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openssl/crypto/rc2/rrc2.doc

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-Article 23601 of sci.crypt:
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->From: pgut01@cs.auckland.ac.nz (Peter Gutmann)
-Newsgroups: sci.crypt
-Subject: Specification for Ron Rivests Cipher No.2
-Date: 11 Feb 1996 06:45:03 GMT
-Organization: University of Auckland
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-
-                           Ron Rivest's Cipher No.2
-                           ------------------------
- 
-Ron Rivest's Cipher No.2 (hereafter referred to as RRC.2, other people may
-refer to it by other names) is word oriented, operating on a block of 64 bits
-divided into four 16-bit words, with a key table of 64 words.  All data units
-are little-endian.  This functional description of the algorithm is based in
-the paper "The RC5 Encryption Algorithm" (RC5 is a trademark of RSADSI), using
-the same general layout, terminology, and pseudocode style.
- 
- 
-Notation and RRC.2 Primitive Operations
- 
-RRC.2 uses the following primitive operations:
- 
-1. Two's-complement addition of words, denoted by "+".  The inverse operation,
-   subtraction, is denoted by "-".
-2. Bitwise exclusive OR, denoted by "^".
-3. Bitwise AND, denoted by "&".
-4. Bitwise NOT, denoted by "~".
-5. A left-rotation of words; the rotation of word x left by y is denoted
-   x <<< y.  The inverse operation, right-rotation, is denoted x >>> y.
- 
-These operations are directly and efficiently supported by most processors.
- 
- 
-The RRC.2 Algorithm
- 
-RRC.2 consists of three components, a *key expansion* algorithm, an
-*encryption* algorithm, and a *decryption* algorithm.
- 
- 
-Key Expansion
- 
-The purpose of the key-expansion routine is to expand the user's key K to fill
-the expanded key array S, so S resembles an array of random binary words
-determined by the user's secret key K.
- 
-Initialising the S-box
- 
-RRC.2 uses a single 256-byte S-box derived from the ciphertext contents of
-Beale Cipher No.1 XOR'd with a one-time pad.  The Beale Ciphers predate modern
-cryptography by enough time that there should be no concerns about trapdoors
-hidden in the data.  They have been published widely, and the S-box can be
-easily recreated from the one-time pad values and the Beale Cipher data taken
-from a standard source.  To initialise the S-box:
- 
-  for i = 0 to 255 do
-    sBox[ i ] = ( beale[ i ] mod 256 ) ^ pad[ i ]
- 
-The contents of Beale Cipher No.1 and the necessary one-time pad are given as
-an appendix at the end of this document.  For efficiency, implementors may wish
-to skip the Beale Cipher expansion and store the sBox table directly.
- 
-Expanding the Secret Key to 128 Bytes
- 
-The secret key is first expanded to fill 128 bytes (64 words).  The expansion
-consists of taking the sum of the first and last bytes in the user key, looking
-up the sum (modulo 256) in the S-box, and appending the result to the key.  The
-operation is repeated with the second byte and new last byte of the key until
-all 128 bytes have been generated.  Note that the following pseudocode treats
-the S array as an array of 128 bytes rather than 64 words.
- 
-  for j = 0 to length-1 do
-    S[ j ] = K[ j ]
-  for j = length to 127 do
-    s[ j ] = sBox[ ( S[ j-length ] + S[ j-1 ] ) mod 256 ];
- 
-At this point it is possible to perform a truncation of the effective key
-length to ease the creation of espionage-enabled software products.  However
-since the author cannot conceive why anyone would want to do this, it will not
-be considered further.
- 
-The final phase of the key expansion involves replacing the first byte of S
-with the entry selected from the S-box:
- 
-  S[ 0 ] = sBox[ S[ 0 ] ]
- 
- 
-Encryption
- 
-The cipher has 16 full rounds, each divided into 4 subrounds.  Two of the full
-rounds perform an additional transformation on the data.  Note that the
-following pseudocode treats the S array as an array of 64 words rather than 128
-bytes.
- 
-  for i = 0 to 15 do
-    j = i * 4;
-    word0 = ( word0 + ( word1 & ~word3 ) + ( word2 & word3 ) + S[ j+0 ] ) <<< 1
-    word1 = ( word1 + ( word2 & ~word0 ) + ( word3 & word0 ) + S[ j+1 ] ) <<< 2
-    word2 = ( word2 + ( word3 & ~word1 ) + ( word0 & word1 ) + S[ j+2 ] ) <<< 3
-    word3 = ( word3 + ( word0 & ~word2 ) + ( word1 & word2 ) + S[ j+3 ] ) <<< 5
- 
-In addition the fifth and eleventh rounds add the contents of the S-box indexed
-by one of the data words to another of the data words following the four
-subrounds as follows:
- 
-    word0 = word0 + S[ word3 & 63 ];
-    word1 = word1 + S[ word0 & 63 ];
-    word2 = word2 + S[ word1 & 63 ];
-    word3 = word3 + S[ word2 & 63 ];
- 
- 
-Decryption
- 
-The decryption operation is simply the inverse of the encryption operation.
-Note that the following pseudocode treats the S array as an array of 64 words
-rather than 128 bytes.
