



Internet Research Task Force (IRTF)                           B. Viguier
Request for Comments: 9861                                 ABN AMRO Bank
Category: Informational                                     D. Wong, Ed.
ISSN: 2070-1721                                               zkSecurity
                                                      G. Van Assche, Ed.
                                                      STMicroelectronics
                                                            Q. Dang, Ed.
                                                                    NIST
                                                          J. Daemen, Ed.
                                                      Radboud University
                                                            October 2025


                     KangarooTwelve and TurboSHAKE

Abstract

   This document defines four eXtendable-Output Functions (XOFs), hash
   functions with output of arbitrary length, named TurboSHAKE128,
   TurboSHAKE256, KT128, and KT256.

   All four functions provide efficient and secure hashing primitives,
   and the last two are able to exploit the parallelism of the
   implementation in a scalable way.

   This document is a product of the Crypto Forum Research Group.  It
   builds up on the definitions of the permutations and of the sponge
   construction in NIST FIPS 202 and is meant to serve as a stable
   reference and an implementation guide.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Research Task Force
   (IRTF).  The IRTF publishes the results of Internet-related research
   and development activities.  These results might not be suitable for
   deployment.  This RFC represents the consensus of the Crypto Forum
   Research Group of the Internet Research Task Force (IRTF).  Documents
   approved for publication by the IRSG are not candidates for any level
   of Internet Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9861.

Copyright Notice

   Copyright (c) 2025 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.

Table of Contents

   1.  Introduction
     1.1.  Conventions
   2.  TurboSHAKE
     2.1.  Interface
     2.2.  Specifications
   3.  KangarooTwelve: Tree Hashing over TurboSHAKE
     3.1.  Interface
     3.2.  Specification of KT128
     3.3.  length_encode( x )
     3.4.  Specification of KT256
   4.  Message Authentication Codes
   5.  Test Vectors
   6.  IANA Considerations
   7.  Security Considerations
   8.  References
     8.1.  Normative References
     8.2.  Informative References
   Appendix A.  Pseudocode
     A.1.  Keccak-p[1600,n_r=12]
     A.2.  TurboSHAKE128
     A.3.  TurboSHAKE256
     A.4.  KT128
     A.5.  KT256
   Authors' Addresses

1.  Introduction

   This document defines the TurboSHAKE128, TurboSHAKE256 [TURBOSHAKE],
   KT128, and KT256 [KT] eXtendable-Output Functions (XOFs), i.e., hash
   function generalizations that can return an output of arbitrary
   length.  Both TurboSHAKE128 and TurboSHAKE256 are based on a Keccak-p
   permutation specified in [FIPS202] and have a higher speed than the
   SHA-3 and SHAKE functions.

   TurboSHAKE is a sponge function family that makes use of Keccak-
   p[n_r=12,b=1600], a round-reduced version of the permutation used in
   SHA-3.  Similarly to the SHAKE's security, it proposes two security
   strengths: 128 bits for TurboSHAKE128 and 256 bits for TurboSHAKE256.
   Halving the number of rounds compared to the original SHAKE functions
   makes TurboSHAKE roughly two times faster.

   KangarooTwelve applies tree hashing on top of TurboSHAKE and
   comprises two functions, KT128 and KT256.  Note that [KT] only
   defined KT128 under the name KangarooTwelve.  KT256 is defined in
   this document.

   The SHA-3 and SHAKE functions process data in a serial manner and are
   strongly limited in exploiting available parallelism in modern CPU
   architectures.  Similar to ParallelHash [SP800-185], KangarooTwelve
   splits the input message into fragments.  It then applies TurboSHAKE
   on each of them separately before applying TurboSHAKE again on the
   combination of the first fragment and the digests.  More precisely,
   KT128 uses TurboSHAKE128 and KT256 uses TurboSHAKE256.  They make use
   of Sakura coding for ensuring soundness of the tree hashing mode
   [SAKURA].  The use of TurboSHAKE in KangarooTwelve makes it faster
   than ParallelHash.

   The security of TurboSHAKE128, TurboSHAKE256, KT128, and KT256 builds
   on the public scrutiny that Keccak has received since its publication
   [KECCAK_CRYPTANALYSIS] [TURBOSHAKE].

   With respect to functions defined in [FIPS202] and [SP800-185],
   TurboSHAKE128, TurboSHAKE256, KT128, and KT256 feature the following
   advantages:

   *  Unlike SHA3-224, SHA3-256, SHA3-384, and SHA3-512, the TurboSHAKE
      and KangarooTwelve functions have an extendable output.

   *  Unlike any functions in [FIPS202], and similar to functions in
      [SP800-185], KT128 and KT256 allow the use of a customization
      string.

   *  Unlike any functions in [FIPS202] and [SP800-185] except for
      ParallelHash, KT128 and KT256 exploit available parallelism.

   *  Unlike ParallelHash, KT128 and KT256 do not have overhead when
      processing short messages.

   *  The permutation in the TurboSHAKE functions has half the number of
      rounds compared to the one in the SHA-3 and SHAKE functions,
      making them faster than any function defined in [FIPS202].  The
      KangarooTwelve functions immediately benefit from the same
      speedup, improving over [FIPS202] and [SP800-185].

   With respect to SHA-256, SHA-512, and other functions defined in
   [FIPS180], TurboSHAKE128, TurboSHAKE256, KT128, and KT256 feature the
   following advantages:

   *  Unlike any functions in [FIPS180], the TurboSHAKE and
      KangarooTwelve functions have an extendable output.

   *  The TurboSHAKE functions produce output at the same rate as they
      process input, whereas SHA-256 and SHA-512, when used in a mask
      generation function (MGF) construction, produce output half as
      fast as they process input.

   *  Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
      TurboSHAKE256, KT128, and KT256 do not suffer from the length
      extension weakness.

   *  Unlike any functions in [FIPS180], TurboSHAKE128, TurboSHAKE256,
      KT128, and KT256 use a round function with algebraic degree 2,
      which makes them more suitable to masking techniques for
      protections against side-channel attacks.

   This document represents the consensus of the Crypto Forum Research
   Group (CFRG) in the IRTF.  It has been reviewed by two members of the
   Crypto Review Panel, as well as by several members of the CFRG.  It
   is not an IETF product and is not a standard.

1.1.  Conventions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The following notations are used throughout the document:

   *  `...` denotes a string of bytes given in hexadecimal.  For
      example, `0B 80`.

   *  |s| denotes the length of a byte string `s`.  For example, |`FF
      FF`| = 2.

   *  `00`^b denotes a byte string consisting of the concatenation of b
      bytes `00`. For example, `00`^7 = `00 00 00 00 00 00 00`.

   *  `00`^0 denotes the empty byte string.

   *  a||b denotes the concatenation of two strings, a and b.  For
      example, `10`||`F1` = `10 F1`.

   *  s[n:m] denotes the selection of bytes from n (inclusive) to m
      (exclusive) of a string s.  The indexing of a byte string starts
      at 0.  For example, for s = `A5 C6 D7`, s[0:1] = `A5` and s[1:3] =
      `C6 D7`.

   *  s[n:] denotes the selection of bytes from n to the end of a string
      s.  For example, for s = `A5 C6 D7`, s[0:] = `A5 C6 D7` and s[2:]
      = `D7`.

   In the following, x and y are byte strings of equal length:

   *  x^=y denotes x takes the value x XOR y.

   *  x & y denotes x AND y.

   In the following, x and y are integers:

   *  x+=y denotes x takes the value x + y.

   *  x-=y denotes x takes the value x - y.

   *  x**y denotes the exponentiation of x by y.

