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+Network Working Group                                       M. Boesgaard
+Request for Comments: 4503                                 M. Vesterager
+Category: Informational                                        E. Zenner
+                                                            Cryptico A/S
+                                                                May 2006
+
+
+          A Description of the Rabbit Stream Cipher 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 (2006).
+
+Abstract
+
+   This document describes the encryption algorithm Rabbit.  It is a
+   stream cipher algorithm with a 128-bit key and 64-bit initialization
+   vector (IV).  The method was published in 2003 and has been subject
+   to public security and performance revision.  Its high performance
+   makes it particularly suited for the use with Internet protocols
+   where large amounts of data have to be processed.
+
+Table of Contents
+
+   1. Introduction ....................................................2
+   2. Algorithm Description ...........................................2
+      2.1. Notation ...................................................2
+      2.2. Inner State ................................................3
+      2.3. Key Setup Scheme ...........................................3
+      2.4. IV Setup Scheme ............................................3
+      2.5. Counter System .............................................4
+      2.6. Next-State Function ........................................4
+      2.7. Extraction Scheme ..........................................5
+      2.8. Encryption/Decryption Scheme ...............................5
+   3. Security Considerations .........................................6
+      3.1. Message Length .............................................6
+      3.2. Initialization Vector ......................................6
+   4. Informative References ..........................................7
+   Appendix A: Test Vectors ...........................................8
+      A.1. Testing without IV Setup ...................................8
+      A.2. Testing with IV Setup ......................................8
+   Appendix B: Debugging Vectors ......................................9
+
+
+
+Boesgaard, et al.            Informational                      [Page 1]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+      B.1. Testing Round Function and Key Setup .......................9
+      B.2. Testing the IV setup ......................................10
+
+1.  Introduction
+
+   Rabbit is a stream cipher algorithm that has been designed for high
+   performance in software implementations.  Both key setup and
+   encryption are very fast, making the algorithm particularly suited
+   for all applications where large amounts of data or large numbers of
+   data packages have to be encrypted.  Examples include, but are not
+   limited to, server-side encryption, multimedia encryption, hard-disk
+   encryption, and encryption on limited-resource devices.
+
+   The cipher is based on ideas derived from the behavior of certain
+   chaotic maps.  These maps have been carefully discretized, resulting
+   in a compact stream cipher.  Rabbit has been openly published in 2003
+   [1] and has not displayed any weaknesses as of the time of this
+   writing.  To ensure ongoing security evaluation, it was also
+   submitted to the ECRYPT eSTREAM project[2].
+
+   Technically, Rabbit consists of a pseudorandom bitstream generator
+   that takes a 128-bit key and a 64-bit initialization vector (IV) as
+   input and generates a stream of 128-bit blocks.  Encryption is
+   performed by combining this output with the message, using the
+   exclusive-OR operation.  Decryption is performed in exactly the same
+   way as encryption.
+
+   Further information about Rabbit, including reference implementation,
+   test vectors, performance figures, and security white papers, is
+   available from http://www.cryptico.com/.
+
+2.  Algorithm Description
+
+2.1.  Notation
+
+   This document uses the following elementary operators:
+
+    +     integer addition.
+    *     integer multiplication.
+   div    integer division.
+   mod    integer modulus.
+    ^     bitwise exclusive-OR operation.
+   <<<    left rotation operator.
+    ||    concatenation operator.
+
+   When labeling bits of a variable, A, the least significant bit is
+   denoted by A[0].  The notation A[h..g] represents bits h through g of
+   variable A, where h is more significant than g.  Similar variables
+
+
+
+Boesgaard, et al.            Informational                      [Page 2]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+   are labeled by A0,A1,... with the notation A(0),A(1),... being used
+   to denote those same variables if this improves readability.
+
+   Given a 64-bit word, the function MSW extracts the most significant
+   32 bits, whereas the function LSW extracts the least significant 32
+   bits.
+
+   Constants prefixed with 0x are in hexadecimal notation.  In
+   particular, the constant WORDSIZE is defined to be 0x100000000.
