Crypto Forum Research Group | R. Tse |
Internet-Draft | Ribose |
Intended status: Informational | W. Wong |
Expires: April 21, 2018 | Hang Seng Management College |
October 18, 2017 |
The SM4 Block Cipher Algorithm And Its Modes Of Operations
draft-ribose-cfrg-sm4-02
This document describes the SM4 symmetric blockcipher algorithm published as GB/T 32907-2016 by the Organization of State Commercial Administration of China (OSCCA).
This document is a product of the Crypto Forum Research Group (CFRG).
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SM4 [GBT.32907-2016] [ISO.IEC.18033-3.AMD2] is a cryptographic standard issued by the Organization of State Commercial Administration of China [OSCCA] as an authorized cryptographic algorithm for the use within China. The algorithm is published in public.
SM4 is a symmetric encryption algorithm, specifically a blockcipher, designed for data encryption.
This document does not aim to introduce a new algorithm, but to provide a clear and open description of the SM4 algorithm in English, and also to serve as a stable reference for IETF documents that utilize this algorithm.
While this document is similar to [SM4-En] in nature, [SM4-En] is a textual translation of the "SMS4" algorithm [SM4] published in 2006, while this document follows the updated description and structure of [GBT.32907-2016] published in 2016. Sections 1 to 7 of this document directly map to the corresponding sections numbers of the [GBT.32907-2016] standard for convenience of the reader.
This document also provides additional information on the practical usage and implementation of SM4, specifying multiple modes of operations that are known to be used with SM4 and providing the SM4 OIDs.
The "SMS4" algorithm (the former name of SM4) was invented by Shu-Wang Lu [LSW-Bio], first published in 2003 as part of [GB.15629.11-2003], then published independently in 2006 [SM4] by the OSCCA, officially renamed to "SM4" in 2012 in [GMT-0002-2012] published by the OSCCA, and finally standardized in 2016 as a Chinese National Standard (GB Standard) [GBT.32907-2016]. SM4 is also standardized in [ISO.IEC.18033-3.AMD2] by the International Organization for Standardization in 2017.
SMS4 was originally created for use in protecting wireless networks [SM4], and is mandated in the Chinese National Standard for Wireless LAN WAPI (Wired Authentication and Privacy Infrastructure) [GB.15629.11-2003]. A proposal was made to adopt SMS4 into the IEEE 802.11i standard, but the algorithm was eventually not included due to concerns of introducing inoperability with existing ciphers.
The latest SM4 standard [GBT.32907-2016] was proposed by the OSCCA, standardized through TC 260 of the Standardization Administration of the People's Republic of China (SAC), and was drafted by the following individuals at the Data Assurance and Communication Security Research Center (DAS Center) of the Chinese Academy of Sciences, the China Commercial Cryptography Testing Center and the Beijing Academy of Information Science & Technology (BAIST):
SM4 (and SMS4) has prevalent hardware implementations [SM4-FPGA] [SM4-VLSI], due to its being the only OSCCA-approved symmetric encryption algorithm allowed for use in China.
SM4 can be used with multiple modes (See Section 8).
A number of attacks have been attempted on SM4, such as [SM4-Analysis] [SM4-Linear], but there are no known feasible attacks against the SM4 algorithm by the time of publishing this document.
There are, however, security concerns with regards to side-channel attacks [SideChannel] when the SM4 algorithm is implemented in a hardware device [SM4-Power].
For instance, [SM4-Power] illustrated an attack by measuring the power consumption of the device. A chosen ciphertext attack, assuming a fixed correlation between the round keys and data mask, is able to recover the round key successfully. When the SM4 algorithm is implemented in hardware, the parameters and keys SHOULD be randomly generated without fixed correlation.
There have been improvements to the hardware embodiment design for SM4, such as [SM4-VLSI], that may resist such attacks.
In order to improve security of the SM4 cryptographic process, secure white-box implementations such as [SM4-WhiteBox] have been proposed. Speed enhancements, such as [SM4-HiSpeed], have also been proposed.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].