   *  x mod y denotes the remainder of the division of x by y.

   *  x / y denotes the integer dividend of the division of x by y.

2.  TurboSHAKE

2.1.  Interface

   TurboSHAKE is a family of eXtendable-Output Functions (XOFs).
   Internally, it makes use of the sponge construction, parameterized by
   two integers, the rate and the capacity, that sum to the permutation
   width (here, 1600 bits).  The rate gives the number of bits processed
   or produced per call to the permutation, whereas the capacity
   determines the security level; see [FIPS202] for more details.  This
   document focuses on only two instances, namely TurboSHAKE128 and
   TurboSHAKE256.  (Note that the original definition includes a wider
   range of instances parameterized by their capacity [TURBOSHAKE].)

   A TurboSHAKE instance takes a byte string M, an OPTIONAL byte D, and
   a positive integer L as input parameters, where:

   *  M byte string is the message,

   *  D byte in the range [`01`, `02`, .. , `7F`] is an OPTIONAL domain
      separation byte, and

   *  L positive integer is the requested number of output bytes.

   Conceptually, an XOF can be viewed as a hash function with an
   infinitely long output truncated to L bytes.  This means that calling
   an XOF with the same input parameters but two different lengths
   yields outputs such that the shorter one is a prefix of the longer
   one.  Specifically, if L1 < L2, then TurboSHAKE(M, D, L1) is the same
   as the first L1 bytes of TurboSHAKE(M, D, L2).

   By default, the domain separation byte is `1F`. For an API that does
   not support a domain separation byte, D MUST be the `1F`.

   The TurboSHAKE instance produces output that is a hash of the (M, D)
   couple.  If D is fixed, this becomes a hash of the message M.
   However, a protocol that requires a number of independent hash
   functions can choose different values for D to implement these.
   Specifically, for distinct values D1 and D2, TurboSHAKE(M, D1, L1)
   and TurboSHAKE(M, D2, L2) yield independent hashes of M.

   Note that an implementation MAY propose an incremental input
   interface where the input string M is given in pieces.  If so, the
   output MUST be the same as if the function was called with M equal to
   the concatenation of the different pieces in the order they were
   given.  Independently, an implementation MAY propose an incremental
   output interface where the output string is requested in pieces of
   given lengths.  When the output is formed by concatenating the pieces
   in the requested order, it MUST be the same as if the function was
   called with L equal to the sum of the given lengths.

2.2.  Specifications

   TurboSHAKE makes use of the permutation Keccak-p[1600,n_r=12], i.e.,
   the permutation used in SHAKE and SHA-3 functions reduced to its last
   n_r=12 rounds as specified in FIPS 202; see Sections 3.3 and 3.4 of
   [FIPS202].  KP denotes this permutation.

   Similarly to SHAKE128, TurboSHAKE128 is a sponge function calling
   this permutation KP with a rate of 168 bytes or 1344 bits.  It
   follows that TurboSHAKE128 has a capacity of 1600 - 1344 = 256 bits
   or 32 bytes.  Respectively to SHAKE256, TurboSHAKE256 makes use of a
   rate of 136 bytes or 1088 bits and has a capacity of 512 bits or 64
   bytes.

                 +---------------+===========+==========+
                 |               | Rate      | Capacity |
                 +===============+===========+==========+
                 | TurboSHAKE128 | 168 Bytes | 32 Bytes |
                 +===============+-----------+----------+
                 | TurboSHAKE256 | 136 Bytes | 64 Bytes |
                 +===============+-----------+----------+

                                 Table 1

   We now describe the operations inside TurboSHAKE128.

   *  First, the input M' is formed by appending the domain separation
      byte D to the message M.

   *  If the length of M' is not a multiple of 168 bytes, then it is
      padded with zeros at the end to make it a multiple of 168 bytes.
      If M' is already a multiple of 168 bytes, then no padding is
      added.  Then, a byte `80` is XORed to the last byte of the padded
      input M' and the resulting string is split into a sequence of
      168-byte blocks.

   *  M' never has a length of 0 bytes due to the presence of the domain
      separation byte.

   *  As defined by the sponge construction, the process operates on a
      state and consists of two phases: the absorbing phase, which
      processes the padded input M', and the squeezing phase, which
      produces the output.

   *  In the absorbing phase, the state is initialized to all zero.  The
      message blocks are XORed into the first 168 bytes of the state.
      Each block absorbed is followed with an application of KP to the
      state.

   *  In the squeezing phase, the output is formed by taking the first
      168 bytes of the state, applying KP to the state, and repeating as
      many times as is necessary.

   TurboSHAKE256 performs the same steps but makes use of 136-byte
   blocks with respect to the padding, absorbing, and squeezing phases.

   The definition of the TurboSHAKE functions equivalently implements
   the pad10*1 rule; see Section 5.1 of [FIPS202] for a definition of
   pad10*1.  While M can be empty, the D byte is always present and is
   in the `01`-`7F` range.  This last byte serves as domain separation
   and integrates the first bit of padding of the pad10*1 rule (hence,
   it cannot be `00`).  Additionally, it must leave room for the second
   bit of padding (hence, it cannot have the most significant bit (MSB)
   set to 1), should it be the last byte of the block.  For more
   details, refer to Section 6.1 of [KT] and Section 3 of [TURBOSHAKE].

   The pseudocode versions of TurboSHAKE128 and TurboSHAKE256 are
   provided in Appendices A.2 and A.3, respectively.

3.  KangarooTwelve: Tree Hashing over TurboSHAKE

3.1.  Interface

   KangarooTwelve is a family of eXtendable-Output Functions (XOFs)
   consisting of the KT128 and KT256 instances.  A KangarooTwelve
   instance takes two byte strings (M, C) and a positive integer L as
   input parameters, where:

   *  M byte string is the message,

   *  C byte string is an OPTIONAL customization string, and

   *  L positive integer is the requested number of output bytes.

   The customization string MAY serve as domain separation.  It is
   typically a short string such as a name or an identifier (e.g., URI,
   Object Identifier (OID), etc.).  It can serve the same purpose as
   TurboSHAKE's D input parameter (see Section 2.1) but with a larger
   range.

   By default, the customization string is the empty string.  For an API
   that does not support a customization string parameter, C MUST be the
   empty string.

   Note that an implementation MAY propose an interface with the input
   and/or output provided incrementally, as specified in Section 2.1.

3.2.  Specification of KT128

   On top of the sponge function TurboSHAKE128, KT128 uses a Sakura-
   compatible tree hash mode [SAKURA].  First, merge M and the OPTIONAL
   C to a single input string S in a reversible way.
   length_encode( |C| ) gives the length in bytes of C as a byte string.
   See Section 3.3.

       S = M || C || length_encode( |C| )

   Then, split S into n chunks of 8192 bytes.

       S = S_0 || .. || S_(n-1)
       |S_0| = .. = |S_(n-2)| = 8192 bytes
       |S_(n-1)| <= 8192 bytes

   From S_1 .. S_(n-1), compute the 32-byte chaining values CV_1 ..
   CV_(n-1).  In order to be optimally efficient, this computation MAY
   exploit the parallelism available on the platform, such as single
   instruction, multiple data (SIMD) instructions.

       CV_i = TurboSHAKE128( S_i, `0B`, 32 )

   Compute the final node: FinalNode.

   *  If |S| <= 8192 bytes, FinalNode = S.

