Network Working Group
Request for Comments: 4269
Obsoletes: 4009
Category: Informational

H.J. Lee
S.J. Lee
J.H. Yoon
D.H. Cheon
J.I. Lee
KISA
December 2005

The SEED Encryption Algorithm

Status of This Memo

This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited.

Copyright Notice

Abstract

This document describes the SEED encryption algorithm, which has been adopted by most of the security systems in the Republic of Korea. Included are a description of the encryption and the key scheduling algorithm (Section 2), the S-boxes (Appendix A), and a set of test vectors (Appendix B).

This document obsoletes RFC 4009.

1. Introduction

1.1. Changes from RFC 4009

This specification obsoletes RFC 4009, because RFC 4009 had ambiguous function and SS-boxes definitions cryptographically. Thus, some definitions have been changed, and for better understanding, the SEED pseudo codes have been modified. This update is to provide clarity and facilitate the development of interoperable implementations. The SEED algorithm itself has not been changed.

This specification updates RFC 4009 in the following areas:

Pseudo code changes. The pseudo code in Section 2 of RFC 4009 is insufficient for the explanation of the structure of SEED. Thus, detailed pseudo code is introduced.

Some corrections of errata, which are the definitions of R1', Z, X, and SS-boxes.

1.2. SEED Overview

SEED is a 128-bit symmetric key block cipher that has been developed by KISA (Korea Information Security Agency) since 1998. SEED is a national standard encryption algorithm in the Republic of Korea [TTASSEED] and is designed to use the S-boxes and permutations that balance with the current computing technology. It has the Feistel structure with 16-round and is strong against DC (Differential Cryptanalysis), LC (Linear Cryptanalysis), and related key attacks, balanced with security/efficiency trade-off.

The features of SEED are outlined as follows:

- The Feistel structure with 16-round
- 128-bit input/output data block size
- 128-bit key length
- A round function that is strong against known attacks
- Two 8x8 S-boxes
- Mixed operations of XOR and modular addition

SEED has been widely used in the Republic of Korea for confidential services such as electronic commerce; e.g., financial services provided in wired and wireless communication.

1.3. Notation

The following notation is used in the description of the SEED encryption algorithm:

      &             bitwise AND
      ^             bitwise exclusive OR
      +             addition in modular 2**32
      -             subtraction in modular 2**32
      ||            concatenation
      << n          left circular rotation by n bits
      >> n          right circular rotation by n bits
      0x            hexadecimal representation

2. The Structure of SEED

The input/output block size of SEED is 128 bits, and the key length is also 128 bits. SEED has the 16-round Feistel structure. A 128-bit input is divided into two 64-bit blocks (L, R), and the right 64-bit block is an input to the round function F, with a 64-bit subkey Ki generated from the key schedule. L is the most significant 64 bits of 128-bit input, and R is the least significant 64 bits.

A pseudo code for the structure of SEED is as follows:

Input : (L, R)

        for i = 1 to 15
        
            T = R;
            R = L ^ F(Ki, R);
            L = T;
        
        L = L ^ F(K16, R), R=R

Output : (L, R)

Where T is a temporary.

2.1. The Round Function F

SEED uses two 8x8 S-boxes, permutations, rotations, and basic modular operations such as exclusive OR (XOR) and additions to provide strong security, high speed, and simplicity in its implementation.

A 64-bit input block of the round function F is divided into two 32-bit blocks (R0, R1) and wrapped with 4 phases:

- A mixing phase of two 32-bit subkey blocks (Ki0, Ki1)
- 3 layers of function G (see Section 2.2), with additions for

mixing two 32-bit blocks

Where R0 is the most significant 32 bits of R, and R1 is the least significant 32 bits.

The outputs (R0', R1') of function F are as follows:

   R0' = G[ G[ G[(R0 ^ Ki0) ^ (R1 ^ Ki1)] + (R0 ^ Ki0)] + G[(R0 ^ Ki0) ^
         (R1 ^ Ki1)]] + G[ G[(R0 ^ Ki0) ^ (R1 ^ Ki1)] + (R0 ^ Ki0)]
   
   R1' = G[ G[ G[(R0 ^ Ki0) ^ (R1 ^ Ki1)] + (R0 ^ Ki0)] + G[(R0 ^ Ki0) ^
         (R1 ^ Ki1)]]

2.2. The Function G

The function G has two layers: a layer of two 8x8 S-boxes and a layer of block permutation of sixteen 8-bit sub-blocks. The outputs Z (= Z3 || Z2 || Z1 || Z0) of the function G with four 8-bit inputs X (= X3 || X2 || X1 || X0) are as follows:

     Z0 = {S0(X0) & m0} ^ {S1(X1) & m1} ^ {S0(X2) & m2} ^ {S1(X3) & m3}
     Z1 = {S0(X0) & m1} ^ {S1(X1) & m2} ^ {S0(X2) & m3} ^ {S1(X3) & m0}
     Z2 = {S0(X0) & m2} ^ {S1(X1) & m3} ^ {S0(X2) & m0} ^ {S1(X3) & m1}
     Z3 = {S0(X0) & m3} ^ {S1(X1) & m0} ^ {S0(X2) & m1} ^ {S1(X3) & m2}

where m0 = 0xFC, m1 = 0xF3, m2 = 0xCF, and m3 = 0x3F.