The following terms and definitions apply to this document.
The SM4 algorithm is a blockcipher, with block size of 128 bits and a key length of 128 bits.
Both encryption and key expansion uses 32 rounds of a nonlinear key schedule per block. Each round processes one of the four 32-bit words that constitute the block.
The structure of encryption and decryption are identical, except that the round key schedule has its order reversed during decryption.
Using a 8-bit S-box, it only uses exclusive-or, cyclic bit shifts and S-box lookups to execute.
Encryption key length is 128-bits, and represented below, where each MK_i, (i = 0, 1, 2, 3) is 32-bits wide.
MK = (MK_0, MK_1, MK_2, MK_3)
The round key schedule is derived from the encryption key, represented as below where each rk_i (i = 0, ..., 31) is a word:
(rk_0, rk_1, ... , rk_31)
The family key used for key expansion is represented as FK, where each FK_i (i = 0, ..., 3) is a word:
FK = (FK_0, FK_1, FK_2, FK_3)
The constant key used for key expansion is represented as CK, where each CK_i (i = 0, ..., 31) is a word:
CK = (CK_0, CK_1, ... , CK_31)
The round function F is defined as:
F(X_0, X_1, X_2, X_3, rk) = X_0 xor T(X_1 xor X_2 xor X_3 xor rk)
Where:
T is a reversible permutation that outputs 32 bits from an input of 32 bits.
It consists of a non-linear transform tau and linear transform L.
T(.) = L(tau(.))
The permutation T' is created from T by replacing the linear transform function L with L'.
T'(.) = L'(tau(.))
tau is composed of four parallel S-boxes.
Given a 32-bit input A, where each a_i is a 8-bit string:
A = (a_0, a_1, a_2, a_3)
The output is a 32-bit B, where each b_i is a 8-bit string:
B = (b_0, b_1, b_2, b_3)
B is calculated as follows:
(b_0, b_1, b_2, b_3) = tau(A)
tau(A) = (S(a_0), S(a_1), S(a_2), S(a_3))
The output of non-linear transformation function tau is used as input to linear transformation function L.
Given B, a 32-bit input.
The linear transformation L' is defined as follows.
L(B) = B xor (B <<< 2) xor (B <<< 10) xor (B <<< 18) xor (B <<< 24)
The linear transformation L' is defined as follows.
L'(B) = B xor (B <<< 13) xor (B <<< 23)
The S-box S used in tau is given in this lookup table in hexadecimal form:
| 0 1 2 3 4 5 6 7 8 9 A B C D E F ---|------------------------------------------------- 0 | D6 90 E9 FE CC E1 3D B7 16 B6 14 C2 28 FB 2C 05 1 | 2B 67 9A 76 2A BE 04 C3 AA 44 13 26 49 86 06 99 2 | 9C 42 50 F4 91 EF 98 7A 33 54 0B 43 ED CF AC 62 3 | E4 B3 1C A9 C9 08 E8 95 80 DF 94 FA 75 8F 3F A6 4 | 47 07 A7 FC F3 73 17 BA 83 59 3C 19 E6 85 4F A8 5 | 68 6B 81 B2 71 64 DA 8B F8 EB 0F 4B 70 56 9D 35 6 | 1E 24 0E 5E 63 58 D1 A2 25 22 7C 3B 01 21 78 87 7 | D4 00 46 57 9F D3 27 52 4C 36 02 E7 A0 C4 C8 9E 8 | EA BF 8A D2 40 C7 38 B5 A3 F7 F2 CE F9 61 15 A1 9 | E0 AE 5D A4 9B 34 1A 55 AD 93 32 30 F5 8C B1 E3 A | 1D F6 E2 2E 82 66 CA 60 C0 29 23 AB 0D 53 4E 6F B | D5 DB 37 45 DE FD 8E 2F 03 FF 6A 72 6D 6C 5B 51 C | 8D 1B AF 92 BB DD BC 7F 11 D9 5C 41 1F 10 5A D8 D | 0A C1 31 88 A5 CD 7B BD 2D 74 D0 12 B8 E5 B4 B0 E | 89 69 97 4A 0C 96 77 7E 65 B9 F1 09 C5 6E C6 84 F | 18 F0 7D EC 3A DC 4D 20 79 EE 5F 3E D7 CB 39 48
For example, input "EF" will produce an output read from the S-box table row E and column F, giving the result S(EF) = 84.