   *  Otherwise, compute FinalNode as follows:

       FinalNode = S_0 || `03 00 00 00 00 00 00 00`
       FinalNode = FinalNode || CV_1
                   ..
       FinalNode = FinalNode || CV_(n-1)
       FinalNode = FinalNode || length_encode(n-1)
       FinalNode = FinalNode || `FF FF`

   Finally, the KT128 output is retrieved:

   *  If |S| <= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L )

          KT128( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )

   *  Otherwise, from TurboSHAKE128( FinalNode, `06`, L )

          KT128( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L )

   The following figure illustrates the computation flow of KT128
   for |S| <= 8192 bytes:

       +--------------+  TurboSHAKE128(.., `07`, L)
       |      S       |----------------------------->  output
       +--------------+

   The following figure illustrates the computation flow of KT128
   for |S| > 8192 bytes and where TurboSHAKE128 and length_encode( x )
   are abbreviated as TSHK128 and l_e( x ), respectively:

                                   +--------------+
                                   |     S_0      |
                                   +--------------+
                                         ||
                                   +--------------+
                                   | `03`||`00`^7 |
                                   +--------------+
                                         ||
 +---------+  TSHK128(..,`0B`,32)  +--------------+
 |   S_1   |---------------------->|     CV_1     |
 +---------+                       +--------------+
                                         ||
 +---------+  TSHK128(..,`0B`,32)  +--------------+
 |   S_2   |---------------------->|     CV_2     |
 +---------+                       +--------------+
                                         ||
                ..                       ..
                                         ||
 +---------+  TSHK128(..,`0B`,32)  +--------------+
 | S_(n-1) |----------------------->|   CV_(n-1)  |
 +---------+                       +--------------+
                                         ||
                                   +--------------+
                                   |  l_e( n-1 )  |
                                   +--------------+
                                         ||
                                   +--------------+
                                   |   `FF FF`    |
                                   +--------------+
                                          | TSHK128(.., `06`, L)
                                          +-------------------->  output

   A pseudocode version is provided in Appendix A.4.

   The table below gathers the values of the domain separation bytes
   used by the tree hash mode:

                        +==================+======+
                        | Type             | Byte |
                        +==================+======+
                        | SingleNode       | `07` |
                        +------------------+------+
                        | IntermediateNode | `0B` |
                        +------------------+------+
                        | FinalNode        | `06` |
                        +------------------+------+

                                  Table 2

3.3.  length_encode( x )

   The function length_encode takes as inputs a non-negative integer x <
   256**255 and outputs a string of bytes x_(n-1) || .. || x_0 || n
   where

       x = sum of 256**i * x_i for i from 0 to n-1

   and where n is the smallest non-negative integer such that x <
   256**n.  n is also the length of x_(n-1) || .. || x_0.

   For example, length_encode(0) = `00`, length_encode(12) = `0C 01`,
   and length_encode(65538) = `01 00 02 03`.

   A pseudocode version is as follows, where { b } denotes the byte of
   numerical value b.

     length_encode(x):
       S = `00`^0

       while x > 0
           S = { x mod 256 } || S
           x = x / 256

       S = S || { |S| }

       return S
       end

3.4.  Specification of KT256

   KT256 is specified exactly like KT128, with two differences:

   *  All the calls to TurboSHAKE128 in KT128 are replaced with calls to
      TurboSHAKE256 in KT256.

   *  The chaining values CV_1 to CV_(n-1) are 64 bytes long in KT256
      and are computed as follows:

          CV_i = TurboSHAKE256( S_i, `0B`, 64 )

   A pseudocode version is provided in Appendix A.5.

4.  Message Authentication Codes

   Implementing a Message Authentication Code (MAC) with KT128 or KT256
   MAY use a hash-then-MAC construction.  This document defines and
   recommends a method called HopMAC:

       HopMAC128(Key, M, C, L) = KT128(Key, KT128(M, C, 32), L)
       HopMAC256(Key, M, C, L) = KT256(Key, KT256(M, C, 64), L)

   Similarly to Hashed Message Authentication Code (HMAC), HopMAC
   consists of two calls: an inner call compressing the message M and
   the optional customization string C to a digest and an outer call
   computing the tag from the key and the digest.

   Unlike HMAC, the inner call to KangarooTwelve in HopMAC is keyless
   and does not require additional protection against side channel
   attacks (SCAs).  Consequently, in an implementation that has to
   protect the HopMAC key against an SCA, only the outer call needs
   protection, and this amounts to a single execution of the underlying
   permutation (assuming the key length is at most 69 bytes).

   In any case, TurboSHAKE128, TurboSHAKE256, KT128, and KT256 MAY be
   used to compute a MAC with the key reversibly prepended or appended
   to the input.  For instance, one MAY compute a MAC on short messages
   simply calling KT128 with the key as the customization string, i.e.,
   MAC = KT128(M, Key, L).

5.  Test Vectors

   Test vectors are based on the repetition of the pattern `00 01 02 ..
   F9 FA` with a specific length. ptn(n) defines a string by repeating
   the pattern `00 01 02 .. F9 FA` as many times as necessary and
   truncated to n bytes, for example:

       Pattern for a length of 17 bytes:
       ptn(17) =
         `00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10`

       Pattern for a length of 17**2 bytes:
       ptn(17**2) =
         `00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
          10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
          20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F
          30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F
          40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F
          50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F
          60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F
          70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F
          80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F
          90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F
          A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF
          B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF
          C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF
          D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF
          E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF
          F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA
          00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
          10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
          20 21 22 23 24 25`

     TurboSHAKE128(M=`00`^0, D=`1F`, 32):
       `1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53
        8C D9 45 A3 97 DD EC 54 1F 1C E4 1A F2 C1 B7 4C`

     TurboSHAKE128(M=`00`^0, D=`1F`, 64):
       `1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53
        8C D9 45 A3 97 DD EC 54 1F 1C E4 1A F2 C1 B7 4C
        3E 8C CA E2 A4 DA E5 6C 84 A0 4C 23 85 C0 3C 15
        E8 19 3B DF 58 73 73 63 32 16 91 C0 54 62 C8 DF`

     TurboSHAKE128(M=`00`^0, D=`1F`, 10032), last 32 bytes:
       `A3 B9 B0 38 59 00 CE 76 1F 22 AE D5 48 E7 54 DA
        10 A5 24 2D 62 E8 C6 58 E3 F3 A9 23 A7 55 56 07`

     TurboSHAKE128(M=ptn(17**0 bytes), D=`1F`, 32):
       `55 CE DD 6F 60 AF 7B B2 9A 40 42 AE 83 2E F3 F5
        8D B7 29 9F 89 3E BB 92 47 24 7D 85 69 58 DA A9`

     TurboSHAKE128(M=ptn(17**1 bytes), D=`1F`, 32):
       `9C 97 D0 36 A3 BA C8 19 DB 70 ED E0 CA 55 4E C6
        E4 C2 A1 A4 FF BF D9 EC 26 9C A6 A1 11 16 12 33`

     TurboSHAKE128(M=ptn(17**2 bytes), D=`1F`, 32):
       `96 C7 7C 27 9E 01 26 F7 FC 07 C9 B0 7F 5C DA E1
        E0 BE 60 BD BE 10 62 00 40 E7 5D 72 23 A6 24 D2`

     TurboSHAKE128(M=ptn(17**3 bytes), D=`1F`, 32):
       `D4 97 6E B5 6B CF 11 85 20 58 2B 70 9F 73 E1 D6
        85 3E 00 1F DA F8 0E 1B 13 E0 D0 59 9D 5F B3 72`

     TurboSHAKE128(M=ptn(17**4 bytes), D=`1F`, 32):
       `DA 67 C7 03 9E 98 BF 53 0C F7 A3 78 30 C6 66 4E
        14 CB AB 7F 54 0F 58 40 3B 1B 82 95 13 18 EE 5C`

