a,s) 	sm9_bn_from_hex((a),(s))
+#define sm9_fp_to_hex(a,s)	sm9_bn_to_hex((a),(s))
+#define sm9_fp_copy(r,a)	sm9_bn_copy((r),(a))
+
+static int sm9_fp_equ(const sm9_fp_t a, const sm9_fp_t b);
+static void sm9_fp_add(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b);
+static void sm9_fp_sub(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b);
+static void sm9_fp_dbl(sm9_fp_t r, const sm9_fp_t a);
+static void sm9_fp_tri(sm9_fp_t r, const sm9_fp_t a);
+static void sm9_fp_div2(sm9_fp_t r, const sm9_fp_t a);
+static void sm9_fp_neg(sm9_fp_t r, const sm9_fp_t a);
+static void sm9_fp_mul(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b);
+static void sm9_fp_sqr(sm9_fp_t r, const sm9_fp_t a);
+static void sm9_fp_pow(sm9_fp_t r, const sm9_fp_t a, const sm9_bn_t e);
+static void sm9_fp_inv(sm9_fp_t r, const sm9_fp_t a);
+
+static int sm9_barrett_bn_cmp(const sm9_barrett_bn_t a, const sm9_barrett_bn_t b);
+static void sm9_barrett_bn_add(sm9_barrett_bn_t r, const sm9_barrett_bn_t a, const sm9_barrett_bn_t b);
+static void sm9_barrett_bn_sub(sm9_barrett_bn_t ret, const sm9_barrett_bn_t a, const sm9_barrett_bn_t b);
+
+#define sm9_fp2_init(a)		memset((a), 0, sizeof(sm9_fp2_t))
+#define sm9_fp2_clean(a)	memset((a), 0, sizeof(sm9_fp2_t))
+#define sm9_fp2_is_zero(a)	(memcmp((a), &SM9_FP2_ZERO, sizeof(sm9_fp2_t)) == 0)
+#define sm9_fp2_is_one(a)	(memcmp((a), &SM9_FP2_ONE, sizeof(sm9_fp2_t)) == 0)
+#define sm9_fp2_copy(r,a)	memcpy((r), (a), sizeof(sm9_fp2_t))
+#define sm9_fp2_equ(a,b)	(memcmp((a),(b),sizeof(sm9_fp2_t)) == 0)
+
+static void sm9_fp2_from_hex(sm9_fp2_t r, const char hex[65 * 2]);
+static void sm9_fp2_to_hex(const sm9_fp2_t a, char hex[65 * 2]);
+static void sm9_fp2_print(const char *prefix, const sm9_fp2_t a);
+#define sm9_fp2_set_zero(a)	memset((a), 0, sizeof(sm9_fp2_t))
+#define sm9_fp2_set_one(a)	memcpy((a), &SM9_FP2_ONE, sizeof(sm9_fp2_t))
+static void sm9_fp2_set_fp(sm9_fp2_t r, const sm9_fp_t a);
+#define sm9_fp2_set_u(a)	memcpy((a), &SM9_FP2_U, sizeof(sm9_fp2_t))
+static void sm9_fp2_set(sm9_fp2_t r, const sm9_fp_t a0, const sm9_fp_t a1);
+
+static void sm9_fp2_add(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b);
+static void sm9_fp2_dbl(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_tri(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_sub(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b);
+static void sm9_fp2_neg(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_mul(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b);
+static void sm9_fp2_mul_u(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b);
+static void sm9_fp2_mul_fp(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp_t k);
+static void sm9_fp2_sqr(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_sqr_u(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_inv(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_div(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b);
+static void sm9_fp2_div2(sm9_fp2_t r, const sm9_fp2_t a);
+
+#define sm9_fp4_init(r)	memcpy((r), &SM9_FP4_ZERO, sizeof(sm9_fp4_t))
+#define sm9_fp4_clean(r)	memcpy((r), &SM9_FP4_ZERO, sizeof(sm9_fp4_t))
+#define sm9_fp4_set_zero(r)	memcpy((r), &SM9_FP4_ZERO, sizeof(sm9_fp4_t))
+#define sm9_fp4_set_one(r)	memcpy((r), &SM9_FP4_ONE, sizeof(sm9_fp4_t))
+#define sm9_fp4_is_zero(a)	(memcmp((a), &SM9_FP4_ZERO, sizeof(sm9_fp4_t)) == 0)
