<?xmlversion="1.0" encoding="US-ASCII"?>version='1.0' encoding='UTF-8'?> <!DOCTYPE rfcSYSTEM "rfc2629.dtd"[ <!ENTITYrfc2119 SYSTEM "http://xml.resource.org/public/rfc/bibxml/reference.RFC.2119.xml">nbsp " "> <!ENTITYrfc8174 SYSTEM "http://xml.resource.org/public/rfc/bibxml/reference.RFC.8174.xml">zwsp "​"> <!ENTITY nbhy "‑"> <!ENTITY wj "⁠"> ]><?rfc toc="yes"?> <?rfc symrefs="yes"?> <?rfc compact="yes"?> <?rfc subcompact="no"?> <?rfc strict="no"?> <?rfc rfcedstyle="yes"?> <?rfc comments="yes"?> <?rfc inline="yes"?><rfc xmlns:xi="http://www.w3.org/2001/XInclude" category="info" docName="draft-irtf-cfrg-kangarootwelve-17"ipr="trust200902">number="9861" consensus="true" ipr="trust200902" obsoletes="" updates="" submissionType="IRTF" xml:lang="en" tocInclude="true" symRefs="true" version="3"> <!--[rfced] Please ensure that the guidelines listed in Section 2.1 of RFC 5743 have been adhered to in this document. --> <!--[rfced] Should the document's short title, which can be seen in the header of the PDF output, include "TurboSHAKE" to reflect the full document title? Original: KangarooTwelve Perhaps: KangarooTwelve and TurboSHAKE --> <front> <title abbrev="KangarooTwelve">KangarooTwelve and TurboSHAKE</title><!-- If the author is acting as editor, use the <role=editor> attribute--> <!-- see RFC2223 for guidelines regarding author names --><seriesInfo name="RFC" value="9861"/> <authorfullname="Benoîtfullname="Benoît Viguier" initials="B" surname="Viguier"> <organization>ABN AMRO Bank</organization> <address> <postal> <street>Groenelaan 2</street> <city>Amstelveen</city><country>The Netherlands</country><country>Netherlands</country> </postal> <email>cs.ru.nl@viguier.nl</email> </address> </author> <author fullname="David Wong" initials="D" surname="Wong" role="editor"> <organization>zkSecurity</organization> <address> <email>davidwong.crypto@gmail.com</email> </address> </author> <author fullname="Gilles Van Assche" initials="G" surname="Van Assche" role="editor"> <organization>STMicroelectronics</organization> <address> <email>gilles.vanassche@st.com</email> </address> </author> <author fullname="Quynh Dang" initials="Q" surname="Dang" role="editor"> <organization abbrev="NIST">National Institute of Standards and Technology</organization> <address> <email>quynh.dang@nist.gov</email> </address> </author> <author fullname="Joan Daemen" initials="J" surname="Daemen" role="editor"> <organization>Radboud University</organization> <address> <email>joan@cs.ru.nl</email> </address> </author><!-- <author fullname="Stanislav V. Smyshlyaev" initials="S" surname="Smyshlyaev"> <organization>CryptoPro</organization> <address> <email>smyshsv@gmail.com</email> </address> </author> --> <!-- <author fullname="John Mattsson" initials="J" surname="Mattsson"> <organization>Ericsson</organization> <address> <email>john.mattsson@ericsson.com</email> </address> </author> --> <!-- month and day will be generated automatically by XL2RFC; be sure the year is current.--><date year="2025"/> <!--WG name at the upperleft corner of the doc, IETF is fine for non-WG IETF submissions -->month="September"/> <workgroup>Crypto Forum</workgroup> <keyword>Keccak</keyword> <keyword>Sakura</keyword> <keyword>KangarooTwelve</keyword> <keyword>TurboSHAKE</keyword> <keyword>Cryptographic Hash</keyword> <keyword>eXtendable Output Function</keyword> <abstract> <t>This document defines foureXtendable OutputeXtendable-Output Functions(XOF),(XOFs), hash functions with output of arbitrary length, named TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256.</t> <t>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.</t> <t>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[FIPS 202],NIST FIPS 202 and is meant to serve as a stable reference and an implementation guide.</t> </abstract> </front> <middle> <sectiontitle="Introduction">numbered="true" toc="default"> <name>Introduction</name> <t>This document defines the TurboSHAKE128, TurboSHAKE256 <xreftarget="TURBOSHAKE"></xref>, KT128target="TURBOSHAKE" format="default"/>, KT128, and KT256 <xreftarget="KT"></xref> eXtendable Outputtarget="KT" format="default"/> eXtendable-Output Functions(XOF),(XOFs), i.e.,ahash functiongeneralizationgeneralizations that can return an output of arbitrary length. Both TurboSHAKE128 and TurboSHAKE256 are based on a Keccak-p permutation specified in <xreftarget="FIPS202"></xref>target="FIPS202" format="default"/> and have a higher speed than the SHA-3 and SHAKE functions.</t> <!--[rfced] May we clarify that "similarly to the SHAKE's" is referring to the SHAKE's security? Original: Similarly to the SHAKE's, it proposes two security strengths: 128 bits for TurboSHAKE128 and 256 bits for TurboSHAKE256. Perhaps: Similarly to the SHAKE's security, it proposes two security strengths: 128 bits for TurboSHAKE128 and 256 bits for TurboSHAKE256. --> <t>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, 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.</t> <t> KangarooTwelve applies tree hashing on top of TurboSHAKE and comprises two functions, KT128 and KT256. Note that <xreftarget="KT"></xref>target="KT" format="default"/> only defined KT128 under the name KangarooTwelve. KT256 is defined in this document. </t> <t> 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 <xreftarget="SP800-185"></xref>,target="SP800-185" format="default"/>, 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 <xreftarget="SAKURA"/>.target="SAKURA" format="default"/>. The use of TurboSHAKE in KangarooTwelve makes it faster than ParallelHash.</t> <t>The security of TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 builds on the public scrutiny that Keccak has received since its publication <xreftarget="KECCAK_CRYPTANALYSIS"/><xref target="TURBOSHAKE"/>.</t>target="KECCAK_CRYPTANALYSIS" format="default"/> <xref target="TURBOSHAKE" format="default"/>.