     TurboSHAKE128(M=ptn(17**5 bytes), D=`1F`, 32):
       `B9 7A 90 6F BF 83 EF 7C 81 25 17 AB F3 B2 D0 AE
        A0 C4 F6 03 18 CE 11 CF 10 39 25 12 7F 59 EE CD`

     TurboSHAKE128(M=ptn(17**6 bytes), D=`1F`, 32):
       `35 CD 49 4A DE DE D2 F2 52 39 AF 09 A7 B8 EF 0C
        4D 1C A4 FE 2D 1A C3 70 FA 63 21 6F E7 B4 C2 B1`

     TurboSHAKE128(M=`FF FF FF`, D=`01`, 32):
       `BF 32 3F 94 04 94 E8 8E E1 C5 40 FE 66 0B E8 A0
        C9 3F 43 D1 5E C0 06 99 84 62 FA 99 4E ED 5D AB`

     TurboSHAKE128(M=`FF`, D=`06`, 32):
       `8E C9 C6 64 65 ED 0D 4A 6C 35 D1 35 06 71 8D 68
        7A 25 CB 05 C7 4C CA 1E 42 50 1A BD 83 87 4A 67`

     TurboSHAKE128(M=`FF FF FF`, D=`07`, 32):
       `B6 58 57 60 01 CA D9 B1 E5 F3 99 A9 F7 77 23 BB
        A0 54 58 04 2D 68 20 6F 72 52 68 2D BA 36 63 ED`

     TurboSHAKE128(M=`FF FF FF FF FF FF FF`, D=`0B`, 32):
       `8D EE AA 1A EC 47 CC EE 56 9F 65 9C 21 DF A8 E1
        12 DB 3C EE 37 B1 81 78 B2 AC D8 05 B7 99 CC 37`

     TurboSHAKE128(M=`FF`, D=`30`, 32):
       `55 31 22 E2 13 5E 36 3C 32 92 BE D2 C6 42 1F A2
        32 BA B0 3D AA 07 C7 D6 63 66 03 28 65 06 32 5B`

     TurboSHAKE128(M=`FF FF FF`, D=`7F`, 32):
       `16 27 4C C6 56 D4 4C EF D4 22 39 5D 0F 90 53 BD
        A6 D2 8E 12 2A BA 15 C7 65 E5 AD 0E 6E AF 26 F9`

     TurboSHAKE256(M=`00`^0, D=`1F`, 64):
       `36 7A 32 9D AF EA 87 1C 78 02 EC 67 F9 05 AE 13
        C5 76 95 DC 2C 66 63 C6 10 35 F5 9A 18 F8 E7 DB
        11 ED C0 E1 2E 91 EA 60 EB 6B 32 DF 06 DD 7F 00
        2F BA FA BB 6E 13 EC 1C C2 0D 99 55 47 60 0D B0`

     TurboSHAKE256(M=`00`^0, D=`1F`, 10032), last 32 bytes:
       `AB EF A1 16 30 C6 61 26 92 49 74 26 85 EC 08 2F
        20 72 65 DC CF 2F 43 53 4E 9C 61 BA 0C 9D 1D 75`

     TurboSHAKE256(M=ptn(17**0 bytes), D=`1F`, 64):
       `3E 17 12 F9 28 F8 EA F1 05 46 32 B2 AA 0A 24 6E
        D8 B0 C3 78 72 8F 60 BC 97 04 10 15 5C 28 82 0E
        90 CC 90 D8 A3 00 6A A2 37 2C 5C 5E A1 76 B0 68
        2B F2 2B AE 74 67 AC 94 F7 4D 43 D3 9B 04 82 E2`

     TurboSHAKE256(M=ptn(17**1 bytes), D=`1F`, 64):
       `B3 BA B0 30 0E 6A 19 1F BE 61 37 93 98 35 92 35
        78 79 4E A5 48 43 F5 01 10 90 FA 2F 37 80 A9 E5
        CB 22 C5 9D 78 B4 0A 0F BF F9 E6 72 C0 FB E0 97
        0B D2 C8 45 09 1C 60 44 D6 87 05 4D A5 D8 E9 C7`

     TurboSHAKE256(M=ptn(17**2 bytes), D=`1F`, 64):
       `66 B8 10 DB 8E 90 78 04 24 C0 84 73 72 FD C9 57
        10 88 2F DE 31 C6 DF 75 BE B9 D4 CD 93 05 CF CA
        E3 5E 7B 83 E8 B7 E6 EB 4B 78 60 58 80 11 63 16
        FE 2C 07 8A 09 B9 4A D7 B8 21 3C 0A 73 8B 65 C0`

     TurboSHAKE256(M=ptn(17**3 bytes), D=`1F`, 64):
       `C7 4E BC 91 9A 5B 3B 0D D1 22 81 85 BA 02 D2 9E
        F4 42 D6 9D 3D 42 76 A9 3E FE 0B F9 A1 6A 7D C0
        CD 4E AB AD AB 8C D7 A5 ED D9 66 95 F5 D3 60 AB
        E0 9E 2C 65 11 A3 EC 39 7D A3 B7 6B 9E 16 74 FB`

     TurboSHAKE256(M=ptn(17**4 bytes), D=`1F`, 64):
       `02 CC 3A 88 97 E6 F4 F6 CC B6 FD 46 63 1B 1F 52
        07 B6 6C 6D E9 C7 B5 5B 2D 1A 23 13 4A 17 0A FD
        AC 23 4E AB A9 A7 7C FF 88 C1 F0 20 B7 37 24 61
        8C 56 87 B3 62 C4 30 B2 48 CD 38 64 7F 84 8A 1D`

     TurboSHAKE256(M=ptn(17**5 bytes), D=`1F`, 64):
       `AD D5 3B 06 54 3E 58 4B 58 23 F6 26 99 6A EE 50
        FE 45 ED 15 F2 02 43 A7 16 54 85 AC B4 AA 76 B4
        FF DA 75 CE DF 6D 8C DC 95 C3 32 BD 56 F4 B9 86
        B5 8B B1 7D 17 78 BF C1 B1 A9 75 45 CD F4 EC 9F`

     TurboSHAKE256(M=ptn(17**6 bytes), D=`1F`, 64):
       `9E 11 BC 59 C2 4E 73 99 3C 14 84 EC 66 35 8E F7
        1D B7 4A EF D8 4E 12 3F 78 00 BA 9C 48 53 E0 2C
        FE 70 1D 9E 6B B7 65 A3 04 F0 DC 34 A4 EE 3B A8
        2C 41 0F 0D A7 0E 86 BF BD 90 EA 87 7C 2D 61 04`

     TurboSHAKE256(M=`FF FF FF`, D=`01`, 64):
       `D2 1C 6F BB F5 87 FA 22 82 F2 9A EA 62 01 75 FB
        02 57 41 3A F7 8A 0B 1B 2A 87 41 9C E0 31 D9 33
        AE 7A 4D 38 33 27 A8 A1 76 41 A3 4F 8A 1D 10 03
        AD 7D A6 B7 2D BA 84 BB 62 FE F2 8F 62 F1 24 24`

     TurboSHAKE256(M=`FF`, D=`06`, 64):
       `73 8D 7B 4E 37 D1 8B 7F 22 AD 1B 53 13 E3 57 E3
        DD 7D 07 05 6A 26 A3 03 C4 33 FA 35 33 45 52 80
        F4 F5 A7 D4 F7 00 EF B4 37 FE 6D 28 14 05 E0 7B
        E3 2A 0A 97 2E 22 E6 3A DC 1B 09 0D AE FE 00 4B`