The encryption algorithm consists of 32 rounds and 1 reverse transform R.
Given a 128-bit plaintext input, where each X_i is a 32-bit word:
(X_0, X_1, X_2, X_3)
The output is a 128-bit ciphertext, where each Y_i is a 32-bit word:
(Y_0, Y_1, Y_2, Y_3)
Each round key is designated as rk_i, where each rk_i is a 32-bit word and i = 0, 1, 2, ..., 31.
a. 32 rounds of calculation
i = 0, 1, ..., 31
X_{i+4} = F(X_i, X_{i+1}, X_{i+2}, X_{i+3}, rk_i)
b. reverse transformation
(Y_0, Y_1, Y_2, Y_3) = R(X_32, X_33, X_34, X_35)
R(X_32, X_33, X_34, X_35) = (X_35, X_34, X_33, X_32)
Please refer to Section 12 for sample calculations.
Decryption takes an identical process as encryption, with the only difference the order of the round key sequence.
During decryption, the round key sequence is:
(rk_31, rk_30, ..., rk_0)
Round keys used during encryption are derived from the encryption key.
Specifically, given the encryption key MK, where each MK_i is 32 bits wide:
MK = (MK_0, MK_1, MK_2, MK_3)
Each round key rk_i is created as follows, where i = 0, 1, ..., 31.
(K_0, K_1, K_2, K_3) = (MK_0 xor FK_0, MK_1 xor FK_1, MK_2 xor FK_2, MK_3 xor FK_3)
rk_i = K_{i + 4}
K_{i + 4} = K_i xor T' (K_{i + 1} xor K_{i + 2} xor K_{i + 3} xor CK_i)
Since the decryption key is identical to the encryption key, the round keys used in the decryption process are derived from the decryption key through the identical process to that of during encryption.
Family key FK given in hexadecimal notation, is:
FK_0 = A3B1BAC6 FK_1 = 56AA3350 FK_2 = 677D9197 FK_3 = B27022DC
The method to retrieve values from the constant key CK is as follows.
Let ck_{i, j} be the j-th byte (i = 0, 1, ..., 31; j = 0, 1, 2, 3) of CK_i.
Therefore, each ck_{i, j} is a 8-bit string, and each CK_i a 32-bit word.
CK_i = (ck_{i, 0}, ck_{i, 1}, ck_{i, 2}, ck_{i, 3})
ck_{i, j} = (4i + j) x 7 (mod 256)
The values of the constant key CK_i, where (i = 0, 1, ..., 31), in hexadecimal, are:
CK_0 = 00070E15 CK_16 = C0C7CED5 CK_1 = 1C232A31 CK_17 = DCE3EAF1 CK_2 = 383F464D CK_18 = F8FF060D CK_3 = 545B6269 CK_19 = 141B2229 CK_4 = 70777E85 CK_20 = 30373E45 CK_5 = 8C939AA1 CK_21 = 4C535A61 CK_6 = A8AFB6BD CK_22 = 686F767D CK_7 = C4CBD2D9 CK_23 = 848B9299 CK_8 = E0E7EEF5 CK_24 = A0A7AEB5 CK_9 = FC030A11 CK_25 = BCC3CAD1 CK_10 = 181F262D CK_26 = D8DFE6ED CK_11 = 343B4249 CK_27 = F4FB0209 CK_12 = 50575E65 CK_28 = 10171E25 CK_13 = 6C737A81 CK_29 = 2C333A41 CK_14 = 888F969D CK_30 = 484F565D CK_15 = A4ABB2B9 CK_31 = 646B7279
This document defines multiple modes of operation for the SM4 blockcipher algorithm.