To increase the efficiency of G function, four extended S-boxes "SS-box" (see Appendix A.2) are defined as follows:

   SS0(X0)= {S0(X0)& m3} || {S0(X0)& m2} || {S0(X0)& m1} || {S0(X0)& m0}
   SS1(X1)= {S1(X1)& m0} || {S1(X1)& m3} || {S1(X1)& m2} || {S1(X1)& m1}
   SS2(X2)= {S0(X2)& m1} || {S0(X2)& m0} || {S0(X2)& m3} || {S0(X2)& m2}
   SS3(X3)= {S1(X3)& m2} || {S1(X3)& m1} || {S1(X3)& m0} || {S1(X3)& m3}

New G function, Z, can be defined as follows:

     Z = SS0(X0) ^ SS1(X1) ^ SS2(X2) ^ SS3(X3)

This new G function is faster than the original G function but takes more memory to store four SS-boxes.

2.3. Key Schedule

The key schedule generates each round's subkeys. It uses the function G, addition in modular 2**32, subtraction in modular 2**32, and (left/right) circular rotation. A 128-bit input key is divided into four 32-bit blocks (Key0, Key1, Key2, Key3). The two 32-bit subkeys of the ith round, Ki0 and Ki1, are generated as follows:

      - Type 1 : Odd round
      
        Ki0 = G(Key0 + Key2 - KCi)
        Ki1 = G(Key1 - Key3 + KCi)
        Key0 || Key1 = (Key0 || Key1) >> 8
      
      - Type 2 : Even round
        Ki0 = G(Key0 + Key2 - KCi)
        Ki1 = G(Key1 - Key3 + KCi)
        Key2 || Key3 = (Key2 || Key3) << 8

Where Ki0 is the most significant 32 bits of Ki, and Ki1 is the least significant 32 bits of Ki (where i=0,...,3).

The following table shows constants used in KCi:

          i    |    Value          i    |    Value
         ============================================
         KC1   |  0x9E3779B9      KC2   |  0x3C6EF373
         KC3   |  0x78DDE6E6      KC4   |  0xF1BBCDCC
         KC5   |  0xE3779B99      KC6   |  0xC6EF3733
         KC7   |  0x8DDE6E67      KC8   |  0x1BBCDCCF
         KC9   |  0x3779B99E      KC10  |  0x6EF3733C
         KC11  |  0xDDE6E678      KC12  |  0xBBCDCCF1
         KC13  |  0x779B99E3      KC14  |  0xEF3733C6
         KC15  |  0xDE6E678D      KC16  |  0xBCDCCF1B

A pseudo code for the key schedule is as follows:

         Input : (Key0, Key1, Key2, Key3)
         
         for i = 1 to 16
           Ki0 = G(Key0 + Key2 - KCi)
           Ki1 = G(Key1 - Key3 + KCi)
           if i is odd
                  Key0 || Key1 = (Key0 || Key1) >> 8
           else
                  Key2 || Key3 = (Key2 || Key3) << 8
         
         Output : (Keyi0, Keyi1), i=1 to 16

2.4. Decryption Procedure

Decryption procedure is the reverse step of the encryption procedure. It can be implemented by using the encryption algorithm with reverse order of the round subkeys.

2.5. SEED Object Identifiers

For those who may be using SEED in algorithm negotiation within a protocol, or in any other context that may require the use of Object Identifiers (OIDs), the following three OIDs have been defined.

     algorithm OBJECT IDENTIFIER ::= { iso(1) member-body(2) korea(410)
     
       kisa(200004) algorithm(1) }
     
     id-seedCBC OBJECT IDENTIFIER ::= { algorithm seedCBC(4) }
     
     seedCBCParameter ::= OCTET STRING (SIZE(16))
     -- 128-bit Initialization Vector

The id-seedCBC OID is used when the Cipher Block Chaining (CBC) mode of operation based on the SEED block cipher is provided.

     id-seedMAC OBJECT IDENTIFIER ::= { algorithm seedMAC(7) }
     
     seedMACParameter ::= INTEGER  -- MAC length, in bits

The id-seedMAC OID is used when the message authentication code (MAC) algorithm based on the SEED block cipher is provided.

pbeWithSHA1AndSEED-CBC OBJECT IDENTIFIER ::=

{ algorithm seedCBCwithSHA1(15) }

     PBEParameters ::= SEQUENCE { salt          OCTET STRING, iteration
       INTEGER }  -- Total number of hash iterations

This OID is used when a password-based encryption in CBC mode based on SHA-1 and the SEED block cipher is provided. The details of the Password-Based Encryption (PBE) computation are well described in Section 6.1 of [RFC2898].

3. Security Considerations

No security problem has been found on SEED. See [ISOSEED] and [CRYPTREC].

4. References

4.1. Normative References

   [TTASSEED] Telecommunications Technology Association(TTA),"128-bit
              Symmetric Block Cipher (SEED)", TTAS.KO-12.0004,
              September, 1998 (In Korean)
              http://www.tta.or.kr/English/new/main/index.htm
   
   [RFC2898]  Kaliski, B., "PKCS #5: Password-Based Cryptography
              Specification Version 2.0", RFC 2898, September 2000.