</t> <t>With respect to functions defined in <xreftarget="FIPS202"></xref>target="FIPS202" format="default"/> and <xreftarget="SP800-185"></xref> functions,target="SP800-185" format="default"/>, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 feature the following advantages:</t><t><list style="symbols"><ul spacing="normal"> <li> <t>Unlike SHA3-224, SHA3-256, SHA3-384, and SHA3-512, the TurboSHAKE and KangarooTwelve functions have an extendable output.</t> </li> <li> <t>Unlike any functions in <xreftarget="FIPS202"></xref> defined function, similarlytarget="FIPS202" format="default"/>, and similar to functionsdefinedin <xreftarget="SP800-185"></xref>,target="SP800-185" format="default"/>, KT128 and KT256 allow the use of a customization string.</t> </li> <li> <!--[rfced] Section 1. We rephrased the following sentence for consistency with the other sentences in the list and to avoid using citations as adjectives. If it changes the intended meaning, please let us know. Original: * Unlike any [FIPS202] and [SP800-185] functions but ParallelHash, KT128 and KT256 exploit available parallelism. Perhaps: * Unlike any functions in [FIPS202] and [SP800-185] except for ParallelHash, KT128 and KT256 exploit available parallelism. --> <t>Unlike any functions in <xreftarget="FIPS202"></xref>target="FIPS202" format="default"/> and <xreftarget="SP800-185"></xref> functions buttarget="SP800-185" format="default"/> except for ParallelHash, KT128 and KT256 exploit available parallelism.</t> </li> <li> <t>Unlike ParallelHash, KT128 and KT256 do not have overhead when processing short messages.</t> </li> <li> <t>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 <xreftarget="FIPS202"></xref>.target="FIPS202" format="default"/>. The KangarooTwelve functions immediately benefit from the same speedup, improving over <xreftarget="FIPS202"></xref>target="FIPS202" format="default"/> and <xreftarget="SP800-185"></xref>.</t> </list></t>target="SP800-185" format="default"/>.</t> </li> </ul> <t>With respect toSHA-256 and SHA-512SHA-256, SHA-512, and other functions defined in <xreftarget="FIPS180"/> functions,target="FIPS180" format="default"/>, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 feature the following advantages:</t><t><list style="symbols"><ul spacing="normal"> <li> <t>Unlike any functions in <xreftarget="FIPS180"/> functions,target="FIPS180" format="default"/>, the TurboSHAKE and KangarooTwelve functions have an extendable output.</t> </li> <li> <t>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.</t> </li> <li> <t>Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 do not suffer from the length extension weakness.</t> </li> <li> <t>Unlike any functions in <xreftarget="FIPS180"></xref> functions,target="FIPS180" format="default"/>, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 use a round function with algebraic degree 2, which makes them more suitable to masking techniques for protections against side-channel attacks.</t></list></t></li> </ul> <t>This document represents the consensus of the Crypto Forum Research Group (CFRG) in the IRTF. It is not an IETF product and is not a standard.</t> <sectiontitle="Conventions"> <t>Thenumbered="true" toc="default"> <name>Conventions</name> <t> The key words"MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY","<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", "<bcp14>MAY</bcp14>", and"OPTIONAL""<bcp14>OPTIONAL</bcp14>" in this document are to be interpreted as described inBCP 14BCP 14 <xreftarget="RFC2119"></xref>target="RFC2119"/> <xreftarget="RFC8174"></xref>target="RFC8174"/> when, and only when, they appear in all capitals, as shownhere.</t>here. </t> <t>The following notations are used throughout the document:</t><t><list style="hanging"> <t hangText="`...`">denotes<ul spacing="normal"> <li>`...` denotes a string of bytes given in hexadecimal. For example, `0B80`.</t> <t hangText="|s|">denotes80`.</li> <li>|s| denotes the length of a byte string `s`. For example, |`FF FF`| =2.</t> <t hangText="`00`^b">denotes2.</li> <li>`00`^b denotes a byte string consisting of the concatenation of b bytes `00`. For example, `00`^7 = `00 00 00 00 00 0000`.</t> <t hangText="`00`^0">denotes00`.</li> <li>`00`^0 denotes the emptybyte-string.</t> <t hangText="a||b">denotesbyte string.</li> <li>a||b denotes the concatenation of twostringsstrings, a and b. For example, `10`||`F1` = `10F1`</t> <t hangText="s[n:m]">denotesF1`.</li> <li>s[n:m] denotes the selection of bytes from n (inclusive) to m (exclusive) of a string s. The indexing of abyte-stringbyte string starts at 0. For example, for s = `A5 C6 D7`, s[0:1] = `A5` and s[1:3] = `C6D7`.</t> <t hangText="s[n:]">denotesD7`.</li> <li>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`.</t> </list></t>`D7`.</li> </ul> <t>In the following, x and y are byte strings of equal length:</t><t><list style="hanging"> <t hangText="x^=y"><ul spacing="normal"> <li>x^=y denotes x takes the value x XORy.</t> <t hangText="xy.</li> <li>x &y">y denotes x ANDy.</t> </list></t>y.</li> </ul> <t>In the following, x and y are integers:</t><t><list style="hanging"> <t hangText="x+=y"><ul spacing="normal"> <li>x+=y denotes x takes the value x +y.</t> <t hangText="x-=y">y.</li> <li>x-=y denotes x takes the value x -y.</t> <t hangText="x**y">y.</li> <li>x**y denotes the exponentiation of x byy.</t> <t hangText="xy.</li> <li>x mody">y denotes the remainder of the division of x byy.</t> <t hangText="xy.</li> <li>x /y">y denotes the integer dividend of the division of x byy.</t> </list></t>y.</li> </ul> </section> </section> <sectiontitle="TurboSHAKE">numbered="true" toc="default"> <name>TurboSHAKE</name> <section anchor="TurboSHAKE_Interface"title="Interface">numbered="true" toc="default"> <name>Interface</name> <t>TurboSHAKE is a family ofeXtendable OutputeXtendable-Output Functions(XOF).