A Description of the RC2(r) Encryption Algorithm
RFC 2268
Document  Type 
RFC  Informational
(March 1998; Errata)
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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 (secretkey) 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 16bit 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 16bit quantity. The symbol + will denote twoscomplement addition. The symbol & will denote the bitwise "and" operation. The term XOR will denote the bitwise "exclusiveor" 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 (variablelength) 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 64bit 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 eightbit byte operations as well as 16bit 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 16bit word. For byte operations, we will refer to the key buffer as L[0], ..., L[127]; each L[i] is an eightbit 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 loworder byte of each K word is given before the highorder 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 keyexpansion 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 Tbyte key into bytes L[0], ..., L[T1] 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 2aShow full document text