C.2 SM2橢圓曲線消息加解密

C.2 SM2橢圓曲線消息加解密

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橢圓曲線方程為：y^2 ^= x^3^ + ax + b

示例：*Fp *-256

素數p：FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFF

系數a：FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFC

系數b：28E9FA9E 9D9F5E34 4D5A9E4B CF6509A7 F39789F5 15AB8F92 DDBCBD41 4D940E93

基點G = (xG *, *yG)，其階記為n。

坐標xG：32C4AE2C 1F198119 5F990446 6A39C994 8FE30BBF F2660BE1 715A4589 334C74C7

坐標yG： BC3736A2 F4F6779C 59BDCEE3 6B692153 D0A9877C C62A4740 02DF32E5 2139F0A0

階n： FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF 7203DF6B 21C6052B 53BBF409 39D54123

待加密的消息M：encryption standard

消息M的16進制表示：656E63 72797074 696F6E20 7374616E 64617264

私鑰dB：3945208F 7B2144B1 3F36E38A C6D39F95 88939369 2860B51A 42FB81EF 4DF7C5B8

公鑰PB=(xB, yB)為：

坐標xB：09F9DF31 1E5421A1 50DD7D16 1E4BC5C6 72179FAD 1833FC07 6BB08FF3 56F35020

坐標yB：CCEA490C E26775A5 2DC6EA71 8CC1AA60 0AED05FB F35E084A 6632F607 2DA9AD13

加密各步驟中的有關值：

產生隨機數k：59276E27 D506861A 16680F3A D9C02DCC EF3CC1FA 3CDBE4CE 6D54B80D EAC1BC21

計算橢圓曲線點C1=[k]G=(x1, y1)：

坐標x1：04EBFC71 8E8D1798 62043226 8E77FEB6 415E2EDE 0E073C0F 4F640ECD 2E149A73

坐標y1：E858F9D8 1E5430A5 7B36DAAB 8F950A3C 64E6EE6A 63094D99 283AFF76 7E124DF0

在此C1選用未壓縮的表示形式，點轉換成字節串的形式為PC||x1||y1，其中PC為單一字節且PC=04，仍記為C1。

計算橢圓曲線點[k]PB=(x2,y2)：

坐標x2：335E18D7 51E51F04 0E27D468 138B7AB1 DC86AD7F 981D7D41 6222FD6A B3ED230D

坐標y2：AB743EBC FB22D64F 7B6AB791 F70658F2 5B48FA93 E54064FD BFBED3F0 BD847AC9

消息M的比特長度klen=152

計算t=KDF(x2||y2，klen)：44E60F DBF0BAE8 14376653 74BEF267 49046C9E

計算C~2 ~=M ⊕*t *：21886C A989CA9C 7D580873 07CA9309 2D651EFA

計算C3 ~=Hash(x2||M||y2~)：

x2||M|| y2：

335E18D7 51E51F04 0E27D468 138B7AB1 DC86AD7F 981D7D41 6222FD6A B3ED230D

656E6372 79707469 6F6E2073 74616E64 617264AB 743EBCFB 22D64F7B 6AB791F7

0658F25B 48FA93E 54064FDB FBED3F0B D847AC9

C3：59983C18 F809E262 923C53AE C295D303 83B54E39 D609D160 AFCB1908 D0BD8766

輸出密文M=C1||C3||C2：

04 04EBFC71 8E8D1798 62043226 8E77FEB6 415E2EDE 0E073C0F 4F640ECD 2E149A73

E858F9D8 1E5430A5 7B36DAAB 8F950A3C 64E6EE6A 63094D99 283AFF76 7E124DF0

59983C18 F809E262 923C53AE C295D303 83B54E39 D609D160 AFCB1908 D0BD8766

21886CA9 89CA9C7D 58087307 CA93092D 651EFA

解密各步驟中的有關值**：**

計算橢圓曲線點[dB]C1=(x2 ,y2)：

坐標x2：335E18D7 51E51F040 E27D4681 38B7AB1D C86AD7F9 81D7D416 222FD6AB 3ED230D

坐標y2：AB743EBC FB22D64F 7B6AB791 F70658F2 5B48FA93 E54064FD BFBED3F0 BD847AC9

計算t=KDF(x2||y2，klen)：44E60F DBF0BAE8 14376653 74BEF267 49046C9E

計算M’=C2⊕*t *：656E63 72797074 696F6E20 7374616E 64617264

計算u= Hash(x2||M’||y2 )：

59983C18 F809E262 923C53AE C295D303 83B54E39 D609D160 AFCB1908 D0BD8766

明文M’： 656E63 72797074 696F6E20 7374616E 64617264，即為：encryption standard