(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 securitylevel,level; see <xreftarget="FIPS202"/>target="FIPS202" format="default"/> for more details. This document focuses on only two instances,namely,namely TurboSHAKE128 and TurboSHAKE256. (Note that the original definition includes a wider range of instances parameterized by their capacity <xreftarget="TURBOSHAKE"/>.)target="TURBOSHAKE" format="default"/>.) </t> <t> <!--[rfced] Section 2.1. We rephrased this text to match similar text in the first paragraph of Section 3.1. If it changes the intended meaning, please let us know. Original: An instance of TurboSHAKE takes as input parameters a byte-string M, an OPTIONAL byte D and a positive integer Lwhere<list style="hanging"> <t hangText="M"> byte-string,where Current: A TurboSHAKE instance takes a byte string M, an OPTIONAL byte D, and a positive integer L as input parameters, where: --> A TurboSHAKE instance takes a byte string M, an <bcp14>OPTIONAL</bcp14> byte D, and a positive integer L as input parameters, where:</t> <ul spacing="normal"> <li>M byte string is theMessage and</t> <t hangText="D">Message,</li> <li>D byte in the range [`01`, `02`, .. ,`7F`],`7F`] is anOPTIONAL Domain<bcp14>OPTIONAL</bcp14> domain separationbyte and</t> <t hangText="L">byte, and</li> <li>L positiveinteger,integer is the requested number of outputbytes.</t> </list></t>bytes.</li> </ul> <t> Conceptually,aan XOF can be viewed as a hash function with an infinitely long output truncated to L bytes. This means that callingaan 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). </t> <t>By default, theDomaindomain separation byte is `1F`. For an API that does not support a domain separation byte, DMUST<bcp14>MUST</bcp14> be the `1F`.</t> <t> 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. <!--[rfced] Please clarify "for any distinct values D1 and D2". Is the current text correct or is the intended meaning "for distinct values D1 and D2" (i.e., without "any")? Original: Specifically, for any distinct values D1 and D2, TurboSHAKE(M, D1, L1) and TurboSHAKE(M, D2, L2) yield independent hashes of M. Perhaps: Specifically, for distinct values D1 and D2, TurboSHAKE(M, D1, L1) and TurboSHAKE(M, D2, L2) yield independent hashes of M. --> Specifically, for any distinct values D1 and D2, TurboSHAKE(M, D1, L1) and TurboSHAKE(M, D2, L2) yield independent hashes of M. </t> <t> Note that an implementationMAY<bcp14>MAY</bcp14> propose an incremental input interface where the input string M is given in pieces. If so, the outputMUST<bcp14>MUST</bcp14> 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 implementationMAY<bcp14>MAY</bcp14> 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, itMUST<bcp14>MUST</bcp14> be the same as if the function was called with L equal to the sum of the given lengths. </t> </section> <sectiontitle="Specifications">numbered="true" toc="default"> <name>Specifications</name> <t>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 roundsandas specified in FIPS202,202; see Sections 3.3 and 3.4 of <xreftarget="FIPS202"></xref>.target="FIPS202" format="default"/>. KP denotes this permutation.</t> <t>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 1088bits,bits and has a capacity of 512 bits or 64 bytes.</t><t><figure><artwork><![CDATA[ +-------------+--------------+ | Rate | Capacity | +----------------+-------------+--------------+ | TurboSHAKE128 | 168 Bytes | 32 Bytes | | | | | | TurboSHAKE256 | 136 Bytes | 64 Bytes | +----------------+-------------+--------------+]]></artwork> </figure></t><table> <thead> <tr> <td></td> <th>Rate</th> <th>Capacity</th> </tr> </thead> <tbody> <tr> <th>TurboSHAKE128</th> <td>168 Bytes</td> <td>32 Bytes</td> </tr> <tr> <th>TurboSHAKE256</th> <td>136 Bytes</td> <td>64 Bytes</td> </tr> </tbody> </table> <t>We now describe the operations insideTurboSHAKE128.<list style="symbols"> <t>FirstTurboSHAKE128.</t> <ul spacing="normal"> <li> <t>First, the input M' is formed by appending the domain separation byte D to the message M.</t> </li> <li> <t> If the length of M' is not a multiple of 168bytesbytes, then it is padded with zeros at the end to make it a multiple of 168 bytes. If M' is already a multiple of 168bytesbytes, then no padding is added.ThenThen, 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. </t> </li> <li> <t>M' never has a length of 0 bytes due to the presence of the domain separation byte.</t> </li> <li> <t>As defined by the sponge construction, the process operates on a state and consists of two phases: the absorbingphase thatphase, which processes the padded inputM'M', and the squeezingphase thatphase, which produces the output.</t> </li> <li> <t>In the absorbingphasephase, the state is initialized toall-zero.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.</t> </li> <li> <t> In the squeezingphasephase, 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.</t></list></t></li> </ul> <t>TurboSHAKE256 performs the same steps but makes use of 136-byte blocks with respect to the padding, absorbing, and squeezing phases.</t> <t> The definition of the TurboSHAKE functions equivalently implements the pad10*1 rule; see Section 5.1 of <xreftarget="FIPS202"/>target="FIPS202" format="default"/> 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(hence, it cannot be `00`). Additionally, it must leave room for the second bit of padding(hence(hence, it cannot have theMSBmost significant bit (MSB) set to 1), should it be the last byte of the block. For more details, refer to Section 6.1 of <xreftarget="KT"></xref>target="KT" format="default"/> and Section 3 of <xreftarget="TURBOSHAKE"></xref>.</t>target="TURBOSHAKE" format="default"/>.</t> <t>The pseudocode versions of TurboSHAKE128 and TurboSHAKE256 are providedrespectivelyin Appendices <xreftarget="TSHK128_PC"/>target="TSHK128_PC" format="counter"/> and <xreftarget="TSHK256_PC"/>.