+
+2.2.  Inner State
+
+   The internal state of the stream cipher consists of 513 bits.  512
+   bits are divided between eight 32-bit state variables, X0,...,X7 and
+   eight 32-bit counter variables, C0,...,C7.  In addition, there is one
+   counter carry bit, b.
+
+2.3.  Key Setup Scheme
+
+   The counter carry bit b is initialized to zero.  The state and
+   counter words are derived from the key K[127..0].
+
+   The key is divided into subkeys K0 = K[15..0], K1 = K[31..16], ... K7
+   = K[127..112].  The initial state is initialized as follows:
+
+     for j=0 to 7:
+       if j is even:
+         Xj = K(j+1 mod 8) || Kj
+         Cj = K(j+4 mod 8) || K(j+5 mod 8)
+       else:
+         Xj = K(j+5 mod 8) || K(j+4 mod 8)
+         Cj = Kj || K(j+1 mod 8)
+
+   The system is then iterated four times, each iteration consisting of
+   counter update (Section 2.5) and next-state function (Section 2.6).
+   After that, the counter variables are reinitialized to
+
+     for j=0 to 7:
+       Cj = Cj ^ X(j+4 mod 8)
+
+2.4.  IV Setup Scheme
+
+   If an IV is used for encryption, the counter variables are modified
+   after the key setup.  Denoting the IV bits by IV[63..0], the setup
+   proceeds as follows:
+
+     C0 = C0 ^ IV[31..0]        C1 = C1 ^ (IV[63..48] || IV[31..16])
+     C2 = C2 ^ IV[63..32]       C3 = C3 ^ (IV[47..32] || IV[15..0])
+
+
+
+Boesgaard, et al.            Informational                      [Page 3]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+     C4 = C4 ^ IV[31..0]        C5 = C5 ^ (IV[63..48] || IV[31..16])
+     C6 = C6 ^ IV[63..32]       C7 = C7 ^ (IV[47..32] || IV[15..0])
+
+   The system is then iterated another 4 times, each iteration
+   consisting of counter update (Section 2.5) and next-state function
+   (Section 2.6).
+
+   The relationship between key and IV setup is as follows:
+
+   - After the key setup, the resulting inner state is saved as a master
+     state.  Then the IV setup is run to obtain the first encryption
+     starting state.
+
+   - Whenever re-initialization under a new IV is necessary, the IV
+     setup is run on the master state again to derive the next
+     encryption starting state.
+
+2.5.  Counter System
+
+   Before each execution of the next-state function (Section 2.6), the
+   counter system has to be updated.  This system uses constants
+   A1,...,A7, as follows:
+
+     A0 = 0x4D34D34D         A1 = 0xD34D34D3
+     A2 = 0x34D34D34         A3 = 0x4D34D34D
+     A4 = 0xD34D34D3         A5 = 0x34D34D34
+     A6 = 0x4D34D34D         A7 = 0xD34D34D3
+
+   It also uses the counter carry bit b to update the counter system, as
+   follows:
+
+     for j=0 to 7:
+       temp = Cj + Aj + b
+       b    = temp div WORDSIZE
+       Cj   = temp mod WORDSIZE
+
+   Note that on exiting this loop, the variable b has to be preserved
+   for the next iteration of the system.
+
+2.6.  Next-State Function
+
+   The core of the Rabbit algorithm is the next-state function.  It is
+   based on the function g, which transforms two 32-bit inputs into one
+   32-bit output, as follows:
+
+     g(u,v) = LSW(square(u+v)) ^ MSW(square(u+v))
+
+   where square(u+v) = ((u+v mod WORDSIZE) * (u+v mod WORDSIZE)).