- 
-  for i = 15 downto 0 do
-    j = i * 4;
-    word3 = ( word3 >>> 5 ) - ( word0 & ~word2 ) - ( word1 & word2 ) - S[ j+3 ]
-    word2 = ( word2 >>> 3 ) - ( word3 & ~word1 ) - ( word0 & word1 ) - S[ j+2 ]
-    word1 = ( word1 >>> 2 ) - ( word2 & ~word0 ) - ( word3 & word0 ) - S[ j+1 ]
-    word0 = ( word0 >>> 1 ) - ( word1 & ~word3 ) - ( word2 & word3 ) - S[ j+0 ]
- 
-In addition the fifth and eleventh rounds subtract the contents of the S-box
-indexed by one of the data words from another one of the data words following
-the four subrounds as follows:
- 
-    word3 = word3 - S[ word2 & 63 ]
-    word2 = word2 - S[ word1 & 63 ]
-    word1 = word1 - S[ word0 & 63 ]
-    word0 = word0 - S[ word3 & 63 ]
- 
- 
-Test Vectors
- 
-The following test vectors may be used to test the correctness of an RRC.2
-implementation:
- 
-  Key:      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
-  Plain:    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
-  Cipher:   0x1C, 0x19, 0x8A, 0x83, 0x8D, 0xF0, 0x28, 0xB7
- 
-  Key:      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
-  Plain:    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
-  Cipher:   0x21, 0x82, 0x9C, 0x78, 0xA9, 0xF9, 0xC0, 0x74
- 
-  Key:      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
-  Plain:    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
-  Cipher:   0x13, 0xDB, 0x35, 0x17, 0xD3, 0x21, 0x86, 0x9E
- 
-  Key:      0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
-            0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F
-  Plain:    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
-  Cipher:   0x50, 0xDC, 0x01, 0x62, 0xBD, 0x75, 0x7F, 0x31
- 
- 
-Appendix: Beale Cipher No.1, "The Locality of the Vault", and One-time Pad for
-          Creating the S-Box
- 
-Beale Cipher No.1.
- 
-  71, 194,  38,1701,  89,  76,  11,  83,1629,  48,  94,  63, 132,  16, 111,  95,
-  84, 341, 975,  14,  40,  64,  27,  81, 139, 213,  63,  90,1120,   8,  15,   3,
- 126,2018,  40,  74, 758, 485, 604, 230, 436, 664, 582, 150, 251, 284, 308, 231,
- 124, 211, 486, 225, 401, 370,  11, 101, 305, 139, 189,  17,  33,  88, 208, 193,
- 145,   1,  94,  73, 416, 918, 263,  28, 500, 538, 356, 117, 136, 219,  27, 176,
- 130,  10, 460,  25, 485,  18, 436,  65,  84, 200, 283, 118, 320, 138,  36, 416,
- 280,  15,  71, 224, 961,  44,  16, 401,  39,  88,  61, 304,  12,  21,  24, 283,
- 134,  92,  63, 246, 486, 682,   7, 219, 184, 360, 780,  18,  64, 463, 474, 131,
- 160,  79,  73, 440,  95,  18,  64, 581,  34,  69, 128, 367, 460,  17,  81,  12,
- 103, 820,  62, 110,  97, 103, 862,  70,  60,1317, 471, 540, 208, 121, 890, 346,
-  36, 150,  59, 568, 614,  13, 120,  63, 219, 812,2160,1780,  99,  35,  18,  21,
- 136, 872,  15,  28, 170,  88,   4,  30,  44, 112,  18, 147, 436, 195, 320,  37,
- 122, 113,   6, 140,   8, 120, 305,  42,  58, 461,  44, 106, 301,  13, 408, 680,
-  93,  86, 116, 530,  82, 568,   9, 102,  38, 416,  89,  71, 216, 728, 965, 818,
-   2,  38, 121, 195,  14, 326, 148, 234,  18,  55, 131, 234, 361, 824,   5,  81,
- 623,  48, 961,  19,  26,  33,  10,1101, 365,  92,  88, 181, 275, 346, 201, 206
- 
-One-time Pad.
- 
- 158, 186, 223,  97,  64, 145, 190, 190, 117, 217, 163,  70, 206, 176, 183, 194,
- 146,  43, 248, 141,   3,  54,  72, 223, 233, 153,  91, 210,  36, 131, 244, 161,
- 105, 120, 113, 191, 113,  86,  19, 245, 213, 221,  43,  27, 242, 157,  73, 213,
- 193,  92, 166,  10,  23, 197, 112, 110, 193,  30, 156,  51, 125,  51, 158,  67,
- 197, 215,  59, 218, 110, 246, 181,   0, 135,  76, 164,  97,  47,  87, 234, 108,
- 144, 127,   6,   6, 222, 172,  80, 144,  22, 245, 207,  70, 227, 182, 146, 134,
- 119, 176,  73,  58, 135,  69,  23, 198,   0, 170,  32, 171, 176, 129,  91,  24,
- 126,  77, 248,   0, 118,  69,  57,  60, 190, 171, 217,  61, 136, 169, 196,  84,
- 168, 167, 163, 102, 223,  64, 174, 178, 166, 239, 242, 195, 249,  92,  59,  38,
- 241,  46, 236,  31,  59, 114,  23,  50, 119, 186,   7,  66, 212,  97, 222, 182,
- 230, 118, 122,  86, 105,  92, 179, 243, 255, 189, 223, 164, 194, 215,  98,  44,
-  17,  20,  53, 153, 137, 224, 176, 100, 208, 114,  36, 200, 145, 150, 215,  20,
-  87,  44, 252,  20, 235, 242, 163, 132,  63,  18,   5, 122,  74,  97,  34,  97,
- 142,  86, 146, 221, 179, 166, 161,  74,  69, 182,  88, 120, 128,  58,  76, 155,
-  15,  30,  77, 216, 165, 117, 107,  90, 169, 127, 143, 181, 208, 137, 200, 127,
- 170, 195,  26,  84, 255, 132, 150,  58, 103, 250, 120, 221, 237,  37,   8,  99
- 
- 
-Implementation
- 
-A non-US based programmer who has never seen any encryption code before will
-shortly be implementing RRC.2 based solely on this specification and not on
-knowledge of any other encryption algorithms.  Stand by.
-
-
-