4.2. Informative References

   [ISOSEED]  ISO/IEC, ISO/IEC JTC1/SC 27 N 256r1, "National Body
              contributions on NP 18033 Encryption algorithms in
              response to document SC 27 N 2563", October, 2000
   
   [CRYPTREC] Information-technology Promotion Agency (IPA), Japan,
              CRYPTREC. "SEED Evaluation Report", February, 2002
              http://www.kisa.or.kr/seed/data/Document_pdf/
              SEED_Evaluation_Report_by_CRYPTREC.pdf

5. Acknowledgements

Alfred Hoenes (ah@tr-sys.de) has contributed significantly to work on the definitions of R1', Z, X, and SS-boxes. Thanks for his contribution to this document.

6. Authors' Addresses

   Hyangjin Lee
   Korea Information Security Agency
   78, Garak-Dong, Songpa-Gu, Seoul, 138-803
   REPUBLIC OF KOREA
   
   Phone: +82-2-405-5446
   Fax:   +82-2-405-5319
   EMail: jiinii@kisa.or.kr

Sungjae Lee
Korea Information Security Agency

   Phone: +82-2-405-5243
   Fax:   +82-2-405-5499
   EMail: sjlee@kisa.or.kr

Jaeho Yoon
Korea Information Security Agency

   Phone: +82-2-405-5434
   FAX:   +82-2-405-5219
   EMail: jhyoon@kisa.or.kr

Donghyeon Cheon
SEC Laboratory

   Phone: +82-31-788-3161
   FAX:   +82-31-707-4017
   EMail: dhcheon@mmaa.or.kr

Jaeil Lee
Korea Information Security Agency

   Phone: +82-2-405-5300
   FAX:   +82-2-405-5219
   EMail: jilee@kisa.or.kr

Appendix A. S-Boxes

In this part, all data are hexadecimal numbers (not prefixed by "0x").

A.1. S-Boxes(two original S-boxes)

S-Box S0

   A9, 85, D6, D3, 54, 1D, AC, 25, 5D, 43, 18, 1E, 51, FC, CA, 63, 28,
   44, 20, 9D, E0, E2, C8, 17, A5, 8F, 03, 7B, BB, 13, D2, EE, 70, 8C,
   3F, A8, 32, DD, F6, 74, EC, 95, 0B, 57, 5C, 5B, BD, 01, 24, 1C, 73,
   98, 10, CC, F2, D9, 2C, E7, 72, 83, 9B, D1, 86, C9, 60, 50, A3, EB,
   0D, B6, 9E, 4F, B7, 5A, C6, 78, A6, 12, AF, D5, 61, C3, B4, 41, 52,
   7D, 8D, 08, 1F, 99, 00, 19, 04, 53, F7, E1, FD, 76, 2F, 27, B0, 8B,
   0E, AB, A2, 6E, 93, 4D, 69, 7C, 09, 0A, BF, EF, F3, C5, 87, 14, FE,
   64, DE, 2E, 4B, 1A, 06, 21, 6B, 66, 02, F5, 92, 8A, 0C, B3, 7E, D0,
   7A, 47, 96, E5, 26, 80, AD, DF, A1, 30, 37, AE, 36, 15, 22, 38, F4,
   A7, 45, 4C, 81, E9, 84, 97, 35, CB, CE, 3C, 71, 11, C7, 89, 75, FB,
   DA, F8, 94, 59, 82, C4, FF, 49, 39, 67, C0, CF, D7, B8, 0F, 8E, 42,
   23, 91, 6C, DB, A4, 34, F1, 48, C2, 6F, 3D, 2D, 40, BE, 3E, BC, C1,
   AA, BA, 4E, 55, 3B, DC, 68, 7F, 9C, D8, 4A, 56, 77, A0, ED, 46, B5,
   2B, 65, FA, E3, B9, B1, 9F, 5E, F9, E6, B2, 31, EA, 6D, 5F, E4, F0,
   CD, 88, 16, 3A, 58, D4, 62, 29, 07, 33, E8, 1B, 05, 79, 90, 6A, 2A,
   9A

S-Box S1

   38, E8, 2D, A6, CF, DE, B3, B8, AF, 60, 55, C7, 44, 6F, 6B, 5B, C3,
   62, 33, B5, 29, A0, E2, A7, D3, 91, 11, 06, 1C, BC, 36, 4B, EF, 88,
   6C, A8, 17, C4, 16, F4, C2, 45, E1, D6, 3F, 3D, 8E, 98, 28, 4E, F6,
   3E, A5, F9, 0D, DF, D8, 2B, 66, 7A, 27, 2F, F1, 72, 42, D4, 41, C0,
   73, 67, AC, 8B, F7, AD, 80, 1F, CA, 2C, AA, 34, D2, 0B, EE, E9, 5D,
   94, 18, F8, 57, AE, 08, C5, 13, CD, 86, B9, FF, 7D, C1, 31, F5, 8A,
   6A, B1, D1, 20, D7, 02, 22, 04, 68, 71, 07, DB, 9D, 99, 61, BE, E6,
   59, DD, 51, 90, DC, 9A, A3, AB, D0, 81, 0F, 47, 1A, E3, EC, 8D, BF,
   96, 7B, 5C, A2, A1, 63, 23, 4D, C8, 9E, 9C, 3A, 0C, 2E, BA, 6E, 9F,
   5A, F2, 92, F3, 49, 78, CC, 15, FB, 70, 75, 7F, 35, 10, 03, 64, 6D,
   C6, 74, D5, B4, EA, 09, 76, 19, FE, 40, 12, E0, BD, 05, FA, 01, F0,
   2A, 5E, A9, 56, 43, 85, 14, 89, 9B, B0, E5, 48, 79, 97, FC, 1E, 82,
   21, 8C, 1B, 5F, 77, 54, B2, 1D, 25, 4F, 00, 46, ED, 58, 52, EB, 7E,
   DA, C9, FD, 30, 95, 65, 3C, B6, E4, BB, 7C, 0E, 50, 39, 26, 32, 84,
   69, 93, 37, E7, 24, A4, CB, 53, 0A, 87, D9, 4C, 83, 8F, CE, 3B, 4A,
   B7