</t>target="TSHK256_PC" format="counter"/>, respectively.</t> </section> </section> <sectiontitle="KangarooTwelve:numbered="true" toc="default"> <name>KangarooTwelve: TreehashingHashing overTurboSHAKE">TurboSHAKE</name> <sectiontitle="Interface">numbered="true" toc="default"> <name>Interface</name> <t>KangarooTwelve is a family ofeXtendable OutputeXtendable-Output Functions(XOF)(XOFs) consisting of the KT128 and KT256 instances. A KangarooTwelve instance takesas input parameterstwobyte-stringsbyte strings (M, C) and a positive integer Lwhere <list style="hanging"> <t hangText="M"> byte-string,as input parameters, where:</t> <ul spacing="normal"> <li>M byte string is theMessage and</t> <t hangText="C"> byte-string,Message,</li> <li>C byte string is anOPTIONAL<bcp14>OPTIONAL</bcp14> Customizationstring and</t> <t hangText="L">string, and</li> <li>L positiveinteger,integer is the requested number of outputbytes.</t> </list></t>bytes.</li> </ul> <t>The Customization stringMAY<bcp14>MAY</bcp14> serve as domain separation. It is typically a short string such as a name or an identifier(e.g.(e.g., URI,ODI...).Original Dialog Identifier (ODI), etc.). It can serve the same purpose as TurboSHAKE's D input parameter (see <xreftarget="TurboSHAKE_Interface"/>),target="TurboSHAKE_Interface" format="default"/>) but with a larger range. </t> <t>By default, the Customization string is the empty string. For an API that does not support a customization string parameter, CMUST<bcp14>MUST</bcp14> be the empty string.</t> <t>Note that an implementationMAY<bcp14>MAY</bcp14> propose an interface with the input and/or output providedincrementallyincrementally, as specified in <xreftarget="TurboSHAKE_Interface"/>.</t>target="TurboSHAKE_Interface" format="default"/>.</t> </section> <sectiontitle="Specificationnumbered="true" toc="default"> <name>Specification ofKT128">KT128</name> <t>On top of the sponge function TurboSHAKE128, KT128 uses a Sakura-compatible tree hash mode <xreftarget="SAKURA"></xref>.target="SAKURA" format="default"/>. First, merge M and theOPTIONAL<bcp14>OPTIONAL</bcp14> C to a single input string S in a reversible way. length_encode(|C| )|C| ) gives the length in bytes of C as abyte-string.byte string. See <xreftarget="RE"/>.</t> <t><figure><artwork><![CDATA[target="RE" format="default"/>.</t> <artwork name="" type="" align="left" alt=""><![CDATA[ S = M || C || length_encode( |C|) ]]></artwork></figure></t>)]]></artwork> <t>Then, split S into n chunks of 8192 bytes.</t><t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ S = S_0 || .. || S_(n-1) |S_0| = .. = |S_(n-2)| = 8192 bytes |S_(n-1)| <= 8192bytes ]]></artwork></figure></t>bytes]]></artwork> <t>From S_1 .. S_(n-1), compute the 32-byte Chaining Values CV_1 .. CV_(n-1). In order to be optimally efficient, this computationMAY<bcp14>MAY</bcp14> exploit the parallelism available on theplatformplatform, such asSIMDsingle instruction, multiple data (SIMD) instructions.</t><t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ CV_i = TurboSHAKE128( S_i, `0B`, 32)]]></artwork></figure></t>)]]></artwork> <t>Compute the final node:FinalNode. <list style="symbols">FinalNode.</t> <ul spacing="normal"> <li> <t>If |S| <= 8192 bytes, FinalNode =S</t> <t>OtherwiseS.</t> </li> <li> <t>Otherwise, compute FinalNode as follows:</t></list></t> <t><figure><artwork><![CDATA[</li> </ul> <artwork name="" type="" align="left" alt=""><![CDATA[ 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 || `FFFF`]]></artwork></figure></t>FF`]]></artwork> <t>Finally, the KT128 output isretrieved: <list style="symbols"> <t>Ifretrieved:</t> <ul spacing="normal"> <li><t>If |S| <= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L )</t></list></t> <t><figure> <artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ KT128( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L)]]> </artwork></figure></t> <t><list style="symbols"> <t>Otherwise)]]></artwork> </li> <li><t>Otherwise, from TurboSHAKE128( FinalNode, `06`, L )</t></list></t> <t><figure> <artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ KT128( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L)]]> </artwork></figure></t>)]]></artwork> </li> </ul> <t>The following figure illustrates the computation flow of KT128 for |S| <= 8192 bytes:</t><t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ +--------------+ TurboSHAKE128(.., `07`, L) | S |-----------------------------> output+--------------+]]></artwork></figure></t>+--------------+]]></artwork> <!--[rfced] Is the space before the colon in "l_e( x ) :" intentional, or may we update the text as follows to avoid the added space? Current: The following figure illustrates the computation flow of KT128 for |S| > 8192 bytes and where TurboSHAKE128 and length_encode( x ) are abbreviated respectively as TSHK128 and l_e( x ) : Perhaps: 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: --> <t>The following figure illustrates the computation flow of KT128 for |S| > 8192 bytes and where TurboSHAKE128 andlength_encode( x )length_encode( x ) are abbreviatedasrespectively as TSHK128 andl_e( x )l_e( x ) :</t><t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ +--------------+ | 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]]></artwork></figure></t>output]]></artwork> <t>A pseudocode version is provided in <xreftarget="KT128_PC"/>.</t>target="KT128_PC" format="default"/>.