+
+
+
+Boesgaard, et al.            Informational                      [Page 4]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+   Using this function, the algorithm updates the inner state as
+   follows:
+
+     for j=0 to 7:
+       Gj = g(Xj,Cj)
+
+     X0 = G0 + (G7 <<< 16) + (G6 <<< 16) mod WORDSIZE
+     X1 = G1 + (G0 <<<  8) +  G7         mod WORDSIZE
+     X2 = G2 + (G1 <<< 16) + (G0 <<< 16) mod WORDSIZE
+     X3 = G3 + (G2 <<<  8) +  G1         mod WORDSIZE
+     X4 = G4 + (G3 <<< 16) + (G2 <<< 16) mod WORDSIZE
+     X5 = G5 + (G4 <<<  8) +  G3         mod WORDSIZE
+     X6 = G6 + (G5 <<< 16) + (G4 <<< 16) mod WORDSIZE
+     X7 = G7 + (G6 <<<  8) +  G5         mod WORDSIZE
+
+2.7.  Extraction Scheme
+
+   After the key and IV setup are concluded, the algorithm is iterated
+   in order to produce one 128-bit output block, S, per round.  Each
+   round consists of executing steps 2.5 and 2.6 and then extracting an
+   output S[127..0] as follows:
+
+     S[15..0]    = X0[15..0]  ^ X5[31..16]
+     S[31..16]   = X0[31..16] ^ X3[15..0]
+     S[47..32]   = X2[15..0]  ^ X7[31..16]
+     S[63..48]   = X2[31..16] ^ X5[15..0]
+     S[79..64]   = X4[15..0]  ^ X1[31..16]
+     S[95..80]   = X4[31..16] ^ X7[15..0]
+     S[111..96]  = X6[15..0]  ^ X3[31..16]
+     S[127..112] = X6[31..16] ^ X1[15..0]
+
+2.8.  Encryption/Decryption Scheme
+
+   Given a 128-bit message block, M, encryption E and decryption M' are
+   computed via
+
+     E  = M ^ S    and
+     M' = E ^ S.
+
+   If S is the same in both operations (as it should be if the same key
+   and IV are used), then M = M'.
+
+   The encryption/decryption scheme is repeated until all blocks in the
+   message have been encrypted/decrypted.  If the message size is not a
+   multiple of 128 bits, only the needed amount of least significant
+   bits from the last output block S is used for the last message block
+   M.
+
+
+
+
+Boesgaard, et al.            Informational                      [Page 5]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+   If the application requires the encryption of smaller blocks (or even
+   individual bits), a 128-bit buffer is used.  The buffer is
+   initialized by generating a new value, S, and copying it into the
+   buffer.  After that, all data blocks are encrypted using the least
+   significant bits in this buffer.  Whenever the buffer is empty, a new
+   value S is generated and copied into the buffer.
+
+3.  Security Considerations
+
+   For an encryption algorithm, the security provided is, of course, the
+   most important issue.  No security weaknesses have been found to
+   date, neither by the designers nor by independent cryptographers
+   scrutinizing the algorithms after its publication in [1].  Note that
+   a full discussion of Rabbit's security against known cryptanalytic
+   techniques is provided in [3].
+
+   In the following, we restrict ourselves to some rules on how to use
+   the Rabbit algorithm properly.
+
+3.1.  Message Length
+
+   Rabbit was designed to encrypt up to 2 to the power of 64 128-bit
+   message blocks under the same the key.  Should this amount of data
+   ever be exceeded, the key has to be replaced.  It is recommended to
+   follow this rule even when the IV is changed on a regular basis.
+
+3.2.  Initialization Vector
+
+   It is possible to run Rabbit without the IV setup.  However, in this
+   case, the generator must never be reset under the same key, since
+   this would destroy its security (for a recent example, see [4]).
+   However, in order to guarantee synchronization between sender and
+   receiver, ciphers are frequently reset in practice.  This means that
+   both sender and receiver set the inner state of the cipher back to a
+   known value and then derive the new encryption state using an IV.  If
+   this is done, it is important to make sure that no IV is ever reused
+   under the same key.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                      [Page 6]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+4.  Informative References
+
+   [1]   M. Boesgaard, M. Vesterager, T. Pedersen, J. Christiansen, O.