A.2. S-Boxes (four extended S-boxes)

- S-Box SS0

2989A1A8,05858184,16C6D2D4,13C3D3D0,14445054,1D0D111C,2C8CA0AC,25052124,
1D4D515C,03434340,18081018,1E0E121C,11415150,3CCCF0FC,0ACAC2C8,23436360,
28082028,04444044,20002020,1D8D919C,20C0E0E0,22C2E2E0,08C8C0C8,17071314,
2585A1A4,0F8F838C,03030300,3B4B7378,3B8BB3B8,13031310,12C2D2D0,2ECEE2EC,
30407070,0C8C808C,3F0F333C,2888A0A8,32023230,1DCDD1DC,36C6F2F4,34447074,
2CCCE0EC,15859194,0B0B0308,17475354,1C4C505C,1B4B5358,3D8DB1BC,01010100,
24042024,1C0C101C,33437370,18889098,10001010,0CCCC0CC,32C2F2F0,19C9D1D8,
2C0C202C,27C7E3E4,32427270,03838380,1B8B9398,11C1D1D0,06868284,09C9C1C8,
20406060,10405050,2383A3A0,2BCBE3E8,0D0D010C,3686B2B4,1E8E929C,0F4F434C,
3787B3B4,1A4A5258,06C6C2C4,38487078,2686A2A4,12021210,2F8FA3AC,15C5D1D4,
21416160,03C3C3C0,3484B0B4,01414140,12425250,3D4D717C,0D8D818C,08080008,
1F0F131C,19899198,00000000,19091118,04040004,13435350,37C7F3F4,21C1E1E0,
3DCDF1FC,36467274,2F0F232C,27072324,3080B0B0,0B8B8388,0E0E020C,2B8BA3A8,
2282A2A0,2E4E626C,13839390,0D4D414C,29496168,3C4C707C,09090108,0A0A0208,
3F8FB3BC,2FCFE3EC,33C3F3F0,05C5C1C4,07878384,14041014,3ECEF2FC,24446064,
1ECED2DC,2E0E222C,0B4B4348,1A0A1218,06060204,21012120,2B4B6368,26466264,
02020200,35C5F1F4,12829290,0A8A8288,0C0C000C,3383B3B0,3E4E727C,10C0D0D0,
3A4A7278,07474344,16869294,25C5E1E4,26062224,00808080,2D8DA1AC,1FCFD3DC,
2181A1A0,30003030,37073334,2E8EA2AC,36063234,15051114,22022220,38083038,
34C4F0F4,2787A3A4,05454144,0C4C404C,01818180,29C9E1E8,04848084,17879394,
35053134,0BCBC3C8,0ECEC2CC,3C0C303C,31417170,11011110,07C7C3C4,09898188,
35457174,3BCBF3F8,1ACAD2D8,38C8F0F8,14849094,19495158,02828280,04C4C0C4,
3FCFF3FC,09494148,39093138,27476364,00C0C0C0,0FCFC3CC,17C7D3D4,3888B0B8,
0F0F030C,0E8E828C,02424240,23032320,11819190,2C4C606C,1BCBD3D8,2484A0A4,
34043034,31C1F1F0,08484048,02C2C2C0,2F4F636C,3D0D313C,2D0D212C,00404040,
3E8EB2BC,3E0E323C,3C8CB0BC,01C1C1C0,2A8AA2A8,3A8AB2B8,0E4E424C,15455154,
3B0B3338,1CCCD0DC,28486068,3F4F737C,1C8C909C,18C8D0D8,0A4A4248,16465254,
37477374,2080A0A0,2DCDE1EC,06464244,3585B1B4,2B0B2328,25456164,3ACAF2F8,
23C3E3E0,3989B1B8,3181B1B0,1F8F939C,1E4E525C,39C9F1F8,26C6E2E4,3282B2B0,
31013130,2ACAE2E8,2D4D616C,1F4F535C,24C4E0E4,30C0F0F0,0DCDC1CC,08888088,
16061214,3A0A3238,18485058,14C4D0D4,22426260,29092128,07070304,33033330,
28C8E0E8,1B0B1318,05050104,39497178,10809090,2A4A6268,2A0A2228,1A8A9298