</t> <t>The table below gathers the values of the domain separation bytes used by the tree hash mode:</t><t><figure><artwork><![CDATA[ +--------------------+------------------+ | Type | Byte | +--------------------+------------------+ | SingleNode | `07` | | | | | IntermediateNode | `0B` | | | | | FinalNode | `06` | +--------------------+------------------+]]></artwork> </figure></t><table> <thead> <tr> <th>Type</th> <th>Byte</th> </tr> </thead> <tbody> <tr> <td>SingleNode</td> <td>`07`</td> </tr> <tr> <td>IntermediateNode</td> <td>`0B`</td> </tr> <tr> <td>FinalNode</td> <td>`06`</td> </tr> </tbody> </table> </section> <section anchor="RE"title="length_encode(numbered="true" toc="default"> <name>length_encode( x)">)</name> <t>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</t><t><figure> <artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ x = sum of 256**i * x_i for i from 0 ton-1]]></artwork></figure></t>n-1]]></artwork> <t>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.</t><t>As<t>For example, length_encode(0) = `00`, length_encode(12) = `0C01`01`, and length_encode(65538) = `01 00 0203`</t>03`.</t> <t>A pseudocode version is asfollowsfollows, where { b } denotes the byte of numerical value b.</t><t><figure><artwork><![CDATA[<sourcecode type="pseudocode"><![CDATA[ length_encode(x): S = `00`^0 while x > 0 S = { x mod 256 } || S x = x / 256 S = S || { |S| } return Send]]></artwork></figure></t>end]]></sourcecode> </section> <sectiontitle="Specificationnumbered="true" toc="default"> <name>Specification ofKT256">KT256</name> <t>KT256 is specified exactly like KT128, with two differences:</t><list style="symbols"><ul spacing="normal"> <li> <t>All the calls to TurboSHAKE128 in KT128 are replaced with calls to TurboSHAKE256 in KT256.</t> </li> <li> <t>The chaining values CV_1 to CV_(n-1) are64-byte64 bytes long in KT256 and are computed as follows:</t></list> <t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ CV_i = TurboSHAKE256( S_i, `0B`, 64)]]></artwork></figure></t>)]]></artwork> </li> </ul> <t>A pseudocode version is provided in <xreftarget="KT256_PC"/>.</t>target="KT256_PC" format="default"/>.</t> </section> </section> <sectiontitle="Message authentication codes">numbered="true" toc="default"> <name>Message Authentication Codes</name> <t>Implementing aMACMessage Authentication Code (MAC) with KT128 or KT256MAY<bcp14>MAY</bcp14> use a hash-then-MAC construction. This document defines and recommends a method called HopMAC:</t><t><figure> <artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ HopMAC128(Key, M, C, L) = KT128(Key, KT128(M, C, 32), L) HopMAC256(Key, M, C, L) = KT256(Key, KT256(M, C, 64), L)]]></artwork></figure></t><t>Similarly toHMAC,Hashed Message Authentication Code (HMAC), HopMAC consists of two calls: an inner call compressing the message M and the optional customization string C to adigest,digest and an outer call computing the tag from the key and the digest.</t> <t>Unlike HMAC, the inner call to KangarooTwelve in HopMAC is keyless and does not require additional protection against side channel attacks(SCA).(SCAs). Consequently, in an implementation that has to protect the HopMAC key againstSCAan SCA, only the outer calldoes needneeds protection, and this amounts to a single execution of the underlying permutation (assuming the key length is at most 69 bytes).</t> <t>In any case, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256MAY<bcp14>MAY</bcp14> be used to compute a MAC with the key reversibly prepended or appended to the input. For instance, oneMAY<bcp14>MAY</bcp14> compute a MAC on short messages simply calling KT128 with the key as the customization string, i.e., MAC = KT128(M, Key, L).</t> </section> <sectiontitle="Test vectors">numbered="true" toc="default"> <name>Test Vectors</name> <t>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 nbytes e.g.bytes, for example: </t><t><figure><artwork><![CDATA[<artwork name="" type="" align="left" alt=""><![CDATA[ Pattern for a length of 17 bytes: ptn(17) = `00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F10`]]></artwork></figure> </t> <t><figure><artwork><![CDATA[10`]]></artwork> <artwork name="" type="" align="left" alt=""><![CDATA[ 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 2425`]]></artwork></figure></t> <t><figure><artwork><![CDATA[25`]]></artwork> <artwork name="" type="" align="left" alt=""><![CDATA[ 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`]]></artwork></figure></t> <t><figure><artwork><![CDATA[]]></artwork> <artwork name="" type="" align="left" alt=""><![CDATA[ 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`]]></artwork></figure></t> <t><figure><artwork><![CDATA[]]></artwork> <artwork name="" type="" align="left" alt=""><![CDATA[ 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 00AE`]]></artwork></figure></t> <t><figure><artwork><![CDATA[AE`]]></artwork> <artwork name="" type="" align="left" alt=""><![CDATA[ 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 1B8B`]]></artwork></figure></t>8B`]]></artwork> </section> <section anchor="IANA"title="IANA Considerations">numbered="true" toc="default"> <name>IANA Considerations</name> <t> In theNamed"Named Information Hash AlgorithmRegistry,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). </t> <t> In theCOSE Algorithms"COSE Algorithms" registry, IANA has added the following entriesare assigned tofor TurboSHAKE and KangarooTwelve:</t><t><figure><artwork><![CDATA[ +---------------+-------+-------------------+--------------+ | Name | Value | Description | Capabilities | +---------------+-------+-------------------+--------------+ | TurboSHAKE128 | -261 | TurboSHAKE128 XOF | [kty] | | | | | | | TurboSHAKE256 | -262 | TurboSHAKE256 XOF | [kty] | | | | | | | KT128 | -263 | KT128 XOF | [kty] | | | | | | | KT256<!