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diff --git a/doc/rfc/rfc2268.txt b/doc/rfc/rfc2268.txt new file mode 100644 index 0000000..cbbdf3b --- /dev/null +++ b/doc/rfc/rfc2268.txt @@ -0,0 +1,619 @@ + + + + + + +Network Working Group R. Rivest +Request for Comments: 2268 MIT Laboratory for Computer Science +Category: Informational and RSA Data Security, Inc. + March 1998 + + + A Description of the RC2(r) 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 + + Copyright (C) The Internet Society (1998). All Rights Reserved. + +1. Introduction + + This memo is an RSA Laboratories Technical Note. It is meant for + informational use by the Internet community. + + This memo describes a conventional (secret-key) block encryption + algorithm, called RC2, which may be considered as a proposal for a + DES replacement. The input and output block sizes are 64 bits each. + The key size is variable, from one byte up to 128 bytes, although the + current implementation uses eight bytes. + + The algorithm is designed to be easy to implement on 16-bit + microprocessors. On an IBM AT, the encryption runs about twice as + fast as DES (assuming that key expansion has been done). + +1.1 Algorithm description + + We use the term "word" to denote a 16-bit quantity. The symbol + will + denote twos-complement addition. The symbol & will denote the bitwise + "and" operation. The term XOR will denote the bitwise "exclusive-or" + operation. The symbol ~ will denote bitwise complement. The symbol ^ + will denote the exponentiation operation. The term MOD will denote + the modulo operation. + + There are three separate algorithms involved: + + Key expansion. This takes a (variable-length) input key and + produces an expanded key consisting of 64 words K[0],...,K[63]. + + + + + +Rivest Informational [Page 1] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + Encryption. This takes a 64-bit input quantity stored in words + R[0], ..., R[3] and encrypts it "in place" (the result is left in + R[0], ..., R[3]). + + Decryption. The inverse operation to encryption. + +2. Key expansion + + Since we will be dealing with eight-bit byte operations as well as + 16-bit word operations, we will use two alternative notations + + for referring to the key buffer: + + For word operations, we will refer to the positions of the + buffer as K[0], ..., K[63]; each K[i] is a 16-bit word. + + For byte operations, we will refer to the key buffer as + L[0], ..., L[127]; each L[i] is an eight-bit byte. + + These are alternative views of the same data buffer. At all times it + will be true that + + K[i] = L[2*i] + 256*L[2*i+1]. + + (Note that the low-order byte of each K word is given before the + high-order byte.) + + We will assume that exactly T bytes of key are supplied, for some T + in the range 1 <= T <= 128. (Our current implementation uses T = 8.) + However, regardless of T, the algorithm has a maximum effective key + length in bits, denoted T1. That is, the search space is 2^(8*T), or + 2^T1, whichever is smaller. + + The purpose of the key-expansion algorithm is to modify the key + buffer so that each bit of the expanded key depends in a complicated + way on every bit of the supplied input key. + + The key expansion algorithm begins by placing the supplied T-byte key + into bytes L[0], ..., L[T-1] of the key buffer. + + The key expansion algorithm then computes the effective key length in + bytes T8 and a mask TM based on the effective key length in bits T1. + It uses the following operations: + + T8 = (T1+7)/8; + TM = 255 MOD 2^(8 + T1 - 8*T8); + + Thus TM has its 8 - (8*T8 - T1) least significant bits set. + + + +Rivest Informational [Page 2] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + For example, with an effective key length of 64 bits, T1 = 64, T8 = 8 + and TM = 0xff. With an effective key length of 63 bits, T1 = 63, T8 + = 8 and TM = 0x7f. + + Here PITABLE[0], ..., PITABLE[255] is an array of "random" bytes + based on the digits of PI = 3.14159... . More precisely, the array + PITABLE is a random permutation of the values 0, ..., 255. Here is + the PITABLE in hexadecimal notation: + + 0 1 2 3 4 5 6 7 8 9 a b c d e f + 00: d9 78 f9 c4 19 dd b5 ed 28 e9 fd 79 4a a0 d8 9d + 10: c6 7e 37 83 2b 76 53 8e 62 4c 64 88 44 8b fb a2 + 20: 17 9a 59 f5 87 b3 4f 13 61 45 6d 8d 09 81 7d 32 + 30: bd 8f 40 eb 86 b7 7b 0b f0 95 21 22 5c 6b 4e 82 + 40: 54 d6 65 93 ce 60 b2 1c 73 56 c0 14 a7 8c f1 dc + 50: 12 75 