     TurboSHAKE256(M=`FF FF FF`, D=`07`, 64):
       `18 B3 B5 B7 06 1C 2E 67 C1 75 3A 00 E6 AD 7E D7
        BA 1C 90 6C F9 3E FB 70 92 EA F2 7F BE EB B7 55
        AE 6E 29 24 93 C1 10 E4 8D 26 00 28 49 2B 8E 09
        B5 50 06 12 B8 F2 57 89 85 DE D5 35 7D 00 EC 67`

     TurboSHAKE256(M=`FF FF FF FF FF FF FF`, D=`0B`, 64):
       `BB 36 76 49 51 EC 97 E9 D8 5F 7E E9 A6 7A 77 18
        FC 00 5C F4 25 56 BE 79 CE 12 C0 BD E5 0E 57 36
        D6 63 2B 0D 0D FB 20 2D 1B BB 8F FE 3D D7 4C B0
        08 34 FA 75 6C B0 34 71 BA B1 3A 1E 2C 16 B3 C0`

     TurboSHAKE256(M=`FF`, D=`30`, 64):
       `F3 FE 12 87 3D 34 BC BB 2E 60 87 79 D6 B7 0E 7F
        86 BE C7 E9 0B F1 13 CB D4 FD D0 C4 E2 F4 62 5E
        14 8D D7 EE 1A 52 77 6C F7 7F 24 05 14 D9 CC FC
        3B 5D DA B8 EE 25 5E 39 EE 38 90 72 96 2C 11 1A`

     TurboSHAKE256(M=`FF FF FF`, D=`7F`, 64):
       `AB E5 69 C1 F7 7E C3 40 F0 27 05 E7 D3 7C 9A B7
        E1 55 51 6E 4A 6A 15 00 21 D7 0B 6F AC 0B B4 0C
        06 9F 9A 98 28 A0 D5 75 CD 99 F9 BA E4 35 AB 1A
        CF 7E D9 11 0B A9 7C E0 38 8D 07 4B AC 76 87 76`

     KT128(M=`00`^0, C=`00`^0, 32):
       `1A C2 D4 50 FC 3B 42 05 D1 9D A7 BF CA 1B 37 51
        3C 08 03 57 7A C7 16 7F 06 FE 2C E1 F0 EF 39 E5`

     KT128(M=`00`^0, C=`00`^0, 64):
       `1A C2 D4 50 FC 3B 42 05 D1 9D A7 BF CA 1B 37 51
        3C 08 03 57 7A C7 16 7F 06 FE 2C E1 F0 EF 39 E5
        42 69 C0 56 B8 C8 2E 48 27 60 38 B6 D2 92 96 6C
        C0 7A 3D 46 45 27 2E 31 FF 38 50 81 39 EB 0A 71`

     KT128(M=`00`^0, C=`00`^0, 10032), last 32 bytes:
       `E8 DC 56 36 42 F7 22 8C 84 68 4C 89 84 05 D3 A8
        34 79 91 58 C0 79 B1 28 80 27 7A 1D 28 E2 FF 6D`

     KT128(M=ptn(1 bytes), C=`00`^0, 32):
       `2B DA 92 45 0E 8B 14 7F 8A 7C B6 29 E7 84 A0 58
        EF CA 7C F7 D8 21 8E 02 D3 45 DF AA 65 24 4A 1F`

     KT128(M=ptn(17 bytes), C=`00`^0, 32):
       `6B F7 5F A2 23 91 98 DB 47 72 E3 64 78 F8 E1 9B
        0F 37 12 05 F6 A9 A9 3A 27 3F 51 DF 37 12 28 88`

     KT128(M=ptn(17**2 bytes), C=`00`^0, 32):
       `0C 31 5E BC DE DB F6 14 26 DE 7D CF 8F B7 25 D1
        E7 46 75 D7 F5 32 7A 50 67 F3 67 B1 08 EC B6 7C`

     KT128(M=ptn(17**3 bytes), C=`00`^0, 32):
       `CB 55 2E 2E C7 7D 99 10 70 1D 57 8B 45 7D DF 77
        2C 12 E3 22 E4 EE 7F E4 17 F9 2C 75 8F 0D 59 D0`

     KT128(M=ptn(17**4 bytes), C=`00`^0, 32):
       `87 01 04 5E 22 20 53 45 FF 4D DA 05 55 5C BB 5C
        3A F1 A7 71 C2 B8 9B AE F3 7D B4 3D 99 98 B9 FE`

     KT128(M=ptn(17**5 bytes), C=`00`^0, 32):
       `84 4D 61 09 33 B1 B9 96 3C BD EB 5A E3 B6 B0 5C
        C7 CB D6 7C EE DF 88 3E B6 78 A0 A8 E0 37 16 82`

     KT128(M=ptn(17**6 bytes), C=`00`^0, 32):
       `3C 39 07 82 A8 A4 E8 9F A6 36 7F 72 FE AA F1 32
        55 C8 D9 58 78 48 1D 3C D8 CE 85 F5 8E 88 0A F8`

     KT128(`00`^0, C=ptn(1 bytes), 32):
       `FA B6 58 DB 63 E9 4A 24 61 88 BF 7A F6 9A 13 30
        45 F4 6E E9 84 C5 6E 3C 33 28 CA AF 1A A1 A5 83`

     KT128(`FF`, C=ptn(41 bytes), 32):
       `D8 48 C5 06 8C ED 73 6F 44 62 15 9B 98 67 FD 4C
        20 B8 08 AC C3 D5 BC 48 E0 B0 6B A0 A3 76 2E C4`

     KT128(`FF FF FF`, C=ptn(41**2 bytes), 32):
       `C3 89 E5 00 9A E5 71 20 85 4C 2E 8C 64 67 0A C0
        13 58 CF 4C 1B AF 89 44 7A 72 42 34 DC 7C ED 74`

     KT128(`FF FF FF FF FF FF FF`, C=ptn(41**3 bytes), 32):
       `75 D2 F8 6A 2E 64 45 66 72 6B 4F BC FC 56 57 B9
        DB CF 07 0C 7B 0D CA 06 45 0A B2 91 D7 44 3B CF`

     KT128(M=ptn(8191 bytes), C=`00`^0, 32):
       `1B 57 76 36 F7 23 64 3E 99 0C C7 D6 A6 59 83 74
        36 FD 6A 10 36 26 60 0E B8 30 1C D1 DB E5 53 D6`

     KT128(M=ptn(8192 bytes), C=`00`^0, 32):
       `48 F2 56 F6 77 2F 9E DF B6 A8 B6 61 EC 92 DC 93
        B9 5E BD 05 A0 8A 17 B3 9A E3 49 08 70 C9 26 C3`

     KT128(M=ptn(8192 bytes), C=ptn(8189 bytes), 32):
       `3E D1 2F 70 FB 05 DD B5 86 89 51 0A B3 E4 D2 3C
        6C 60 33 84 9A A0 1E 1D 8C 22 0A 29 7F ED CD 0B`

     KT128(M=ptn(8192 bytes), C=ptn(8190 bytes), 32):
       `6A 7C 1B 6A 5C D0 D8 C9 CA 94 3A 4A 21 6C C6 46
        04 55 9A 2E A4 5F 78 57 0A 15 25 3D 67 BA 00 AE`

     KT256(M=`00`^0, C=`00`^0, 64):
       `B2 3D 2E 9C EA 9F 49 04 E0 2B EC 06 81 7F C1 0C
        E3 8C E8 E9 3E F4 C8 9E 65 37 07 6A F8 64 64 04
        E3 E8 B6 81 07 B8 83 3A 5D 30 49 0A A3 34 82 35
        3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9`