- S-Box SS1

38380830,E828C8E0,2C2D0D21,A42686A2,CC0FCFC3,DC1ECED2,B03383B3,B83888B0,
AC2F8FA3,60204060,54154551,C407C7C3,44044440,6C2F4F63,682B4B63,581B4B53,
C003C3C3,60224262,30330333,B43585B1,28290921,A02080A0,E022C2E2,A42787A3,
D013C3D3,90118191,10110111,04060602,1C1C0C10,BC3C8CB0,34360632,480B4B43,
EC2FCFE3,88088880,6C2C4C60,A82888A0,14170713,C404C4C0,14160612,F434C4F0,
C002C2C2,44054541,E021C1E1,D416C6D2,3C3F0F33,3C3D0D31,8C0E8E82,98188890,
28280820,4C0E4E42,F436C6F2,3C3E0E32,A42585A1,F839C9F1,0C0D0D01,DC1FCFD3,
D818C8D0,282B0B23,64264662,783A4A72,24270723,2C2F0F23,F031C1F1,70324272,
40024242,D414C4D0,40014141,C000C0C0,70334373,64274763,AC2C8CA0,880B8B83,

F437C7F3,AC2D8DA1,80008080,1C1F0F13,C80ACAC2,2C2C0C20,A82A8AA2,34340430,
D012C2D2,080B0B03,EC2ECEE2,E829C9E1,5C1D4D51,94148490,18180810,F838C8F0,
54174753,AC2E8EA2,08080800,C405C5C1,10130313,CC0DCDC1,84068682,B83989B1,
FC3FCFF3,7C3D4D71,C001C1C1,30310131,F435C5F1,880A8A82,682A4A62,B03181B1,
D011C1D1,20200020,D417C7D3,00020202,20220222,04040400,68284860,70314171,
04070703,D81BCBD3,9C1D8D91,98198991,60214161,BC3E8EB2,E426C6E2,58194951,
DC1DCDD1,50114151,90108090,DC1CCCD0,981A8A92,A02383A3,A82B8BA3,D010C0D0,
80018181,0C0F0F03,44074743,181A0A12,E023C3E3,EC2CCCE0,8C0D8D81,BC3F8FB3,
94168692,783B4B73,5C1C4C50,A02282A2,A02181A1,60234363,20230323,4C0D4D41,
C808C8C0,9C1E8E92,9C1C8C90,383A0A32,0C0C0C00,2C2E0E22,B83A8AB2,6C2E4E62,
9C1F8F93,581A4A52,F032C2F2,90128292,F033C3F3,48094941,78384870,CC0CCCC0,
14150511,F83BCBF3,70304070,74354571,7C3F4F73,34350531,10100010,00030303,
64244460,6C2D4D61,C406C6C2,74344470,D415C5D1,B43484B0,E82ACAE2,08090901,
74364672,18190911,FC3ECEF2,40004040,10120212,E020C0E0,BC3D8DB1,04050501,
F83ACAF2,00010101,F030C0F0,282A0A22,5C1E4E52,A82989A1,54164652,40034343,
84058581,14140410,88098981,981B8B93,B03080B0,E425C5E1,48084840,78394971,
94178793,FC3CCCF0,1C1E0E12,80028282,20210121,8C0C8C80,181B0B13,5C1F4F53,
74374773,54144450,B03282B2,1C1D0D11,24250521,4C0F4F43,00000000,44064642,
EC2DCDE1,58184850,50124252,E82BCBE3,7C3E4E72,D81ACAD2,C809C9C1,FC3DCDF1,
30300030,94158591,64254561,3C3C0C30,B43686B2,E424C4E0,B83B8BB3,7C3C4C70,
0C0E0E02,50104050,38390931,24260622,30320232,84048480,68294961,90138393,
34370733,E427C7E3,24240420,A42484A0,C80BCBC3,50134353,080A0A02,84078783,
D819C9D1,4C0C4C40,80038383,8C0F8F83,CC0ECEC2,383B0B33,480A4A42,B43787B3