+#define sm9_fp4_is_one(a)	(memcmp((a), &SM9_FP4_ONE, sizeof(sm9_fp4_t)) == 0)
+#define sm9_fp4_equ(a,b)	(memcmp((a), (b), sizeof(sm9_fp4_t)) == 0)
+#define sm9_fp4_copy(r,a)	memcpy((r), (a), sizeof(sm9_fp4_t))
+
+static void sm9_fp4_from_hex(sm9_fp4_t r, const char hex[65 * 4]);
+static void sm9_fp4_to_hex(const sm9_fp4_t a, char hex[65 * 4]);
+static void sm9_fp4_set_fp(sm9_fp4_t r, const sm9_fp_t a);
+static void sm9_fp4_set_fp2(sm9_fp4_t r, const sm9_fp2_t a);
+static void sm9_fp4_set(sm9_fp4_t r, const sm9_fp2_t a0, const sm9_fp2_t a1);
+static void sm9_fp4_set_u(sm9_fp4_t r);
+static void sm9_fp4_set_v(sm9_fp4_t r);
+
+static void sm9_fp4_add(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b);
+static void sm9_fp4_dbl(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_sub(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b);
+static void sm9_fp4_neg(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_mul(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b);
+static void sm9_fp4_mul_fp(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp_t k);
+static void sm9_fp4_mul_fp2(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp2_t b0);
+static void sm9_fp4_mul_v(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b);
+static void sm9_fp4_sqr(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_sqr_v(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_inv(sm9_fp4_t r, const sm9_fp4_t a);
+
+#define sm9_fp12_init(r)	memset((r), 0, sizeof(sm9_fp12_t))
+#define sm9_fp12_clean(r)	memset((r), 0, sizeof(sm9_fp12_t))
+#define sm9_fp12_set_zero(r)	memset((r), 0, sizeof(sm9_fp12_t))
+#define sm9_fp12_copy(r, a)	memcpy((r), (a), sizeof(sm9_fp12_t))
+
+static void sm9_fp12_set_one(sm9_fp12_t r);
+static int sm9_fp12_is_one(const sm9_fp12_t a);
+static int sm9_fp12_is_zero(const sm9_fp12_t a);
+static void sm9_fp12_from_hex(sm9_fp12_t r, const char hex[65 * 12]);
+static void sm9_fp12_to_hex(const sm9_fp12_t a, char hex[65 * 12]);
+static void sm9_fp12_print(const char *prefix, const sm9_fp12_t a);
+static void sm9_fp12_set(sm9_fp12_t r, const sm9_fp4_t a0, const sm9_fp4_t a1, const sm9_fp4_t a2);
+static void sm9_fp12_set_fp(sm9_fp12_t r, const sm9_fp_t a);
+static void sm9_fp12_set_fp2(sm9_fp12_t r, const sm9_fp2_t a);
+static void sm9_fp12_set_fp4(sm9_fp12_t r, const sm9_fp4_t a);
+static void sm9_fp12_set_u(sm9_fp12_t r);
+static void sm9_fp12_set_v(sm9_fp12_t r);
+static void sm9_fp12_set_w(sm9_fp12_t r);
+static void sm9_fp12_set_w_sqr(sm9_fp12_t r);
+
+static int sm9_fp12_equ(const sm9_fp12_t a, const sm9_fp12_t b);
+static void sm9_fp12_add(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b);
+static void sm9_fp12_dbl(sm9_fp12_t r, const sm9_fp12_t a);
+static void sm9_fp12_tri(sm9_fp12_t r, const sm9_fp12_t a);
+static void sm9_fp12_sub(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b);
+static void sm9_fp12_neg(sm9_fp12_t r, const sm9_fp12_t a);
+static void sm9_fp12_mul(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b);
+static void sm9_fp12_sqr(sm9_fp12_t r, const sm9_fp12_t a);
+static void sm9_fp12_inv(sm9_fp12_t r, const sm9_fp12_t a);
+static void sm9_fp12_pow(sm9_fp12_t r, const sm9_fp12_t a, const sm9_bn_t k);
+
+static void sm9_fp2_conjugate(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp2_frobenius(sm9_fp2_t r, const sm9_fp2_t a);