The CBC (Cipher Block Chaining), ECB (Electronic CodeBook), CFB (Cipher FeedBack), OFB (Output FeedBack) and CTR (Counter) modes are defined in [NIST.SP.800-38A] and utilized with the SM4 algorithm in the following sections.
Hereinafter we define:
The CBC, CFB and OFB modes require an additional input to the encryption process, called the initialization vector (IV). The identical IV is used in the input of encryption as well as the decryption of the corresponding ciphertext.
Generation of IV values MUST take into account of the considerations in Section 10 recommended by [BC-EVAL].
In SM4-ECB, the same key is utilized to create a fixed assignment for a plaintext block with a ciphertext block, meaning that a given plaintext block always gets encrypted to the same ciphertext block. As described in [NIST.SP.800-38A], this mode should be avoided if this property is undesirable.
This mode requires input plaintext to be a multiple of the block size, which in this case of SM4 it is 128-bits. It also allows multiple blocks to be computed in parallel.
Inputs:
Output:
C is defined as follows.
n = NBlocks(P, b) for i = 1 to n C_i = SM4Encrypt(P_i, K) end for C = C_1 || ... || C_n
Inputs:
Output:
P is defined as follows.
n = NBlocks(C, b) for i = 1 to n P_i = SM4Decrypt(C_i, K) end for P = P_1 || ... || P_n
SM4-CBC is similar to SM4-ECB that the input plaintext MUST be a multiple of the block size, which is 128-bits in SM4. SM4-CBC requires an additional input, the IV, that is unpredictable for a particular execution of the encryption process.
Since CBC encryption relies on a forward cipher operation that depend on results of the previous operation, it cannot be parallelized. However, for decryption, since ciphertext blocks are already available, CBC parallel decryption is possible.
Inputs:
Output:
C is defined as follows.
n = NBlocks(P, b) C_1 = SM4Encrypt(P_1 xor IV, K) for i = 2 to n C_i = SM4Encrypt(P_i xor C_{i - 1}, K) end for C = C_1 || ... || C_n
Inputs:
Output:
P is defined as follows.
n = NBlocks(C, b) P_1 = SM4Decrypt(C_1, K) xor IV for i = 2 to n P_i = SM4Decrypt(C_i, K) xor C_{i - 1} end for P = P_1 || ... || P_n
SM4-CFB relies on feedback provided by successive ciphertext segments to generate output blocks. The plaintext given must be a multiple of the block size.
Similar to SM4-CBC, SM4-CFB requires an IV that is unpredictable for a particular execution of the encryption process.
SM4-CFB further allows setting a positive integer parameter s, that is less than or equal to the block size, to specify the size of each data segment. The same segment size must be used in encryption and decryption.
In SM4-CFB, since the input block to each forward cipher function depends on the output of the previous block (except the first that depends on the IV), encryption is not parallelizable. Decryption, however, can be parallelized.
SM4-CFB takes an integer s to determine segment size in its encryption and decryption routines. We define the following variants of SM4-CFB for various s:
Inputs:
Output:
C# is defined as follows.
n = NBlocks(P#, s) I_1 = IV for i = 2 to n I_i = LSB(b - s, I_{i - 1}) || C#_{j - 1} end for for i = 1 to n O_j = SM4Encrypt(I_i, K) end for for i = 1 to n C#_i = P#_1 xor MSB(s, O_j) end for C# = C#_1 || ... || C#_n
Inputs:
Output:
P is defined as follows.
n = NBlocks(P#, s) I_1 = IV for i = 2 to n I_i = LSB(b - s, I_{i - 1}) || C#_{j - 1} end for for i = 1 to n O_j = SM4Encrypt(I_i, K) end for for i = 1 to n P#_i = C#_1 xor MSB(s, O_j) end for P# = P#_1 || ... || P#_n
SM4-OFB is the application of SM4 through the Output Feedback mode. This mode requires that the IV is a nonce, meaning that the IV MUST be unique for each execution for an input key. OFB does not require the input plaintext to be a multiple of the block size.