--[rfced] In the "COSE Algorithms" registry at <https://www.iana.org/assignments/cose>, IANA lists the values in descending order. Should Table 3 be ordered to match the IANA registry (e.g., list "KT256 | -264 " first and "TurboSHAKE128 |KT256 XOF | [kty] | +---------------+-------+-------------------+--------------+ ]]></artwork> </figure></t>-261" last)? Also, may we include the "Recommended" column in Table 3 to match the IANA registry or include the following sentence in the lead-in text? Please let us know which option is preferred. Current: In the COSE Algorithms "COSE Algorithms" registry, IANA has added the following entries for TurboSHAKE and KangarooTwelve: Perhaps: In the COSE Algorithms "COSE Algorithms" registry, IANA has added the following entries for TurboSHAKE and KangarooTwelve. For each entry, the "Recommended" column contains "No". --> <table> <thead> <tr> <th>Name</th> <th>Value</th> <th>Description</th> <th>Capabilities</th> </tr> </thead> <tbody> <tr> <td>TurboSHAKE128</td> <td>-261</td> <td>TurboSHAKE128 XOF</td> <td>[kty]</td> </tr> <tr> <td>TurboSHAKE256</td> <td>-262</td> <td>TurboSHAKE256 XOF</td> <td>[kty]</td> </tr> <tr> <td>KT128</td> <td>-263</td> <td>KT128 XOF</td> <td>[kty]</td> </tr> <tr> <td>KT256</td> <td>-264</td> <td>KT256 XOF</td> <td>[kty]</td> </tr> </tbody> </table> </section> <section anchor="Security"title="Security Considerations">numbered="true" toc="default"> <name>Security Considerations</name> <t>This document is meant to serve as a stable reference and an implementation guide for the KangarooTwelve and TurboSHAKEeXtendable OutputeXtendable-Output Functions. The security assurance of these functions relies on the cryptanalysis of reduced-round versions ofKeccakKeccak, and they have the same claimed security strength as their corresponding SHAKE functions.</t><t><figure><artwork><![CDATA[ +-------------------------------+ | security claim | +-----------------+-------------------------------+ | TurboSHAKE128 | 128<table> <thead> <tr> <td></td> <th>Security Claim</th> </tr> </thead> <tbody> <tr> <th>TurboSHAKE128</th> <td>128 bits (same asSHAKE128) | | | | | KT128 | 128SHAKE128)</td> </tr> <tr> <th>KT128</th> <td>128 bits (same asSHAKE128) | | | | | TurboSHAKE256 | 256SHAKE128)</td> </tr> <tr> <th>TurboSHAKE256</th> <td>256 bits (same asSHAKE256) | | | | | KT256 | 256SHAKE256)</td> </tr> <tr> <th>KT256</th> <td>256 bits (same asSHAKE256) | +-----------------+-------------------------------+]]></artwork> </figure></t> <t> ToSHAKE256)</td> </tr> </tbody> </table> <t>To be more precise, KT128 is made of twolayers: <list style="symbols">layers:</t> <ul spacing="normal"> <li> <t>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).</t> </li> <li> <t>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 <xreftarget="SAKURA"/>.</t> </list></t>target="SAKURA" format="default"/>.</t> </li> </ul> <t>This reasoning is detailed and formalized in <xreftarget="KT"/>.</t>target="KT" format="default"/>.</t> <t>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.</t> <!--[rfced] To improve the readability of "the output L MUST be chosen long enough", may we update it to "the chose L output MUST be long enough"? Note that this phrasing occurs in two sentences. Original: To achieve 128-bit security strength, the output L MUST be chosen long enough so that there are no generic attacks that violate 128-bit security. ... To achieve 256-bit security strength, the output L MUST be chosen long enough so that there are no generic attacks that violate 256-bit security. Perhaps: To achieve 128-bit security strength, the chosen L output MUST be long enough so that there are no generic attacks that violate 128-bit security. ... To achieve 256-bit security strength, the chosen L output MUST be long enough so that there are no generic attacks that violate 256-bit security. --> <t>TurboSHAKE128 and KT128 aim at 128-bit security. To achieve 128-bit security strength, the output LMUST<bcp14>MUST</bcp14> be chosen long enough so that there are no generic attacks that violate 128-bit security. So for 128-bit (second) preimagesecuritysecurity, the output should be at least 128bits,bits; for 128 bits of security against multi-target preimage attacks with Ttargetstargets, the output should be at least 128+log_2(T)bitsbits; and for 128-bit collisionsecuritysecurity, 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 <xreftarget="NISTPQ"/>.</t>target="NISTPQ" format="default"/>.</t> <t>Similarly, TurboSHAKE256 and KT256 aim at 256-bit security. To achieve 256-bit security strength, the output LMUST<bcp14>MUST</bcp14> be chosen long enough so that there are no generic attacks that violate 256-bit security. So for 256-bit (second) preimagesecuritysecurity, the output should be at least 256bits,bits; for 256 bits of security against multi-target preimage attacks with Ttargetstargets, the output should be at least 256+log_2(T)bitsbits; and for 256-bit collisionsecuritysecurity, 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 <xreftarget="NISTPQ"/>.</t>target="NISTPQ" format="default"/>.</t> <t> Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE256,KT128KT128, and KT256 do not suffer from the length extensionweakness,weakness and therefore do not require the use of the HMACconstructionconstruction, forinstanceinstance, when used for MAC computation <xreftarget="FIPS198"/>.target="FIPS198" format="default"/>. 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 orECDHElliptic Curve Diffie-Hellman (ECDH) protocol, but it needs to have sufficient min-entropy. </t><t>Lastly,<!--[rfced] As the first sentence is not a full sentence, may we combine the two sentences below into one sentence? Original: 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. Perhaps: 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. --> <t>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, <bcp14>SHOULD</bcp14> avoid using these three values for D.</t> </section><!-- <section title="Contributors"> <t><cref>[TEMPLATE TODO] This optional section can be used to mention contributors to your internet draft.</cref></t> </section> --></middle> <back><!