     KT256(M=`00`^0, C=`00`^0, 128):
       `B2 3D 2E 9C EA 9F 49 04 E0 2B EC 06 81 7F C1 0C
        E3 8C E8 E9 3E F4 C8 9E 65 37 07 6A F8 64 64 04
        E3 E8 B6 81 07 B8 83 3A 5D 30 49 0A A3 34 82 35
        3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9
        B0 92 53 19 D8 EA 1E 12 1A 60 98 21 EC 19 EF EA
        89 E6 D0 8D AE E1 66 2B 69 C8 40 28 9F 18 8B A8
        60 F5 57 60 B6 1F 82 11 4C 03 0C 97 E5 17 84 49
        60 8C CD 2C D2 D9 19 FC 78 29 FF 69 93 1A C4 D0`

     KT256(M=`00`^0, C=`00`^0, 10064), last 64 bytes:
       `AD 4A 1D 71 8C F9 50 50 67 09 A4 C3 33 96 13 9B
        44 49 04 1F C7 9A 05 D6 8D A3 5F 1E 45 35 22 E0
        56 C6 4F E9 49 58 E7 08 5F 29 64 88 82 59 B9 93
        27 52 F3 CC D8 55 28 8E FE E5 FC BB 8B 56 30 69`

     KT256(M=ptn(1 bytes), C=`00`^0, 64):
       `0D 00 5A 19 40 85 36 02 17 12 8C F1 7F 91 E1 F7
        13 14 EF A5 56 45 39 D4 44 91 2E 34 37 EF A1 7F
        82 DB 6F 6F FE 76 E7 81 EA A0 68 BC E0 1F 2B BF
        81 EA CB 98 3D 72 30 F2 FB 02 83 4A 21 B1 DD D0`

     KT256(M=ptn(17 bytes), C=`00`^0, 64):
       `1B A3 C0 2B 1F C5 14 47 4F 06 C8 97 99 78 A9 05
        6C 84 83 F4 A1 B6 3D 0D CC EF E3 A2 8A 2F 32 3E
        1C DC CA 40 EB F0 06 AC 76 EF 03 97 15 23 46 83
        7B 12 77 D3 E7 FA A9 C9 65 3B 19 07 50 98 52 7B`

     KT256(M=ptn(17**2 bytes), C=`00`^0, 64):
       `DE 8C CB C6 3E 0F 13 3E BB 44 16 81 4D 4C 66 F6
        91 BB F8 B6 A6 1E C0 A7 70 0F 83 6B 08 6C B0 29
        D5 4F 12 AC 71 59 47 2C 72 DB 11 8C 35 B4 E6 AA
        21 3C 65 62 CA AA 9D CC 51 89 59 E6 9B 10 F3 BA`

     KT256(M=ptn(17**3 bytes), C=`00`^0, 64):
       `64 7E FB 49 FE 9D 71 75 00 17 1B 41 E7 F1 1B D4
        91 54 44 43 20 99 97 CE 1C 25 30 D1 5E B1 FF BB
        59 89 35 EF 95 45 28 FF C1 52 B1 E4 D7 31 EE 26
        83 68 06 74 36 5C D1 91 D5 62 BA E7 53 B8 4A A5`

     KT256(M=ptn(17**4 bytes), C=`00`^0, 64):
       `B0 62 75 D2 84 CD 1C F2 05 BC BE 57 DC CD 3E C1
        FF 66 86 E3 ED 15 77 63 83 E1 F2 FA 3C 6A C8 F0
        8B F8 A1 62 82 9D B1 A4 4B 2A 43 FF 83 DD 89 C3
        CF 1C EB 61 ED E6 59 76 6D 5C CF 81 7A 62 BA 8D`

     KT256(M=ptn(17**5 bytes), C=`00`^0, 64):
       `94 73 83 1D 76 A4 C7 BF 77 AC E4 5B 59 F1 45 8B
        16 73 D6 4B CD 87 7A 7C 66 B2 66 4A A6 DD 14 9E
        60 EA B7 1B 5C 2B AB 85 8C 07 4D ED 81 DD CE 2B
        40 22 B5 21 59 35 C0 D4 D1 9B F5 11 AE EB 07 72`

     KT256(M=ptn(17**6 bytes), C=`00`^0, 64):
       `06 52 B7 40 D7 8C 5E 1F 7C 8D CC 17 77 09 73 82
        76 8B 7F F3 8F 9A 7A 20 F2 9F 41 3B B1 B3 04 5B
        31 A5 57 8F 56 8F 91 1E 09 CF 44 74 6D A8 42 24
        A5 26 6E 96 A4 A5 35 E8 71 32 4E 4F 9C 70 04 DA`

     KT256(`00`^0, C=ptn(1 bytes), 64):
       `92 80 F5 CC 39 B5 4A 5A 59 4E C6 3D E0 BB 99 37
        1E 46 09 D4 4B F8 45 C2 F5 B8 C3 16 D7 2B 15 98
        11 F7 48 F2 3E 3F AB BE 5C 32 26 EC 96 C6 21 86
        DF 2D 33 E9 DF 74 C5 06 9C EE CB B4 DD 10 EF F6`

     KT256(`FF`, C=ptn(41 bytes), 64):
       `47 EF 96 DD 61 6F 20 09 37 AA 78 47 E3 4E C2 FE
        AE 80 87 E3 76 1D C0 F8 C1 A1 54 F5 1D C9 CC F8
        45 D7 AD BC E5 7F F6 4B 63 97 22 C6 A1 67 2E 3B
        F5 37 2D 87 E0 0A FF 89 BE 97 24 07 56 99 88 53`

     KT256(`FF FF FF`, C=ptn(41**2 bytes), 64):
       `3B 48 66 7A 50 51 C5 96 6C 53 C5 D4 2B 95 DE 45
        1E 05 58 4E 78 06 E2 FB 76 5E DA 95 90 74 17 2C
        B4 38 A9 E9 1D DE 33 7C 98 E9 C4 1B ED 94 C4 E0
        AE F4 31 D0 B6 4E F2 32 4F 79 32 CA A6 F5 49 69`

     KT256(`FF FF FF FF FF FF FF`, C=ptn(41**3 bytes), 64):
       `E0 91 1C C0 00 25 E1 54 08 31 E2 66 D9 4A DD 9B
        98 71 21 42 B8 0D 26 29 E6 43 AA C4 EF AF 5A 3A
        30 A8 8C BF 4A C2 A9 1A 24 32 74 30 54 FB CC 98
        97 67 0E 86 BA 8C EC 2F C2 AC E9 C9 66 36 97 24`

     KT256(M=ptn(8191 bytes), C=`00`^0, 64):
       `30 81 43 4D 93 A4 10 8D 8D 8A 33 05 B8 96 82 CE
        BE DC 7C A4 EA 8A 3C E8 69 FB B7 3C BE 4A 58 EE
        F6 F2 4D E3 8F FC 17 05 14 C7 0E 7A B2 D0 1F 03
        81 26 16 E8 63 D7 69 AF B3 75 31 93 BA 04 5B 20`

     KT256(M=ptn(8192 bytes), C=`00`^0, 64):
       `C6 EE 8E 2A D3 20 0C 01 8A C8 7A AA 03 1C DA C2
        21 21 B4 12 D0 7D C6 E0 DC CB B5 34 23 74 7E 9A
        1C 18 83 4D 99 DF 59 6C F0 CF 4B 8D FA FB 7B F0
        2D 13 9D 0C 90 35 72 5A DC 1A 01 B7 23 0A 41 FA`

