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.

   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

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

   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])

     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)).

   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.

   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.

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.

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]

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

     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

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

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