diff --git a/src/sm9_alg.c b/src/sm9_alg.c
index 2b0b7273..b7ab3ab3 100644
--- a/src/sm9_alg.c
+++ b/src/sm9_alg.c
@@ -1702,11 +1702,15 @@ void sm9_twist_point_mul_generator(sm9_twist_point_t *R, const sm9_bn_t k)
 
 void sm9_eval_g_tangent(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t *P, const sm9_point_t *Q)
 {
+	sm9_fp_t x;
+	sm9_fp_t y;
+	sm9_point_get_xy(Q, x, y);
+
 	const sm9_fp_t *XP = P->X;
 	const sm9_fp_t *YP = P->Y;
 	const sm9_fp_t *ZP = P->Z;
-	const uint64_t *xQ = Q->X;
-	const uint64_t *yQ = Q->Y;
+	const uint64_t *xQ = x;
+	const uint64_t *yQ = y;
 
 	sm9_fp_t *a0 = num[0][0];
 	sm9_fp_t *a1 = num[0][1];
@@ -1743,14 +1747,18 @@ void sm9_eval_g_tangent(sm9_fp12_t num, sm9_fp12_t den, const sm9_twist_point_t
 
 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)
 {
+	sm9_fp_t x;
+	sm9_fp_t y;
+	sm9_point_get_xy(Q, x, y);
+
 	const sm9_fp_t *XT = T->X;
 	const sm9_fp_t *YT = T->Y;
 	const sm9_fp_t *ZT = T->Z;
 	const sm9_fp_t *XP = P->X;
 	const sm9_fp_t *YP = P->Y;
 	const sm9_fp_t *ZP = P->Z;
-	const uint64_t *xQ = Q->X;
-	const uint64_t *yQ = Q->Y;
+	const uint64_t *xQ = x;
+	const uint64_t *yQ = y;
 
 	sm9_fp_t *a0 = num[0][0];
 	sm9_fp_t *a1 = num[0][1];
@@ -2209,33 +2217,39 @@ int sm9_point_to_uncompressed_octets(const sm9_point_t *P, uint8_t octets[65])
 	sm9_fp_t x;
 	sm9_fp_t y;
 	sm9_point_get_xy(P, x, y);
-	sm9_bn_to_bytes(x, octets);
-	sm9_bn_to_bytes(y, octets + 32);
+	octets[0] = 0x04;
+	sm9_bn_to_bytes(x, octets + 1);
+	sm9_bn_to_bytes(y, octets + 32 + 1);
 	return 1;
 }
 
 int sm9_point_from_uncompressed_octets(sm9_point_t *P, const uint8_t octets[65])
 {
-	sm9_bn_from_bytes(P->X, octets);
-	sm9_bn_from_bytes(P->Y, octets + 32);
+	assert(octets[0] == 0x04);
+	sm9_bn_from_bytes(P->X, octets + 1);
+	sm9_bn_from_bytes(P->Y, octets + 32 + 1);
 	sm9_fp_set_one(P->Z);
+	if (!sm9_point_is_on_curve(P)) return -1;
 	return 1;
 }
 
 int sm9_twist_point_to_uncompressed_octets(const sm9_twist_point_t *P, uint8_t octets[129])
 {
+	octets[0] = 0x04;
 	sm9_fp2_t x;
 	sm9_fp2_t y;
 	sm9_twist_point_get_xy(P, x, y);
-	sm9_fp2_to_bytes(x, octets);
-	sm9_fp2_to_bytes(y, octets + 32 * 2);
+	sm9_fp2_to_bytes(x, octets + 1);
+	sm9_fp2_to_bytes(y, octets + 32 * 2 + 1);
 	return 1;
 }
 
 int sm9_twist_point_from_uncompressed_octets(sm9_twist_point_t *P, const uint8_t octets[129])
 {
-	sm9_fp2_from_bytes(P->X, octets);
-	sm9_fp2_from_bytes(P->Y, octets + 32 * 2);
+	assert(octets[0] == 0x04);
+	sm9_fp2_from_bytes(P->X, octets + 1);
+	sm9_fp2_from_bytes(P->Y, octets + 32 * 2 + 1);
 	sm9_fp2_set_one(P->Z);
+	if (!sm9_twist_point_is_on_curve(P)) return -1;
 	return 1;
 }
diff --git a/src/sm9_lib.c b/src/sm9_lib.c
index 6eda85ad..5da96d38 100644
--- a/src/sm9_lib.c
+++ b/src/sm9_lib.c
@@ -139,8 +139,6 @@ int sm9_sign_finish(SM9_SIGN_CTX *ctx, const SM9_SIGN_KEY *key, uint8_t *sig, si
 	return 1;
 }
 
-#define hex_r	"00033C8616B06704813203DFD00965022ED15975C662337AED648835DC4B1CBE"
-
 int sm9_do_sign(const SM9_SIGN_KEY *key, const SM3_CTX *sm3_ctx, SM9_SIGNATURE *sig)
 {
 	sm9_fn_t r;
@@ -158,7 +156,6 @@ int sm9_do_sign(const SM9_SIGN_KEY *key, const SM3_CTX *sm3_ctx, SM9_SIGNATURE *
 	do {
 		// A2: rand r in [1, N-1]
 		sm9_fn_rand(r);
-		//sm9_bn_from_hex(r, hex_r);
 
 		// A3: w = g^r
 		sm9_fp12_pow(g, g, r);
@@ -289,7 +286,7 @@ int sm9_kem_encrypt(const SM9_ENC_MASTER_KEY *mpk, const char *id, size_t idlen,
 	SM3_KDF_CTX kdf_ctx;
 
 	// A1: Q = H1(ID||hid,N) * P1 + Ppube
-	sm9_hash1(r, id, idlen, SM9_HID_EXCH);
+	sm9_hash1(r, id, idlen, SM9_HID_ENC);
 	sm9_point_mul(C, r, SM9_P1);
 	sm9_point_add(C, C, &mpk->Ppube);
 
@@ -335,10 +332,11 @@ int sm9_kem_decrypt(const SM9_ENC_KEY *key, const char *id, size_t idlen, const
 	SM3_KDF_CTX kdf_ctx;
 
 	// B1: check C in G1
-	sm9_point_to_uncompressed_octets(C, cbuf + 1);
+	sm9_point_to_uncompressed_octets(C, cbuf);
 
 	// B2: w = e(C, de);
 	sm9_pairing(w, &key->de, C);
+	sm9_fp12_to_bytes(w, wbuf);
 
 	// B3: K = KDF(C || w || ID, klen)
 	sm3_kdf_init(&kdf_ctx, klen);