     KT256(M=ptn(8192 bytes), C=ptn(8189 bytes), 64):
       `74 E4 78 79 F1 0A 9C 5D 11 BD 2D A7 E1 94 FE 57
        E8 63 78 BF 3C 3F 74 48 EF F3 C5 76 A0 F1 8C 5C
        AA E0 99 99 79 51 20 90 A7 F3 48 AF 42 60 D4 DE
        3C 37 F1 EC AF 8D 2C 2C 96 C1 D1 6C 64 B1 24 96`

     KT256(M=ptn(8192 bytes), C=ptn(8190 bytes), 64):
       `F4 B5 90 8B 92 9F FE 01 E0 F7 9E C2 F2 12 43 D4
        1A 39 6B 2E 73 03 A6 AF 1D 63 99 CD 6C 7A 0A 2D
        D7 C4 F6 07 E8 27 7F 9C 9B 1C B4 AB 9D DC 59 D4
        B9 2D 1F C7 55 84 41 F1 83 2C 32 79 A4 24 1B 8B`

6.  IANA Considerations

   In the "Named Information Hash Algorithm Registry", k12-256 refers to
   the hash function obtained by evaluating KT128 on the input message
   with default C (the empty string) and L = 32 bytes (256 bits).
   Similarly, k12-512 refers to the hash function obtained by evaluating
   KT256 on the input message with default C (the empty string) and L =
   64 bytes (512 bits).

   In the "COSE Algorithms" registry, IANA has added the following
   entries for TurboSHAKE and KangarooTwelve:

       +===============+=======+===================+==============+
       | Name          | Value | Description       | Capabilities |
       +===============+=======+===================+==============+
       | TurboSHAKE128 | -261  | TurboSHAKE128 XOF | [kty]        |
       +---------------+-------+-------------------+--------------+
       | TurboSHAKE256 | -262  | TurboSHAKE256 XOF | [kty]        |
       +---------------+-------+-------------------+--------------+
       | KT128         | -263  | KT128 XOF         | [kty]        |
       +---------------+-------+-------------------+--------------+
       | KT256         | -264  | KT256 XOF         | [kty]        |
       +---------------+-------+-------------------+--------------+

                                 Table 3

7.  Security Considerations

   This document is meant to serve as a stable reference and an
   implementation guide for the KangarooTwelve and TurboSHAKE
   eXtendable-Output Functions.  The security assurance of these
   functions relies on the cryptanalysis of reduced-round versions of
   Keccak, and they have the same claimed security strength as their
   corresponding SHAKE functions.

              +---------------+=============================+
              |               | Security Claim              |
              +===============+=============================+
              | TurboSHAKE128 | 128 bits (same as SHAKE128) |
              +===============+-----------------------------+
              | KT128         | 128 bits (same as SHAKE128) |
              +===============+-----------------------------+
              | TurboSHAKE256 | 256 bits (same as SHAKE256) |
              +===============+-----------------------------+
              | KT256         | 256 bits (same as SHAKE256) |
              +===============+-----------------------------+

                                  Table 4

   To be more precise, KT128 is made of two layers:

   *  The inner function TurboSHAKE128.  The security assurance of this
      layer relies on cryptanalysis.  The TurboSHAKE128 function is
      exactly Keccak[r=1344, c=256] (as in SHAKE128) reduced to 12
      rounds.  Any cryptanalysis of reduced-round Keccak is also
      cryptanalysis of reduced-round TurboSHAKE128 (provided the number
      of rounds attacked is not higher than 12).

   *  The tree hashing over TurboSHAKE128.  This layer is a mode on top
      of TurboSHAKE128 that does not introduce any vulnerability thanks
      to the use of Sakura coding proven secure in [SAKURA].

   This reasoning is detailed and formalized in [KT].

   KT256 is structured as KT128, except that it uses TurboSHAKE256 as
   the inner function.  The TurboSHAKE256 function is exactly
   Keccak[r=1088, c=512] (as in SHAKE256) reduced to 12 rounds, and the
   same reasoning on cryptanalysis applies.

   TurboSHAKE128 and KT128 aim at 128-bit security.  To achieve 128-bit
   security strength, L, the chosen output length, MUST be large enough
   so that there are no generic attacks that violate 128-bit security.
   So for 128-bit (second) preimage security, the output should be at
   least 128 bits; for 128 bits of security against multi-target
   preimage attacks with T targets, the output should be at least
   128+log_2(T) bits; and for 128-bit collision security, the output
   should be at least 256 bits.  Furthermore, when the output length is
   at least 256 bits, TurboSHAKE128 and KT128 achieve NIST's post-
   quantum security level 2 [NISTPQ].

   Similarly, TurboSHAKE256 and KT256 aim at 256-bit security.  To
   achieve 256-bit security strength, L, the chosen output length, MUST
   be large enough so that there are no generic attacks that violate
   256-bit security.  So for 256-bit (second) preimage security, the
   output should be at least 256 bits; for 256 bits of security against
   multi-target preimage attacks with T targets, the output should be at
   least 256+log_2(T) bits; and for 256-bit collision security, the
   output should be at least 512 bits.  Furthermore, when the output
   length is at least 512 bits, TurboSHAKE256 and KT256 achieve NIST's
   post-quantum security level 5 [NISTPQ].

   Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
   TurboSHAKE256, KT128, and KT256 do not suffer from the length
   extension weakness and therefore do not require the use of the HMAC
   construction, for instance, when used for MAC computation [FIPS198].
   Also, they can naturally be used as a key derivation function.  The
   input must be an injective encoding of secret and diversification
   material, and the output can be taken as the derived key(s).  The
   input does not need to be uniformly distributed, e.g., it can be a
   shared secret produced by the Diffie-Hellman or Elliptic Curve
   Diffie-Hellman (ECDH) protocol, but it needs to have sufficient min-
   entropy.

   Lastly, as KT128 and KT256 use TurboSHAKE with three values for D,
   namely 0x06, 0x07, and 0x0B, protocols that use both KT128 and
   TurboSHAKE128 or both KT256 and TurboSHAKE256 SHOULD avoid using
   these three values for D.

8.  References

8.1.  Normative References

   [FIPS202]  NIST, "SHA-3 Standard: Permutation-Based Hash and
              Extendable-Output Functions", NIST FIPS 202,
              DOI 10.6028/NIST.FIPS.202, August 2015,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.202.pdf>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [SP800-185]
              Kelsey, J., Chang, S., and R. Perlner, "SHA-3 Derived
              Functions: cSHAKE, KMAC, TupleHash and ParallelHash",
              National Institute of Standards and Technology, NIST
              SP 800-185, DOI 10.6028/NIST.SP.800-185, December 2016,
              <https://doi.org/10.6028/NIST.SP.800-185>.

8.2.  Informative References

   [FIPS180]  NIST, "Secure Hash Standard", NIST FIPS 180-4,
              DOI 10.6028/NIST.FIPS.180-4, August 2015,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.180-4.pdf>.

   [FIPS198]  NIST, "The Keyed-Hash Message Authentication Code (HMAC)",
              NIST FIPS 198-1, DOI 10.6028/NIST.FIPS.198-1, July 2008,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.198-1.pdf>.

   [KECCAK_CRYPTANALYSIS]
              Keccak Team, "Summary of Third-party cryptanalysis of
              Keccak", <https://www.keccak.team/third_party.html>.

   [KT]       Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., Van
              Keer, R., and B. Viguier, "KangarooTwelve: Fast Hashing
              Based on Keccak-p", Applied Cryptography and Network
              Security (ACNS 2018), Lecture Notes in Computer Science,
              vol. 10892, pp. 400-418, DOI 10.1007/978-3-319-93387-0_21,
              June 2018, <https://link.springer.com/
              chapter/10.1007/978-3-319-93387-0_21>.