- S-Box SS2

A1A82989,81840585,D2D416C6,D3D013C3,50541444,111C1D0D,A0AC2C8C,21242505,
515C1D4D,43400343,10181808,121C1E0E,51501141,F0FC3CCC,C2C80ACA,63602343,
20282808,40440444,20202000,919C1D8D,E0E020C0,E2E022C2,C0C808C8,13141707,
A1A42585,838C0F8F,03000303,73783B4B,B3B83B8B,13101303,D2D012C2,E2EC2ECE,
70703040,808C0C8C,333C3F0F,A0A82888,32303202,D1DC1DCD,F2F436C6,70743444,
E0EC2CCC,91941585,03080B0B,53541747,505C1C4C,53581B4B,B1BC3D8D,01000101,
20242404,101C1C0C,73703343,90981888,10101000,C0CC0CCC,F2F032C2,D1D819C9,
202C2C0C,E3E427C7,72703242,83800383,93981B8B,D1D011C1,82840686,C1C809C9,
60602040,50501040,A3A02383,E3E82BCB,010C0D0D,B2B43686,929C1E8E,434C0F4F,
B3B43787,52581A4A,C2C406C6,70783848,A2A42686,12101202,A3AC2F8F,D1D415C5,
61602141,C3C003C3,B0B43484,41400141,52501242,717C3D4D,818C0D8D,00080808,
131C1F0F,91981989,00000000,11181909,00040404,53501343,F3F437C7,E1E021C1,
F1FC3DCD,72743646,232C2F0F,23242707,B0B03080,83880B8B,020C0E0E,A3A82B8B,
A2A02282,626C2E4E,93901383,414C0D4D,61682949,707C3C4C,01080909,02080A0A,
B3BC3F8F,E3EC2FCF,F3F033C3,C1C405C5,83840787,10141404,F2FC3ECE,60642444,
D2DC1ECE,222C2E0E,43480B4B,12181A0A,02040606,21202101,63682B4B,62642646,
02000202,F1F435C5,92901282,82880A8A,000C0C0C,B3B03383,727C3E4E,D0D010C0,
72783A4A,43440747,92941686,E1E425C5,22242606,80800080,A1AC2D8D,D3DC1FCF,
A1A02181,30303000,33343707,A2AC2E8E,32343606,11141505,22202202,30383808,
F0F434C4,A3A42787,41440545,404C0C4C,81800181,E1E829C9,80840484,93941787,
31343505,C3C80BCB,C2CC0ECE,303C3C0C,71703141,11101101,C3C407C7,81880989,
71743545,F3F83BCB,D2D81ACA,F0F838C8,90941484,51581949,82800282,C0C404C4,
F3FC3FCF,41480949,31383909,63642747,C0C000C0,C3CC0FCF,D3D417C7,B0B83888,
030C0F0F,828C0E8E,42400242,23202303,91901181,606C2C4C,D3D81BCB,A0A42484,
30343404,F1F031C1,40480848,C2C002C2,636C2F4F,313C3D0D,212C2D0D,40400040,
B2BC3E8E,323C3E0E,B0BC3C8C,C1C001C1,A2A82A8A,B2B83A8A,424C0E4E,51541545,
33383B0B,D0DC1CCC,60682848,737C3F4F,909C1C8C,D0D818C8,42480A4A,52541646,
73743747,A0A02080,E1EC2DCD,42440646,B1B43585,23282B0B,61642545,F2F83ACA,
E3E023C3,B1B83989,B1B03181,939C1F8F,525C1E4E,F1F839C9,E2E426C6,B2B03282,
31303101,E2E82ACA,616C2D4D,535C1F4F,E0E424C4,F0F030C0,C1CC0DCD,80880888,
12141606,32383A0A,50581848,D0D414C4,62602242,21282909,03040707,33303303,
E0E828C8,13181B0B,01040505,71783949,90901080,62682A4A,22282A0A,92981A8A

- S-Box SS3

08303838,C8E0E828,0D212C2D,86A2A426,CFC3CC0F,CED2DC1E,83B3B033,88B0B838,
8FA3AC2F,40606020,45515415,C7C3C407,44404404,4F636C2F,4B63682B,4B53581B,
C3C3C003,42626022,03333033,85B1B435,09212829,80A0A020,C2E2E022,87A3A427,
C3D3D013,81919011,01111011,06020406,0C101C1C,8CB0BC3C,06323436,4B43480B,
CFE3EC2F,88808808,4C606C2C,88A0A828,07131417,C4C0C404,06121416,C4F0F434,
C2C2C002,45414405,C1E1E021,C6D2D416,0F333C3F,0D313C3D,8E828C0E,88909818,
08202828,4E424C0E,C6F2F436,0E323C3E,85A1A425,C9F1F839,0D010C0D,CFD3DC1F,
C8D0D818,0B23282B,46626426,4A72783A,07232427,0F232C2F,C1F1F031,42727032,
42424002,C4D0D414,41414001,C0C0C000,43737033,47636427,8CA0AC2C,8B83880B,
C7F3F437,8DA1AC2D,80808000,0F131C1F,CAC2C80A,0C202C2C,8AA2A82A,04303434,
C2D2D012,0B03080B,CEE2EC2E,C9E1E829,4D515C1D,84909414,08101818,C8F0F838,
47535417,8EA2AC2E,08000808,C5C1C405,03131013,CDC1CC0D,86828406,89B1B839,
CFF3FC3F,4D717C3D,C1C1C001,01313031,C5F1F435,8A82880A,4A62682A,81B1B031,
C1D1D011,00202020,C7D3D417,02020002,02222022,04000404,48606828,41717031,
07030407,CBD3D81B,8D919C1D,89919819,41616021,8EB2BC3E,C6E2E426,49515819,
CDD1DC1D,41515011,80909010,CCD0DC1C,8A92981A,83A3A023,8BA3A82B,C0D0D010,
81818001,0F030C0F,47434407,0A12181A,C3E3E023,CCE0EC2C,8D818C0D,8FB3BC3F,
86929416,4B73783B,4C505C1C,82A2A022,81A1A021,43636023,03232023,4D414C0D,
C8C0C808,8E929C1E,8C909C1C,0A32383A,0C000C0C,0E222C2E,8AB2B83A,4E626C2E,
8F939C1F,4A52581A,C2F2F032,82929012,C3F3F033,49414809,48707838,CCC0CC0C,
05111415,CBF3F83B,40707030,45717435,4F737C3F,05313435,00101010,03030003,
44606424,4D616C2D,C6C2C406,44707434,C5D1D415,84B0B434,CAE2E82A,09010809,
46727436,09111819,CEF2FC3E,40404000,02121012,C0E0E020,8DB1BC3D,05010405,
CAF2F83A,01010001,C0F0F030,0A22282A,4E525C1E,89A1A829,46525416,43434003,
85818405,04101414,89818809,8B93981B,80B0B030,C5E1E425,48404808,49717839,
87939417,CCF0FC3C,0E121C1E,82828002,01212021,8C808C0C,0B13181B,4F535C1F,
47737437,44505414,82B2B032,0D111C1D,05212425,4F434C0F,00000000,46424406,
CDE1EC2D,48505818,42525012,CBE3E82B,4E727C3E,CAD2D81A,C9C1C809,CDF1FC3D,
00303030,85919415,45616425,0C303C3C,86B2B436,C4E0E424,8BB3B83B,4C707C3C,
0E020C0E,40505010,09313839,06222426,02323032,84808404,49616829,83939013,
07333437,C7E3E427,04202424,84A0A424,CBC3C80B,43535013,0A02080A,87838407,
C9D1D819,4C404C0C,83838003,8F838C0F,CEC2CC0E,0B33383B,4A42480A,87B3B437