+         Scavenius. "Rabbit: A New High-Performance Stream Cipher".
+         Proc. Fast Software Encryption 2003, Lecture Notes in Computer
+         Science 2887, p. 307-329. Springer, 2003.
+
+   [2]   ECRYPT eSTREAM project, available from
+         http://www.ecrypt.eu.org/stream/
+
+   [3]   M. Boesgaard, T. Pedersen, M. Vesterager, E. Zenner. "The
+         Rabbit Stream Cipher - Design and Security Analysis". Proc.
+         SASC Workshop 2004, available from
+         http://www.isg.rhul.ac.uk/research/
+         projects/ecrypt/stvl/sasc.html.
+
+   [4]   H. Wu. "The Misuse of RC4 in Microsoft Word and Excel". IACR
+         eprint archive 2005/007, available from
+         http://eprint.iacr.org/2005/007.pdf.
+
+   [5]   Jonsson, J. and B. Kaliski, "Public-Key Cryptography Standards
+         (PKCS) #1: RSA Cryptography Specifications Version 2.1", RFC
+         3447, February 2003.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                      [Page 7]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+Appendix A: Test Vectors
+
+   This is a set of test vectors for conformance testing, given in octet
+   form.  For use with Rabbit, they have to be transformed into integers
+   by the conversion primitives OS2IP and I2OSP, as described in [5].
+
+A.1.  Testing without IV Setup
+
+     key  = [00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00]
+     S[0] = [B1 57 54 F0 36 A5 D6 EC F5 6B 45 26 1C 4A F7 02]
+     S[1] = [88 E8 D8 15 C5 9C 0C 39 7B 69 6C 47 89 C6 8A A7]
+     S[2] = [F4 16 A1 C3 70 0C D4 51 DA 68 D1 88 16 73 D6 96]
+
+     key  = [91 28 13 29 2E 3D 36 FE 3B FC 62 F1 DC 51 C3 AC]
+     S[0] = [3D 2D F3 C8 3E F6 27 A1 E9 7F C3 84 87 E2 51 9C]
+     S[1] = [F5 76 CD 61 F4 40 5B 88 96 BF 53 AA 85 54 FC 19]
+     S[2] = [E5 54 74 73 FB DB 43 50 8A E5 3B 20 20 4D 4C 5E]
+
+     key  = [83 95 74 15 87 E0 C7 33 E9 E9 AB 01 C0 9B 00 43]
+     S[0] = [0C B1 0D CD A0 41 CD AC 32 EB 5C FD 02 D0 60 9B]
+     S[1] = [95 FC 9F CA 0F 17 01 5A 7B 70 92 11 4C FF 3E AD]
+     S[2] = [96 49 E5 DE 8B FC 7F 3F 92 41 47 AD 3A 94 74 28]
+
+A.2.  Testing with IV Setup
+
+     mkey = [00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00]
+     iv   = [00 00 00 00 00 00 00 00]
+     S[0] = [C6 A7 27 5E F8 54 95 D8 7C CD 5D 37 67 05 B7 ED]
+     S[1] = [5F 29 A6 AC 04 F5 EF D4 7B 8F 29 32 70 DC 4A 8D]
+     S[2] = [2A DE 82 2B 29 DE 6C 1E E5 2B DB 8A 47 BF 8F 66]
+
+     iv   = [C3 73 F5 75 C1 26 7E 59]
+     S[0] = [1F CD 4E B9 58 00 12 E2 E0 DC CC 92 22 01 7D 6D]
+     S[1] = [A7 5F 4E 10 D1 21 25 01 7B 24 99 FF ED 93 6F 2E]
+     S[2] = [EB C1 12 C3 93 E7 38 39 23 56 BD D0 12 02 9B A7]
+
+     iv   = [A6 EB 56 1A D2 F4 17 27]
+     S[0] = [44 5A D8 C8 05 85 8D BF 70 B6 AF 23 A1 51 10 4D]
+     S[1] = [96 C8 F2 79 47 F4 2C 5B AE AE 67 C6 AC C3 5B 03]
+     S[2] = [9F CB FC 89 5F A7 1C 17 31 3D F0 34 F0 15 51 CB]
+
+
+
+
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                      [Page 8]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+Appendix B: Debugging Vectors
+
+   The following set of vectors describes the inner state of Rabbit
+   during key and iv setup.  It is meant mainly for debugging purposes.