+static void sm9_fp4_frobenius(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_conjugate(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_frobenius2(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp4_frobenius3(sm9_fp4_t r, const sm9_fp4_t a);
+static void sm9_fp12_frobenius(sm9_fp12_t r, const sm9_fp12_t x);
+static void sm9_fp12_frobenius2(sm9_fp12_t r, const sm9_fp12_t x);
+static void sm9_fp12_frobenius3(sm9_fp12_t r, const sm9_fp12_t x);
+static void sm9_fp12_frobenius6(sm9_fp12_t r, const sm9_fp12_t x);
+
+static void sm9_point_init(sm9_point_t *R);
+static void sm9_point_from_hex(sm9_point_t *R, const char hex[65 * 2]);
+#define sm9_point_copy(R, P)	memcpy((R), (P), sizeof(sm9_point_t))
+static int sm9_point_is_at_infinity(const sm9_point_t *P);
+static void sm9_point_set_infinity(sm9_point_t *R);
+static void sm9_point_get_xy(const sm9_point_t *P, sm9_fp_t x, sm9_fp_t y);
+
+static int sm9_point_equ(const sm9_point_t *P, const sm9_point_t *Q);
+static int sm9_point_is_on_curve(const sm9_point_t *P);
+static void sm9_point_dbl(sm9_point_t *R, const sm9_point_t *P);
+static void sm9_point_add(sm9_point_t *R, const sm9_point_t *P, const sm9_point_t *Q);
+static void sm9_point_neg(sm9_point_t *R, const sm9_point_t *P);
+static void sm9_point_sub(sm9_point_t *R, const sm9_point_t *P, const sm9_point_t *Q);
+static void sm9_point_mul(sm9_point_t *R, const sm9_bn_t k, const sm9_point_t *P);
+static void sm9_point_mul_generator(sm9_point_t *R, const sm9_bn_t k);
+
+static void sm9_twist_point_from_hex(sm9_twist_point_t *R, const char hex[65 * 4]);
+#define sm9_twist_point_copy(R, P)	memcpy((R), (P), sizeof(sm9_twist_point_t))
+static int sm9_twist_point_is_at_infinity(const sm9_twist_point_t *P);
+static void sm9_twist_point_set_infinity(sm9_twist_point_t *R);
+static void sm9_twist_point_get_xy(const sm9_twist_point_t *P, sm9_fp2_t x, sm9_fp2_t y);
+
+static int sm9_twist_point_equ(const sm9_twist_point_t *P, const sm9_twist_point_t *Q);
+static int sm9_twist_point_is_on_curve(const sm9_twist_point_t *P);
+static void sm9_twist_point_neg(sm9_twist_point_t *R, const sm9_twist_point_t *P);
+static void sm9_twist_point_dbl(sm9_twist_point_t *R, const sm9_twist_point_t *P);
+static void sm9_twist_point_add(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q);
+static void sm9_twist_point_sub(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q);
+static void sm9_twist_point_add_full(sm9_twist_point_t *R, const sm9_twist_point_t *P, const sm9_twist_point_t *Q);
+static void sm9_twist_point_mul(sm9_twist_point_t *R, const sm9_bn_t k, const sm9_twist_point_t *P);
+static void sm9_twist_point_mul_G(sm9_twist_point_t *R, const sm9_bn_t k);
+
+static void sm9_eval_g_tangent(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t *P, const sm9_point_t *Q);
+static void sm9_eval_g_line(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t *T, const sm9_twist_point_t *P, const sm9_point_t *Q);
+
+static void sm9_twist_point_pi1(sm9_twist_point_t *R, const sm9_twist_point_t *P);
+static void sm9_twist_point_pi2(sm9_twist_point_t *R, const sm9_twist_point_t *P);
+static void sm9_twist_point_neg_pi2(sm9_twist_point_t *R, const sm9_twist_point_t *P);
+
+static void sm9_final_exponent_hard_part(sm9_fp12_t r, const sm9_fp12_t f);
+static void sm9_final_exponent(sm9_fp12_t r, const sm9_fp12_t f);
+static void sm9_pairing(sm9_fp12_t r, const sm9_twist_point_t *Q, const sm9_point_t *P);
+
+void sm9_pairing_test();
 
 #  ifdef  __cplusplus
 }