Appendix B. Test Vectors

This appendix provides test vectors for the SEED cipher described in this document.

All data are hexadecimal numbers (not prefixed by "0x").

B.1.

      Key        : 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
      Plaintext  : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      Ciphertext : 5E BA C6 E0 05 4E 16 68 19 AF F1 CC 6D 34 6C DB
   
                            Intermediate Value
   ------------------------------------------------------------------
                 Ki0      Ki1        L0       L1       R0       R1
   ==================================================================
   Round  1 : 7C8F8C7E C737A22C | 00010203 04050607 08090A0B 0C0D0E0F
   Round  2 : FF276CDB A7CA684A | 08090A0B 0C0D0E0F 8081BC57 C4EA8A1F
   Round  3 : 2F9D01A1 70049E41 | 8081BC57 C4EA8A1F 117A8B07 D7358C24
   Round  4 : AE59B3C4 4245E90C | 117A8B07 D7358C24 D1738C94 7326CAB0
   Round  5 : A1D6400F DBC1394E | D1738C94 7326CAB0 577ECE6D 1F8433EC
   Round  6 : 85963508 0C5F1FCB | 577ECE6D 1F8433EC 910F62AB DDA096C1
   Round  7 : B684BDA7 61A4AEAE | 910F62AB DDA096C1 EA4D39B4 B17B1938
   Round  8 : D17E0741 FEE90AA1 | EA4D39B4 B17B1938 B04E251F 97D7442C
   Round  9 : 76CC05D5 E97A7394 | B04E251F 97D7442C B86D31BF A5988C06
   Round 10 : 50AC6F92 1B2666E5 | B86D31BF A5988C06 9008EABF 38DF7430
   Round 11 : 65B7904A 8EC3A7B3 | 9008EABF 38DF7430 33E47DE0 54EFF76C
   Round 12 : 2F7E2E22 A2B121B9 | 33E47DE0 54EFF76C 6BE9C434 BF3F378A
   Round 13 : 4D0BFDE4 4E888D9B | 6BE9C434 BF3F378A B8DC3842 03A02D33
   Round 14 : 631C8DDC 4378A6C4 | B8DC3842 03A02D33 6679FCF7 9791DFCB
   Round 15 : 216AF65F 7878C031 | 6679FCF7 9791DFCB 1A415792 A02B8C54
   Round 16 : 71891150 98B255B0 | 1A415792 A02B8C54 19AFF1CC 6D346CDB

B.2.

      Key        : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
      Plaintext  : 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
      Ciphertext : C1 1F 22 F2 01 40 50 50 84 48 35 97 E4 37 0F 43
   
                            Intermediate Value
   ------------------------------------------------------------------
                 Ki0      Ki1        L0       L1       R0       R1
   ==================================================================
   Round  1 : C119F584 5AE033A0 | 00000000 00000000 00000000 00000000
   Round  2 : 62947390 A600AD14 | 00000000 00000000 9D8DB62C 911F0C19
   Round  3 : F6F6544E 596C4B49 | 9D8DB62C 911F0C19 21229A97 4AB4B7B8
   Round  4 : C1A3DE02 CE483C49 | 21229A97 4AB4B7B8 5A27B404 899D7315
   Round  5 : 5E742E6D 7E25163D | 5A27B404 899D7315 B8489E76 BA0EF3EA
   Round  6 : 8299D2B4 790A46CE | B8489E76 BA0EF3EA 04A3DF29 31A27FB4
   Round  7 : EA67D836 55F354F2 | 04A3DF29 31A27FB4 EC9C17BF 81AA2AA0
   Round  8 : C47329FB F50DB634 | EC9C17BF 81AA2AA0 4FA74E8D CDB21BB8
   Round  9 : 2BD30235 51679CE6 | 4FA74E8D CDB21BB8 D93492FE 4F71A4DA
   Round 10 : FA8D6B76 A9F37E02 | D93492FE 4F71A4DA B14053D9 A911379B
   Round 11 : 8B99CC60 0F6092D4 | B14053D9 A911379B 5A7024D6 3905668B
   Round 12 : BDAEFCFA 489C2242 | 5A7024D6 3905668B 605C8C3A 73DFBB75
   Round 13 : F6357C14 CFCCB126 | 605C8C3A 73DFBB75 40282F39 31CB8987
   Round 14 : A0AA6D85 F8C10774 | 40282F39 31CB8987 E9F834A8 3B9586D4
   Round 15 : 47F4FEC5 353AE1BA | E9F834A8 3B9586D4 4B60324B 761C9958
   Round 16 : FECCEA48 A4EF9F9B | 4B60324B 761C9958 84483597 E4370F43

B.3.