In OFB, the routines for encryption and decryption are identical. As each forward cipher function (except the first) depends on previous results, both routines cannot be parallelized. However given a known IV, output blocks could be generated prior to the input of plaintext (encryption) or ciphertext (decryption).
Inputs:
Output:
C is defined as follows.
n = NBlocks(P, b) I_1 = IV for i = 1 to (n - 1) O_i = SM4Encrypt(I_i) I_{i + 1} = O_i end for for i = 1 to (n - 1) C_i = P_i xor O_i end for C_n = P_n xor MSB(u, O_n) C = C_1 || ... || C_n
Inputs:
Output:
C is defined as follows.
n = NBlocks(C, b) I_1 = IV for i = 1 to (n - 1) O_i = SM4Encrypt(I_i) I_{i + 1} = O_i end for for i = 1 to (n - 1) P_i = C_i xor O_i end for P_n = C_n xor MSB(u, O_n) P = P_1 || ... || P_n
SM4-CTR is an implementation of a stream cipher through a block cipher primitive. It generates a "keystream" of keys that are used to encrypt successive blocks, with the keystream created from the input key, a nonce (the IV) and an incremental counter. The counter could be any sequence that does not repeat within the block size.
Both SM4-CTR encryption and decryption routines could be parallelized, and random access is also possible.
Inputs:
Output:
C is defined as follows.
n = NBlocks(P, b) for i = 1 to n O_i = SM4Encrypt(T_i) end for for i = 1 to (n - 1) C_i = P_i xor O_i end for C_n = P_n xor MSB(u, O_n) C = C_1 || ... || C_n
Inputs:
Output:
P is defined as follows.
n = NBlocks(C, b) for i = 1 to n O_i = SM4Encrypt(T_i) end for for i = 1 to (n - 1) P_i = C_i xor O_i end for P_n = C_n xor MSB(u, O_n) C = C_1 || ... || C_n
The Object Identifier for SM4 is identified through these OIDs.
"1.2.156.10197.1.104" for "SM4 Algorithm" [GMT-0006-2012].
"1.0.18033.3.2.4" for "id-bc128-sm4" [ISO.IEC.18033-3.AMD2], described below.
is18033-3 OID ::= {iso(1) standard(0) is18033(18033) part3(3)} id-bc128 OID ::= {is18033-3 block-cipher-128-bit(2)} id-bc128-sm4 OID ::= {id-bc128 sm4(4)}
When using these modes of operation, the IV SHOULD be random to preserve message confidentiality [BC-EVAL]. It is shown in the same document that CBC, CFB, OFB, the variants #CBC, #CFB that utilize the recommendation of [NIST.SP.800-38A] to make CBC and CFB nonce-based, are SemCPA secure as probabilistic encryption schemes.
Various attack scenarios have been described in [BC-EVAL] and these modes SHOULD NOT be used unless for compatibility reasons.
Users with no need of authenticity, non-malleablility and chosen-ciphertext (CCA) security MAY utilize this mode of operation [BC-EVAL].
This document does not require any action by IANA.
This is example 1 provided by [GBT.32907-2016] to demonstrate encryption of a plaintext.