+   Octet strings are written according to I2OSP conventions.
+
+B.1.  Testing Round Function and Key Setup
+
+     key  = [91 28 13 29 2E ED 36 FE 3B FC 62 F1 DC 51 C3 AC]
+
+     Inner state after key expansion:
+     b  = 0
+     X0 = 0xDC51C3AC, X1 = 0x13292E3D, X2 = 0x3BFC62F1, X3 = 0xC3AC9128,
+     X4 = 0x2E3D36FE, X5 = 0x62F1DC51, X6 = 0x91281329, X7 = 0x36FE3BFC,
+     C0 = 0x36FE2E3D, C1 = 0xDC5162F1, C2 = 0x13299128, C3 = 0x3BFC36FE,
+     C4 = 0xC3ACDC51, C5 = 0x2E3D1329, C6 = 0x62F13BFC, C7 = 0x9128C3AC
+
+     Inner state after first key setup iteration:
+     b  = 1
+     X0 = 0xF2E8C8B1, X1 = 0x38E06FA7, X2 = 0x9A0D72C0, X3 = 0xF21F5334,
+     X4 = 0xCACDCCC3, X5 = 0x4B239CBE, X6 = 0x0565DCCC, X7 = 0xB1587C8D,
+     C0 = 0x8433018A, C1 = 0xAF9E97C4, C2 = 0x47FCDE5D, C3 = 0x89310A4B,
+     C4 = 0x96FA1124, C5 = 0x6310605E, C6 = 0xB0260F49, C7 = 0x6475F87F
+
+     Inner state after fourth key setup iteration:
+     b  = 0
+     X0 = 0x1D059312, X1 = 0xBDDC3E45, X2 = 0xF440927D, X3 = 0x50CBB553,
+     X4 = 0x36709423, X5 = 0x0B6F0711, X6 = 0x3ADA3A7B, X7 = 0xEB9800C8,
+     C0 = 0x6BD17B74, C1 = 0x2986363E, C2 = 0xE676C5FC, C3 = 0x70CF8432,
+     C4 = 0x10E1AF9E, C5 = 0x018A47FD, C6 = 0x97C48931, C7 = 0xDE5D96F9
+
+     Inner state after final key setup xor:
+     b  = 0
+     X0 = 0x1D059312, X1 = 0xBDDC3E45, X2 = 0xF440927D, X3 = 0x50CBB553,
+     X4 = 0x36709423, X5 = 0x0B6F0711, X6 = 0x3ADA3A7B, X7 = 0xEB9800C8,
+     C0 = 0x5DA1EF57, C1 = 0x22E9312F, C2 = 0xDCACFF87, C3 = 0x9B5784FA,
+     C4 = 0x0DE43C8C, C5 = 0xBC5679B8, C6 = 0x63841B4C, C7 = 0x8E9623AA
+
+     Inner state after generation of 48 bytes of output:
+     b  = 1
+     X0 = 0xB5428566, X1 = 0xA2593617, X2 = 0xFF5578DE, X3 = 0x7293950F,
+     X4 = 0x145CE109, X5 = 0xC93875B0, X6 = 0xD34306E0, X7 = 0x43FEEF87,
+     C0 = 0x45406940, C1 = 0x9CD0CFA9, C2 = 0x7B26E725, C3 = 0x82F5FEE2,
+     C4 = 0x87CBDB06, C5 = 0x5AD06156, C6 = 0x4B229534, C7 = 0x087DC224
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                      [Page 9]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+     The 48 output bytes:
+     S[0] = [3D 2D F3 C8 3E F6 27 A1 E9 7F C3 84 87 E2 51 9C]
+     S[1] = [F5 76 CD 61 F4 40 5B 88 96 BF 53 AA 85 54 FC 19]
+     S[2] = [E5 54 74 73 FB DB 43 50 8A E5 3B 20 20 4D 4C 5E]
+
+B.2.  Testing the IV Setup
+
+     key  = [91 28 13 29 2E ED 36 FE 3B FC 62 F1 DC 51 C3 AC]
+     iv   = [C3 73 F5 75 C1 26 7E 59]
+
+     Inner state during key setup:
+     as above
+
+     Inner state after IV expansion:
+     b  = 0
+     X0 = 0x1D059312, X1 = 0xBDDC3E45, X2 = 0xF440927D, X3 = 0x50CBB553,
+     X4 = 0x36709423, X5 = 0x0B6F0711, X6 = 0x3ADA3A7B, X7 = 0xEB9800C8,
+     C0 = 0x9C87910E, C1 = 0xE19AF009, C2 = 0x1FDF0AF2, C3 = 0x6E22FAA3,
+     C4 = 0xCCC242D5, C5 = 0x7F25B89E, C6 = 0xA0F7EE39, C7 = 0x7BE35DF3
+
+     Inner state after first IV setup iteration:
+     b  = 1
+     X0 = 0xC4FF831A, X1 = 0xEF5CD094, X2 = 0xC5933855, X3 = 0xC05A5C03,
+     X4 = 0x4A50522F, X5 = 0xDF487BE4, X6 = 0xA45FA013, X7 = 0x05531179,
+     C0 = 0xE9BC645B, C1 = 0xB4E824DC, C2 = 0x54B25827, C3 = 0xBB57CDF0,
+     C4 = 0xA00F77A8, C5 = 0xB3F905D3, C6 = 0xEE2CC186, C7 = 0x4F3092C6
+
+     Inner state after fourth IV setup iteration:
+     b  = 1
+     X0 = 0x6274E424, X1 = 0xE14CE120, X2 = 0xDA8739D9, X3 = 0x65E0402D,
+     X4 = 0xD1281D10, X5 = 0xBD435BAA, X6 = 0x4E9E7A02, X7 = 0x9B467ABD,
+     C0 = 0xD15ADE44, C1 = 0x2ECFC356, C2 = 0xF32C3FC6, C3 = 0xA2F647D7,
+     C4 = 0x19F71622, C5 = 0x5272ED72, C6 = 0xD5CB3B6E, C7 = 0xC9183140
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                     [Page 10]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+Authors' Addresses
+
+   Martin Boesgaard
+   Cryptico A/S
+   Fruebjergvej 3
+   2100 Copenhagen
+   Denmark
+
+   Phone: +45 39 17 96 06
+   EMail: mab@cryptico.com
+   URL:   http://www.cryptico.com
+
+
+   Mette Vesterager
+   Cryptico A/S
+   Fruebjergvej 3
+   2100 Copenhagen
+   Denmark
+
+   Phone: +45 39 17 96 06
+   EMail: mvp@cryptico.com
+   URL:   http://www.cryptico.com
+
+
+   Erik Zenner
+   Cryptico A/S
+   Fruebjergvej 3
+   2100 Copenhagen
+   Denmark
+
+   Phone: +45 39 17 96 06
+   EMail: ez@cryptico.com
+   URL:   http://www.cryptico.com
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                     [Page 11]
+
+RFC 4503                   Rabbit Encryption                    May 2006
+
+
+Full Copyright Statement
+
+   Copyright (C) The Internet Society (2006).
+
+   This document is subject to the rights, licenses and restrictions
+   contained in BCP 78, and except as set forth therein, the authors
+   retain all their rights.
+
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+
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+
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+
+Acknowledgement
+
+   Funding for the RFC Editor function is provided by the IETF
+   Administrative Support Activity (IASA).
+
+
+
+
+
+
+
+Boesgaard, et al.            Informational                     [Page 12]
+