-- References Section --> <references title="Normative References"> &rfc2119; &rfc8174;<references> <name>References</name> <references> <name>Normative References</name> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2119.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8174.xml"/> <referenceanchor="FIPS202">anchor="FIPS202" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf"> <front><title>FIPS PUB 202 - SHA-3<title>SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology </organization>Technology</organization> </author> <date month="August"year="2015"></date>year="2015"/> </front> <seriesInfoname="WWW" value="http://dx.doi.org/10.6028/NIST.FIPS.202" />name="NIST FIPS" value="202"/> <seriesInfo name="DOI" value="10.6028/NIST.FIPS.202"/> </reference> <reference anchor="SP800-185"> <front><title>NIST Special Publication 800-185 SHA-3<title>SHA-3 Derived Functions: cSHAKE, KMAC, TupleHash and ParallelHash</title><author> <organization>National Institute of Standards and<author fullname="John Kelsey" surname="Kelsey"> <organization>Information Technology</organization>Laboratory</organization> </author> <author fullname="Shu-jen Chang" surname="Chang"> <organization>Information Technology Laboratory</organization> </author> <author fullname="Ray Perlner" surname="Perlner"> <organization>Information Technology Laboratory</organization> </author> <date month="December"year="2016"></date>year="2016"/> </front> <seriesInfoname="WWW" value="https://doi.org/10.6028/NIST.SP.800-185" />name="NIST SP" value="800-185"/> <seriesInfo name="DOI" value="10.6028/NIST.SP.800-185"/> <refcontent>National Institute of Standards and Technology</refcontent> </reference> </references><references title="Informative References"><references> <name>Informative References</name> <referenceanchor="TURBOSHAKE">anchor="TURBOSHAKE" target="http://eprint.iacr.org/2023/342"> <front> <title>TurboSHAKE</title> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="S." surname="Hoffert" fullname="Seth Hoffert"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/> <author initials="B." surname="Viguier"fullname="Benoîtfullname="Benoît Viguier"/> <date month="March" year="2023"/> </front><seriesInfo name="WWW" value="http://eprint.iacr.org/2023/342"/><refcontent>Cryptology ePrint Archive, Paper 2023/342</refcontent> </reference><reference anchor="KT"> <front> <title>KangarooTwelve:<!-- [rfced] References a) Would you like the references to be alphabetized or left in their current order? b) We note that the original [KT] reference entry contained two URL strings. The first URL is to a pre-print version of this article available from the Cryptology ePrint Archive with the most recent version being added in May 2018: http://eprint.iacr.org/2016/770.pdf. The other URL is to the published conference paper with a date of June 2018: https://link.springer.com/chapter/10.1007/978-3-319-93387-0_21. We have modified this reference to use the Springer Link URL as this appears to be the most recently published version that also includes a DOI. Please review and let us know if you have any objections. Original: [KT] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., Van Keer, R., and B. Viguier, "KangarooTwelve: fast hashing based on Keccak-p", WWW https://link.springer.com/ chapter/10.1007/978-3-319-93387-0_21, WWW http://eprint.iacr.org/2016/770.pdf, July 2018. Current: [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>. c) We note that the original [SAKURA] reference entry contained two URL strings. The first URL is to a pre-print version of this article available from the Cryptology ePrint Archive with the most recent version being added in April 2014: https://eprint.iacr.org/2013/231.pdf. The other URL is to the published conference paper with a date of 2014: https://link.springer.com/chapter/10.1007/978-3-319-07536-5_14. We have modified this reference to use the Springer Link URL as this appears to be the most recently published version that also includes a DOI. Please review and let us know if you have any objections. Original: [SAKURA] Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche, "Sakura: a flexible coding for tree hashing", WWW https://link.springer.com/ chapter/10.1007/978-3-319-07536-5_14, WWW http://eprint.iacr.org/2013/231.pdf, June 2014. Current: [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>. d) Since this reference is to a GitHub repository, please provide a commit hash in accordance with Part 2 of the RFC Style Guide: https://www.rfc-editor.org/styleguide/part2/#ref_repo. [XKCP] "eXtended Keccak Code Package", December 2022, <https://github.com/XKCP/XKCP>. --> <reference anchor="KT" target="https://link.springer.com/chapter/10.1007/978-3-319-93387-0_21"> <front> <title>KangarooTwelve: Fast Hashing Based on Keccak-p</title> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/> <author initials="B." surname="Viguier"fullname="Benoîtfullname="Benoît Viguier"/> <datemonth="July"month="June" year="2018"/> </front> <refcontent>Applied Cryptography and Network Security (ACNS 2018), Lecture Notes in Computer Science, vol. 10892, pp. 400-418</refcontent> <seriesInfoname="WWW" value="https://link.springer.com/chapter/10.1007/978-3-319-93387-0_21"/> <seriesInfo name="WWW" value="http://eprint.iacr.org/2016/770.pdf"/>name="DOI" value="10.1007/978-3-319-93387-0_21"/> </reference> <referenceanchor="SAKURA">anchor="SAKURA" target="https://link.springer.com/chapter/10.1007/978-3-319-07536-5_14"> <front> <title>Sakura: aflexible codingFlexible Coding fortree hashing</title>Tree Hashing</title> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <datemonth="June"year="2014"/> </front> <refcontent>Applied Cryptography and Network Security (ACNS 2014), Lecture Notes in Computer Science, vol. 8479, pp. 217-234</refcontent> <seriesInfoname="WWW" value="https://link.springer.com/chapter/10.1007/978-3-319-07536-5_14"/> <seriesInfo