      Key        : 47 06 48 08 51 E6 1B E8 5D 74 BF B3 FD 95 61 85
      Plaintext  : 83 A2 F8 A2 88 64 1F B9 A4 E9 A5 CC 2F 13 1C 7D
      Ciphertext : EE 54 D1 3E BC AE 70 6D 22 6B C3 14 2C D4 0D 4A
   
                            Intermediate Value
   ------------------------------------------------------------------
                 Ki0      Ki1        L0       L1       R0       R1
   ==================================================================
   Round  1 : 56BE4A0F E9F62877 | 83A2F8A2 88641FB9 A4E9A5CC 2F131C7D
   Round  2 : 68BCB66C 078911DD | A4E9A5CC 2F131C7D 7CE5F012 47F8C1E6
   Round  3 : 5B82740B FD24D09B | 7CE5F012 47F8C1E6 AAC99520 609F4CB7
   Round  4 : 8D608015 A120E0BE | AAC99520 609F4CB7 3E126D1F 44FA99F0
   Round  5 : 810A75AE 1BF223E5 | 3E126D1F 44FA99F0 11716365 9BA775AC
   Round  6 : F9C0D2D0 0F676C02 | 11716365 9BA775AC 32C9838F BA5757CB
   Round  7 : 8F9B5C84 8A7C8DDD | 32C9838F BA5757CB 77E00C64 CF9F6B32
   Round  8 : D4AB4896 18E93447 | 77E00C64 CF9F6B32 3F09B1F7 DE7D6D58
   Round  9 : CF090F51 5A4C8202 | 3F09B1F7 DE7D6D58 300E5CAA D0BF2345
   Round 10 : 4EC3196F 61B1A0DC | 300E5CAA D0BF2345 9574FDD7 4DF050D1
   Round 11 : 244E07C1 D0D10B12 | 9574FDD7 4DF050D1 A15EDA6F 624265FD
   Round 12 : 69917C6C 7FF94FB3 | A15EDA6F 624265FD 9F39B682 D841C76F
   Round 13 : 9A7EB482 723B5738 | 9F39B682 D841C76F EEBBAD8B C1F488EF
   Round 14 : B97522C5 39CC6349 | EEBBAD8B C1F488EF 45CF5D4E BEEA4AA2
   Round 15 : FFC2AFD5 1412E731 | 45CF5D4E BEEA4AA2 43B7FE1B BCF87781
   Round 16 : A9AF7241 A3E67359 | 43B7FE1B BCF87781 226BC314 2CD40D4A

B.4.

      Key        : 28 DB C3 BC 49 FF D8 7D CF A5 09 B1 1D 42 2B E7
      Plaintext  : B4 1E 6B E2 EB A8 4A 14 8E 2E ED 84 59 3C 5E C7
      Ciphertext : 9B 9B 7B FC D1 81 3C B9 5D 0B 36 18 F4 0F 51 22
   
                            Intermediate Value
   ------------------------------------------------------------------
                 Ki0      Ki1        L0       L1       R0       R1
   ==================================================================
   Round  1 : B2B11B63 2EE9E2D1 | B41E6BE2 EBA84A14 8E2EED84 593C5EC7
   Round  2 : 11967260 71A62F24 | 8E2EED84 593C5EC7 1B31F2F7 3DDE00BA
   Round  3 : 2E017A5A 35DAD7A7 | 1B31F2F7 3DDE00BA 35CC49C0 2AFB59EA
   Round  4 : 1B2AB5FF A3ADA69F | 35CC49C0 2AFB59EA D7AB53AA AE82F1C7
   Round  5 : 519C9903 DA90AAEE | D7AB53AA AE82F1C7 24139958 B840E56F
   Round  6 : 29FD95AD B94C3F13 | 24139958 B840E56F 24AB5291 544C9DBA
   Round  7 : 6F629D19 8ACE692F | 24AB5291 544C9DBA E8152994 75D0B424
   Round  8 : 30A26E73 2F22338E | E8152994 75D0B424 A2CD1153 F32BB23A
   Round  9 : 9721073A 98EE8DAE | A2CD1153 F32BB23A C386008B E3257731
   Round 10 : C597A8A9 27DCDC97 | C386008B E3257731 98396BFD 814F8972
   Round 11 : F5163A00 5FFD0003 | 98396BFD 814F8972 E74D2D0D 11D889D1
   Round 12 : 5CBE65DA A73403E4 | E74D2D0D 11D889D1 29D8C7B3 D1B71C0C
   Round 13 : 7D5CF070 1D3B8092 | 29D8C7B3 D1B71C0C C4E692C2 D2F57F18
   Round 14 : 388C702B 1BAA4945 | C4E692C2 D2F57F18 2FAFB300 5F0C4BFF
   Round 15 : 87D1AB5A FA13FB5C | 2FAFB300 5F0C4BFF 60E5F17C 5626BB68
   Round 16 : C97D7EED 90724A6E | 60E5F17C 5626BB68 5D0B3618 F40F5122

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