ca 1f 3b be e4 d1 42 3d d4 30 a3 3c b6 26 + 60: 6f bf 0e da 46 69 07 57 27 f2 1d 9b bc 94 43 03 + 70: f8 11 c7 f6 90 ef 3e e7 06 c3 d5 2f c8 66 1e d7 + 80: 08 e8 ea de 80 52 ee f7 84 aa 72 ac 35 4d 6a 2a + 90: 96 1a d2 71 5a 15 49 74 4b 9f d0 5e 04 18 a4 ec + a0: c2 e0 41 6e 0f 51 cb cc 24 91 af 50 a1 f4 70 39 + b0: 99 7c 3a 85 23 b8 b4 7a fc 02 36 5b 25 55 97 31 + c0: 2d 5d fa 98 e3 8a 92 ae 05 df 29 10 67 6c ba c9 + d0: d3 00 e6 cf e1 9e a8 2c 63 16 01 3f 58 e2 89 a9 + e0: 0d 38 34 1b ab 33 ff b0 bb 48 0c 5f b9 b1 cd 2e + f0: c5 f3 db 47 e5 a5 9c 77 0a a6 20 68 fe 7f c1 ad + + The key expansion operation consists of the following two loops and + intermediate step: + + for i = T, T+1, ..., 127 do + L[i] = PITABLE[L[i-1] + L[i-T]]; + + L[128-T8] = PITABLE[L[128-T8] & TM]; + + for i = 127-T8, ..., 0 do + L[i] = PITABLE[L[i+1] XOR L[i+T8]]; + + (In the first loop, the addition of L[i-1] and L[i-T] is performed + modulo 256.) + + The "effective key" consists of the values L[128-T8],..., L[127]. + The intermediate step's bitwise "and" operation reduces the search + space for L[128-T8] so that the effective number of key bits is T1. + The expanded key depends only on the effective key bits, regardless + + + + + + +Rivest Informational [Page 3] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + of the supplied key K. Since the expanded key is not itself modified + during encryption or decryption, as a pragmatic matter one can expand + the key just once when encrypting or decrypting a large block of + data. + +3. Encryption algorithm + + The encryption operation is defined in terms of primitive "mix" and + "mash" operations. + + Here the expression "x rol k" denotes the 16-bit word x rotated left + by k bits, with the bits shifted out the top end entering the bottom + end. + +3.1 Mix up R[i] + + The primitive "Mix up R[i]" operation is defined as follows, where + s[0] is 1, s[1] is 2, s[2] is 3, and s[3] is 5, and where the indices + of the array R are always to be considered "modulo 4," so that R[i-1] + refers to R[3] if i is 0 (these values are + + "wrapped around" so that R always has a subscript in the range 0 to 3 + inclusive): + + R[i] = R[i] + K[j] + (R[i-1] & R[i-2]) + ((~R[i-1]) & R[i-3]); + j = j + 1; + R[i] = R[i] rol s[i]; + + In words: The next key word K[j] is added to R[i], and j is advanced. + Then R[i-1] is used to create a "composite" word which is added to + R[i]. The composite word is identical with R[i-2] in those positions + where R[i-1] is one, and identical to R[i-3] in those positions where + R[i-1] is zero. Then R[i] is rotated left by s[i] bits (bits rotated + out the left end of R[i] are brought back in at the right). Here j is + a "global" variable so that K[j] is always the first key word in the + expanded key which has not yet been used in a "mix" operation. + +3.2 Mixing round + + A "mixing round" consists of the following operations: + + Mix up R[0] + Mix up R[1] + Mix up R[2] + Mix up R[3] + + + + + + +Rivest Informational [Page 4] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + +3.3 Mash R[i] + + The primitive "Mash R[i]" operation is defined as follows (using the + previous conventions regarding subscripts for R): + + R[i] = R[i] + K[R[i-1] & 63]; + + In words: R[i] is "mashed" by adding to it one of the words of the + expanded key. The key word to be used is determined by looking at the + low-order six bits of R[i-1], and using that as an index into the key + array K. + +3.4 Mashing round + + A "mashing round" consists of: + + Mash R[0] + Mash R[1] + Mash R[2] + Mash R[3] + +3.5 Encryption operation + + The entire encryption operation can now be described as follows. Here + j is a global integer variable which is affected by the mixing + operations. + + 1. Initialize words R[0], ..., R[3] to contain the + 64-bit input value. + + 2. Expand the key, so that words K[0], ..., K[63] become + defined. + + 3. Initialize j to zero. + + 4. Perform five mixing rounds. + + 5. Perform one mashing round. + + 6. Perform six mixing rounds. + + 7. Perform one mashing round. + + 8. Perform five mixing rounds. + + Note that each mixing round uses four key words, and that there are + 16 mixing rounds altogether, so that each key word is used exactly + + + + +Rivest Informational [Page 5] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + once in a mixing round. The mashing rounds will refer to up to eight + of the key words in a data-dependent