name="WWW" value="http://eprint.iacr.org/2013/231.pdf"/>name="DOI" value="10.1007/978-3-319-07536-5_14"/> </reference> <referenceanchor="KECCAK_CRYPTANALYSIS">anchor="KECCAK_CRYPTANALYSIS" target="https://www.keccak.team/third_party.html"> <front> <title>Summary of Third-party cryptanalysis of Keccak</title> <author> <organization>Keccak Team</organization> </author><date year="2022"/></front><seriesInfo name="WWW" value="https://www.keccak.team/third_party.html"/></reference> <referenceanchor="XKCP">anchor="XKCP" target="https://github.com/XKCP/XKCP"> <front> <title>eXtended Keccak Code Package</title><author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/><author/> <date month="December" year="2022"/> </front><seriesInfo name="WWW" value="https://github.com/XKCP/XKCP"/></reference> <referenceanchor="NISTPQ">anchor="NISTPQ" target="https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf"> <front> <title>Submission Requirements and Evaluation Criteria for the Post-Quantum Cryptography Standardization Process</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards and Technology </organization> </author><date month="December" year="2016"></date></front><seriesInfo name="WWW" value="https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf" /></reference> <referenceanchor="FIPS180">anchor="FIPS180" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf"> <front> <title>Secure HashStandard (SHS)</title>Standard</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology (NIST)</organization>Technology</organization> </author> <dateyear="2015" month="August"/>month="August" year="2015"/> </front> <seriesInfoname="FIPS PUB"name="NIST FIPS" value="180-4"/> <seriesInfoname="WWW" value="https://doi.org/10.6028/NIST.FIPS.180-4"/>name="DOI" value="10.6028/NIST.FIPS.180-4"/> </reference> <referenceanchor="FIPS198">anchor="FIPS198" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.198-1.pdf"> <front> <title>The Keyed-Hash Message Authentication Code (HMAC)</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology (NIST)</organization>Technology</organization> </author> <dateyear="2008" month="July"/>month="July" year="2008"/> </front> <seriesInfoname="FIPS PUB"name="NIST FIPS" value="198-1"/> <seriesInfoname="WWW" value="https://doi.org/10.6028/NIST.FIPS.198-1"/>name="DOI" value="10.6028/NIST.FIPS.198-1"/> </reference> </references> </references> <section anchor="pseudocode"title="Pseudocode">numbered="true" toc="default"> <name>Pseudocode</name> <t>Thesub-sectionssubsections of this appendix contain pseudocode definitions of TurboSHAKE128,TurboSHAKE256TurboSHAKE256, and KangarooTwelve. Standalone Python versions are also available in the Keccak Code Package <xreftarget="XKCP"></xref>target="XKCP" format="default"/> and in <xreftarget="KT"></xref>target="KT" format="default"/> </t> <section anchor="Keccak_PC"title="Keccak-p[1600,n_r=12]"> <t><figure><artwork><![CDATA[numbered="true" toc="default"> <name>Keccak-p[1600,n_r=12]</name> <sourcecode type="pseudocode"><![CDATA[ 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]]></artwork></figure></t>]]></sourcecode> <t>where ROL64(x, y) is a rotation of the 'x' 64-bit word toward the bits with higher indexes by 'y' positions. The 8-bytesbyte-stringbyte string x is interpreted as a 64-bit word in little-endian format. </t> </section> <section anchor="TSHK128_PC"title="TurboSHAKE128"> <t><figure><artwork><![CDATA[numbered="true" toc="default"> <name>TurboSHAKE128</name> <sourcecode type="pseudocode"><![CDATA[ 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]]></artwork></figure></t>]]></sourcecode> </section> <section anchor="TSHK256_PC"title="TurboSHAKE256"> <t><figure><artwork><![CDATA[numbered="true" toc="default"> <name>TurboSHAKE256</name> <sourcecode type="pseudocode"><![CDATA[ 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]]></artwork></figure></t>]]></sourcecode> </section> <!--[rfced] The following lines are 1 character over the 72-character limit. Please let us know how you would like to adjust the lines/spacing. Appendix A.4: CV = TurboSHAKE128(S[offset : offset + blockSize], `0B`, 32) Appendix A.5: CV = TurboSHAKE256(S[offset : offset + blockSize], `0B`, 64) --> <section anchor="KT128_PC"title="KT128"> <t><figure><artwork><![CDATA[numbered="true" toc="default"> <name>KT128</name> <sourcecode type="pseudocode"><![CDATA[ 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]]></artwork></figure></t>]]></sourcecode> </section> <section anchor="KT256_PC"title="KT256"> <t><figure><artwork><![CDATA[numbered="true" toc="default"> <name>KT256</name> <sourcecode type="pseudocode"><![CDATA[ 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]]></artwork></figure></t>]]></sourcecode> </section> </section> </back> <!--[rfced] Throughout the text, the following terminology appears to be used inconsistently. Please review these occurrences and let us know if/how they may be made consistent. Chaining Value vs. chaining value Customization string vs. customization string Message vs. message --> <!-- [rfced] Abbreviations a) FYI - We have added expansions for the following abbreviations per Section 3.6 of RFC 7322 ("RFC Style Guide"). Please review each expansion in the document carefully to ensure correctness. Elliptic Curve Diffie-Hellman (ECDH) Hashed Message Authentication Code (HMAC) Original Dialog Identifier (ODI) single instruction, multiple data (SIMD) b) FYI: We added a hyphen to the expansion of "XOF" per [FIPS202] and the NIST glossary. eXtendable Output Functions -> eXtendable-Output Functions --> <!-- [rfced] Please review the "Inclusive Language" portion of the online Style Guide <https://www.rfc-editor.org/styleguide/part2/#inclusive_language> and let us know if any changes are needed. Note that our script did not flag any words in particular, but this should still be reviewed as a best practice. --> </rfc>