Plaintext: 01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption key: 01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Status of the round key (rk_i) and round output (X_i) per round:
rk_0 = F12186F9 X_4 = 27FAD345 rk_1 = 41662B61 X_5 = A18B4CB2 rk_2 = 5A6AB19A X_6 = 11C1E22A rk_3 = 7BA92077 X_7 = CC13E2EE rk_4 = 367360F4 X_8 = F87C5BD5 rk_5 = 776A0C61 X_9 = 33220757 rk_6 = B6BB89B3 X_10 = 77F4C297 rk_7 = 24763151 X_11 = 7A96F2EB rk_8 = A520307C X_12 = 27DAC07F rk_9 = B7584DBD X_13 = 42DD0F19 rk_10 = C30753ED X_14 = B8A5DA02 rk_11 = 7EE55B57 X_15 = 907127FA rk_12 = 6988608C X_16 = 8B952B83 rk_13 = 30D895B7 X_17 = D42B7C59 rk_14 = 44BA14AF X_18 = 2FFC5831 rk_15 = 104495A1 X_19 = F69E6888 rk_16 = D120B428 X_20 = AF2432C4 rk_17 = 73B55FA3 X_21 = ED1EC85E rk_18 = CC874966 X_22 = 55A3BA22 rk_19 = 92244439 X_23 = 124B18AA rk_20 = E89E641F X_24 = 6AE7725F rk_21 = 98CA015A X_25 = F4CBA1F9 rk_22 = C7159060 X_26 = 1DCDFA10 rk_23 = 99E1FD2E X_27 = 2FF60603 rk_24 = B79BD80C X_28 = EFF24FDC rk_25 = 1D2115B0 X_29 = 6FE46B75 rk_26 = 0E228AEB X_30 = 893450AD rk_27 = F1780C81 X_31 = 7B938F4C rk_28 = 428D3654 X_32 = 536E4246 rk_29 = 62293496 X_33 = 86B3E94F rk_30 = 01CF72E5 X_34 = D206965E rk_31 = 9124A012 X_35 = 681EDF34
Ciphertext: 68 1E DF 34 D2 06 96 5E 86 B3 E9 4F 53 6E 42 46
This example is provided by [GBT.32907-2016] to demonstrate encryption of a plaintext 1,000,000 times repeatedly, using a fixed encryption key.
Plaintext:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
59 52 98 C7 C6 FD 27 1F 04 02 F8 04 C3 3D 3F 66
The following examples can be verified using open-source cryptographic libraries including:
Plaintext:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
68 1E DF 34 D2 06 96 5E 86 B3 E9 4F 53 6E 42 46
Plaintext:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
IV:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
26 77 F4 6B 09 C1 22 CC 97 55 33 10 5B D4 A2 2A F6 12 5F 72 75 CE 55 2C 3A 2B BC F5 33 DE 8A 3B
Plaintext:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
IV:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
69 3D 9A 53 5B AD 5B B1 78 6F 53 D7 25 3A 70 56 F2 07 5D 28 B5 23 5F 58 D5 00 27 E4 17 7D 2B CE
Plaintext:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
IV:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
69 3D 9A 53 5B AD 5B B1 78 6F 53 D7 25 3A 70 56 9E D2 58 A8 5A 04 67 CC 92 AA B3 93 DD 97 89 95
Plaintext:
AA AA AA AA AA AA AA AA BB BB BB BB BB BB BB BB CC CC CC CC CC CC CC CC DD DD DD DD DD DD DD DD EE EE EE EE EE EE EE EE FF FF FF FF FF FF FF FF EE EE EE EE EE EE EE EE AA AA AA AA AA AA AA AA
Encryption Key:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
IV:
01 23 45 67 89 AB CD EF FE DC BA 98 76 54 32 10
Ciphertext:
C2 B4 75 9E 78 AC 3C F4 3D 08 52 F4 E8 D5 F9 FD 72 56 E8 A5 FC B6 5A 35 0E E0 06 30 91 2E 44 49 2A 0B 17 E1 B8 5B 06 0D 0F BA 61 2D 8A 95 83 16 38 B3 61 FD 5F FA CD 94 2F 08 14 85 A8 3C A3 5D
[GBT.32907-2016] | Standardization Administration of the People's Republic of China, "GB/T 32907-2016: Information security technology -- SM4 block cipher algorithm", August 2016. |
[RFC2119] | Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997. |
The authors would like to thank the following persons for their valuable advice and input.