manner. (There may be + repetitions, and the actual set of words referred to will vary from + encryption to encryption.) + +4. Decryption algorithm + + The decryption operation is defined in terms of primitive operations + that undo the "mix" and "mash" operations of the encryption + algorithm. They are named "r-mix" and "r-mash" (r- denotes the + reverse operation). + + Here the expression "x ror k" denotes the 16-bit word x rotated right + by k bits, with the bits shifted out the bottom end entering the top + end. + +4.1 R-Mix up R[i] + + The primitive "R-Mix up R[i]" operation is defined as follows, where + s[0] is 1, s[1] is 2, s[2] is 3, and s[3] is 5, and where the indices + of the array R are always to be considered "modulo 4," so that R[i-1] + refers to R[3] if i is 0 (these values are "wrapped around" so that R + always has a subscript in the range 0 to 3 inclusive): + + R[i] = R[i] ror s[i]; + R[i] = R[i] - K[j] - (R[i-1] & R[i-2]) - ((~R[i-1]) & R[i-3]); + j = j - 1; + + In words: R[i] is rotated right by s[i] bits (bits rotated out the + right end of R[i] are brought back in at the left). Here j is a + "global" variable so that K[j] is always the key word with greatest + index in the expanded key which has not yet been used in a "r-mix" + operation. The key word K[j] is subtracted from R[i], and j is + decremented. R[i-1] is used to create a "composite" word which is + subtracted from R[i]. The composite word is identical with R[i-2] in + those positions where R[i-1] is one, and identical to R[i-3] in those + positions where R[i-1] is zero. + +4.2 R-Mixing round + + An "r-mixing round" consists of the following operations: + + R-Mix up R[3] + R-Mix up R[2] + R-Mix up R[1] + R-Mix up R[0] + + + + + +Rivest Informational [Page 6] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + +4.3 R-Mash R[i] + + The primitive "R-Mash R[i]" operation is defined as follows (using + the previous conventions regarding subscripts for R): + + R[i] = R[i] - K[R[i-1] & 63]; + + In words: R[i] is "r-mashed" by subtracting from it one of the words + of the expanded key. The key word to be used is determined by looking + at the low-order six bits of R[i-1], and using that as an index into + the key array K. + +4.4 R-Mashing round + + An "r-mashing round" consists of: + + R-Mash R[3] + R-Mash R[2] + R-Mash R[1] + R-Mash R[0] + +4.5 Decryption operation + + The entire decryption operation can now be described as follows. + Here j is a global integer variable which is affected by the mixing + operations. + + 1. Initialize words R[0], ..., R[3] to contain the 64-bit + ciphertext value. + + 2. Expand the key, so that words K[0], ..., K[63] become + defined. + + 3. Initialize j to 63. + + 4. Perform five r-mixing rounds. + + 5. Perform one r-mashing round. + + 6. Perform six r-mixing rounds. + + 7. Perform one r-mashing round. + + 8. Perform five r-mixing rounds. + +5. Test vectors + + Test vectors for encryption with RC2 are provided below. + + + +Rivest Informational [Page 7] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + All quantities are given in hexadecimal notation. + + Key length (bytes) = 8 + Effective key length (bits) = 63 + Key = 00000000 00000000 + Plaintext = 00000000 00000000 + Ciphertext = ebb773f9 93278eff + + Key length (bytes) = 8 + Effective key length (bits) = 64 + Key = ffffffff ffffffff + Plaintext = ffffffff ffffffff + Ciphertext = 278b27e4 2e2f0d49 + + Key length (bytes) = 8 + Effective key length (bits) = 64 + Key = 30000000 00000000 + Plaintext = 10000000 00000001 + Ciphertext = 30649edf 9be7d2c2 + + Key length (bytes) = 1 + Effective key length (bits) = 64 + Key = 88 + Plaintext = 00000000 00000000 + Ciphertext = 61a8a244 adacccf0 + + Key length (bytes) = 7 + Effective key length (bits) = 64 + Key = 88bca90e 90875a + Plaintext = 00000000 00000000 + Ciphertext = 6ccf4308 974c267f + + Key length (bytes) = 16 + Effective key length (bits) = 64 + Key = 88bca90e 90875a7f 0f79c384 627bafb2 + Plaintext = 00000000 00000000 + Ciphertext = 1a807d27 2bbe5db1 + + Key length (bytes) = 16 + Effective key length (bits) = 128 + Key = 88bca90e 90875a7f 0f79c384 627bafb2 + Plaintext = 00000000 00000000 + Ciphertext = 2269552a b0f85ca6 + + Key length (bytes) = 33 + Effective key length (bits) = 129 + Key = 88bca90e 90875a7f 0f79c384 627bafb2 16f80a6f 85920584 + c42fceb0 be255daf 1e + + + +Rivest Informational [Page 8] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + Plaintext = 00000000 00000000 + Ciphertext = 5b78d3a4 3dfff1f1 + +6. RC2 Algorithm Object Identifier + + The Object Identifier for RC2 in cipher block chaining mode is + + rc2CBC OBJECT IDENTIFIER + ::= {iso(1) member-body(2) US(840) rsadsi(113549) + encryptionAlgorithm(3) 2} + + RC2-CBC takes parameters + + RC2-CBCParameter ::= CHOICE { + iv IV, + params SEQUENCE { + version RC2Version, + iv IV + } + } + + where + + IV ::= OCTET STRING -- 8 octets + RC2Version ::= INTEGER -- 1-1024 + + RC2 in CBC mode has two parameters: an 8-byte initialization vector + (IV) and a version number in the range 1-1024 which specifies in a + roundabout manner the number of effective key bits to be used for the + RC2 encryption/decryption. + + The correspondence between effective key bits and version number is + as follows: + + 1. If the number EKB of effective key bits is in the range 1-255, + then the version number is given by Table[EKB], where the 256-byte + translation table Table[] is specified below. Table[] specifies a + permutation on the numbers 0-255; note that it is not the same + table that appears in the key expansion phase of RC2. + + 2. If the number EKB of effective key bits is in the range + 256-1024, then the version number is simply EKB. + + The default number of effective key bits for RC2 is 32. If RC2-CBC + is being performed with 32 effective key bits, the parameters + should be supplied as a simple IV, rather than as a SEQUENCE + containing a version and an IV. + + + + +Rivest Informational [Page 9] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + + 0 1 2 3 4 5 6 7 8 9 a b c d e f + + 00: bd 56 ea f2 a2 f1 ac 2a b0 93 d1 9c 1b 33 fd d0 + 10: 30 04 b6 dc 7d df 32 4b f7 cb 45 9b 31 bb 21 5a + 20: 41 9f e1 d9 4a 4d 9e da a0 68 2c c3 27 5f 80 36 + 30: 3e ee fb 95 1a fe ce a8 34 a9 13 f0 a6 3f d8 0c + 40: 78 24 af 23 52 c1 67 17 f5 66 90 e7 e8 07 b8 60 + 50: 48 e6 1e 53 f3 92 a4 72 8c 08 15 6e 86 00 84 fa + 60: f4 7f 8a 42 19 f6 db cd 14 8d 50 12 ba 3c 06 4e + 70: ec b3 35 11 a1 88 8e 2b 94 99 b7 71 74 d3 e4 bf + 80: 3a de 96 0e bc 0a ed 77 fc 37 6b 03 79 89 62 c6 + 90: d7 c0 d2 7c 6a 8b 22 a3 5b 05 5d 02 75 d5 61 e3 + a0: 18 8f 55 51 ad 1f 0b 5e 85 e5 c2 57 63 ca 3d 6c + b0: b4 c5 cc 70 b2 91 59 0d 47 20 c8 4f 58 e0 01 e2 + c0: 16 38 c4 6f 3b 0f 65 46 be 7e 2d 7b 82 f9 40 b5 + d0: 1d 73 f8 eb 26 c7 87 97 25 54 b1 28 aa 98 9d a5 + e0: 64 6d 7a d4 10 81 44 ef 49 d6 ae 2e dd 76 5c 2f + f0: a7 1c c9 09 69 9a 83 cf 29 39 b9 e9 4c ff 43 ab + +A. Intellectual Property Notice + + RC2 is a registered trademark of RSA Data Security, Inc. RSA's + copyrighted RC2 software is available under license from RSA Data + Security, Inc. + +B. Author's Address + + Ron Rivest + RSA Laboratories + 100 Marine Parkway, #500 + Redwood City, CA 94065 USA + + Phone: (650) 595-7703 + EMail: rsa-labs@rsa.com + + + + + + + + + + + + + + + + + +Rivest Informational [Page 10] + +RFC 2268 RC2(r) Encryption Algorithm March 1998 + + +C. Full Copyright Statement + + Copyright (C) The Internet Society (1998). All Rights Reserved. + + This document and translations of it may be copied and furnished to + others, and derivative works that comment on or otherwise explain it + or assist in its implementation may be prepared, copied, published + and distributed, in whole or in part, without restriction of any + kind, provided that the above copyright notice and this paragraph are + included on all such copies and derivative works. However, this + document itself may not be modified in any way, such as by removing + the copyright notice or references to the Internet Society or other + Internet organizations, except as needed for the purpose of + developing Internet standards in which case the procedures for + copyrights defined in the Internet Standards process must be + followed, or as required to translate it into languages other than + English. + + The limited permissions granted above are perpetual and will not be + revoked by the Internet Society or its successors or assigns. + + This document and the information contained herein is provided on an + "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING + TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING + BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION + HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF + MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. + + + + + + + + + + + + + + + + + + + + + + + + +Rivest Informational [Page 11] + |