   [NISTPQ]   NIST, "Submission Requirements and Evaluation Criteria for
              the Post-Quantum Cryptography Standardization Process",
              <https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-
              Cryptography/documents/call-for-proposals-final-dec-
              2016.pdf>.

   [SAKURA]   Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche,
              "Sakura: a Flexible Coding for Tree Hashing", Applied
              Cryptography and Network Security (ACNS 2014), Lecture
              Notes in Computer Science, vol. 8479, pp. 217-234,
              DOI 10.1007/978-3-319-07536-5_14, 2014,
              <https://link.springer.com/
              chapter/10.1007/978-3-319-07536-5_14>.

   [TURBOSHAKE]
              Bertoni, G., Daemen, J., Hoffert, S., Peeters, M., Van
              Assche, G., Van Keer, R., and B. Viguier, "TurboSHAKE",
              Cryptology ePrint Archive, Paper 2023/342, March 2023,
              <http://eprint.iacr.org/2023/342>.

   [XKCP]     "eXtended Keccak Code Package", commit 64404bee, December
              2022, <https://github.com/XKCP/XKCP>.

Appendix A.  Pseudocode

   The subsections of this appendix contain pseudocode definitions of
   TurboSHAKE128, TurboSHAKE256, and KangarooTwelve.  Standalone Python
   versions are also available in the Keccak Code Package [XKCP] and in
   [KT]

A.1.  Keccak-p[1600,n_r=12]

   KP(state):
     RC[0]  = `8B 80 00 80 00 00 00 00`
     RC[1]  = `8B 00 00 00 00 00 00 80`
     RC[2]  = `89 80 00 00 00 00 00 80`
     RC[3]  = `03 80 00 00 00 00 00 80`
     RC[4]  = `02 80 00 00 00 00 00 80`
     RC[5]  = `80 00 00 00 00 00 00 80`
     RC[6]  = `0A 80 00 00 00 00 00 00`
     RC[7]  = `0A 00 00 80 00 00 00 80`
     RC[8]  = `81 80 00 80 00 00 00 80`
     RC[9]  = `80 80 00 00 00 00 00 80`
     RC[10] = `01 00 00 80 00 00 00 00`
     RC[11] = `08 80 00 80 00 00 00 80`

     for x from 0 to 4
       for y from 0 to 4
         lanes[x][y] = state[8*(x+5*y):8*(x+5*y)+8]

     for round from 0 to 11
       # theta
       for x from 0 to 4
         C[x] = lanes[x][0]
         C[x] ^= lanes[x][1]
         C[x] ^= lanes[x][2]
         C[x] ^= lanes[x][3]
         C[x] ^= lanes[x][4]
       for x from 0 to 4
         D[x] = C[(x+4) mod 5] ^ ROL64(C[(x+1) mod 5], 1)
       for y from 0 to 4
         for x from 0 to 4
           lanes[x][y] = lanes[x][y]^D[x]

       # rho and pi
       (x, y) = (1, 0)
       current = lanes[x][y]
       for t from 0 to 23
         (x, y) = (y, (2*x+3*y) mod 5)
         (current, lanes[x][y]) =
             (lanes[x][y], ROL64(current, (t+1)*(t+2)/2))

       # chi
       for y from 0 to 4
         for x from 0 to 4
           T[x] = lanes[x][y]
         for x from 0 to 4
           lanes[x][y] = T[x] ^((not T[(x+1) mod 5]) & T[(x+2) mod 5])

       # iota
       lanes[0][0] ^= RC[round]

     state = `00`^0
     for y from 0 to 4
       for x from 0 to 4
         state = state || lanes[x][y]

     return state
     end

   where ROL64(x, y) is a rotation of the 'x' 64-bit word toward the
   bits with higher indexes by 'y' positions.  The 8-bytes byte string x
   is interpreted as a 64-bit word in little-endian format.

A.2.  TurboSHAKE128

   TurboSHAKE128(message, separationByte, outputByteLen):
     offset = 0
     state = `00`^200
     input = message || separationByte

     # === Absorb complete blocks ===
     while offset < |input| - 168
         state ^= input[offset : offset + 168] || `00`^32
         state = KP(state)
         offset += 168

     # === Absorb last block and treatment of padding ===
     LastBlockLength = |input| - offset
     state ^= input[offset:] || `00`^(200-LastBlockLength)
     state ^= `00`^167 || `80` || `00`^32
     state = KP(state)

     # === Squeeze ===
     output = `00`^0
     while outputByteLen > 168
         output = output || state[0:168]
         outputByteLen -= 168
         state = KP(state)

     output = output || state[0:outputByteLen]

     return output

A.3.  TurboSHAKE256

   TurboSHAKE256(message, separationByte, outputByteLen):
     offset = 0
     state = `00`^200
     input = message || separationByte

     # === Absorb complete blocks ===
     while offset < |input| - 136
         state ^= input[offset : offset + 136] || `00`^64
         state = KP(state)
         offset += 136

     # === Absorb last block and treatment of padding ===
     LastBlockLength = |input| - offset
     state ^= input[offset:] || `00`^(200-LastBlockLength)
     state ^= `00`^135 || `80` || `00`^64
     state = KP(state)

     # === Squeeze ===
     output = `00`^0
     while outputByteLen > 136
         output = output || state[0:136]
         outputByteLen -= 136
         state = KP(state)

     output = output || state[0:outputByteLen]

     return output

A.4.  KT128

   KT128(inputMessage, customString, outputByteLen):
     S = inputMessage || customString
     S = S || length_encode( |customString| )

     if |S| <= 8192
         return TurboSHAKE128(S, `07`, outputByteLen)
     else
         # === Kangaroo hopping ===
         FinalNode = S[0:8192] || `03` || `00`^7
         offset = 8192
         numBlock = 0
         while offset < |S|
             blockSize = min( |S| - offset, 8192)
             CV = TurboSHAKE128(S[offset : offset+blockSize], `0B`, 32)
             FinalNode = FinalNode || CV
             numBlock += 1
             offset   += blockSize

         FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`

         return TurboSHAKE128(FinalNode, `06`, outputByteLen)
     end

A.5.  KT256

   KT256(inputMessage, customString, outputByteLen):
     S = inputMessage || customString
     S = S || length_encode( |customString| )

     if |S| <= 8192
         return TurboSHAKE256(S, `07`, outputByteLen)
     else
         # === Kangaroo hopping ===
         FinalNode = S[0:8192] || `03` || `00`^7
         offset = 8192
         numBlock = 0
         while offset < |S|
             blockSize = min( |S| - offset, 8192)
             CV = TurboSHAKE256(S[offset : offset+blockSize], `0B`, 64)
             FinalNode = FinalNode || CV
             numBlock += 1
             offset   += blockSize

         FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`

         return TurboSHAKE256(FinalNode, `06`, outputByteLen)
     end

Authors' Addresses

   Benoît Viguier
   ABN AMRO Bank
   Groenelaan 2
   Amstelveen
   Netherlands
   Email: cs.ru.nl@viguier.nl


   David Wong (editor)
   zkSecurity
   Email: davidwong.crypto@gmail.com


   Gilles Van Assche (editor)
   STMicroelectronics
   Email: gilles.vanassche@st.com


   Quynh Dang (editor)
   National Institute of Standards and Technology
   Email: quynh.dang@nist.gov


   Joan Daemen (editor)
   Radboud University
   Email: joan@cs.ru.nl
