rfc9861xml2.original.xml   rfc9861.xml 
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<rfc category="info" docName="draft-irtf-cfrg-kangarootwelve-17" ipr="trust20090
2">
<front>
<title abbrev="KangarooTwelve">KangarooTwelve and TurboSHAKE</title>
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<author fullname="Beno&icirc;t Viguier" initials="B" surname="Viguier"> <front>
<title abbrev="KangarooTwelve and TurboSHAKE">KangarooTwelve and TurboSHAKE<
/title>
<seriesInfo name="RFC" value="9861"/>
<author fullname="Benoît Viguier" initials="B" surname="Viguier">
<organization>ABN AMRO Bank</organization> <organization>ABN AMRO Bank</organization>
<address> <address>
<postal> <postal>
<street>Groenelaan 2</street> <street>Groenelaan 2</street>
<city>Amstelveen</city> <city>Amstelveen</city>
<country>The Netherlands</country> <country>Netherlands</country>
</postal> </postal>
<email>cs.ru.nl@viguier.nl</email> <email>cs.ru.nl@viguier.nl</email>
</address> </address>
</author> </author>
<author fullname="David Wong" initials="D" surname="Wong" role="editor"> <author fullname="David Wong" initials="D" surname="Wong" role="editor">
<organization>zkSecurity</organization> <organization>zkSecurity</organization>
<address> <address>
<email>davidwong.crypto@gmail.com</email> <email>davidwong.crypto@gmail.com</email>
</address> </address>
</author> </author>
<author fullname="Gilles Van Assche" initials="G" surname="Van Assche" role= "editor"> <author fullname="Gilles Van Assche" initials="G" surname="Van Assche" role= "editor">
<organization>STMicroelectronics</organization> <organization>STMicroelectronics</organization>
<address> <address>
<email>gilles.vanassche@st.com</email> <email>gilles.vanassche@st.com</email>
</address> </address>
</author> </author>
<author fullname="Quynh Dang" initials="Q" surname="Dang" role="editor"> <author fullname="Quynh Dang" initials="Q" surname="Dang" role="editor">
<organization abbrev="NIST">National Institute of Standards and Technology </organization> <organization abbrev="NIST">National Institute of Standards and Technology </organization>
<address> <address>
<email>quynh.dang@nist.gov</email> <email>quynh.dang@nist.gov</email>
</address> </address>
</author> </author>
<author fullname="Joan Daemen" initials="J" surname="Daemen" role="editor"> <author fullname="Joan Daemen" initials="J" surname="Daemen" role="editor">
<organization>Radboud University</organization> <organization>Radboud University</organization>
<address> <address>
<email>joan@cs.ru.nl</email> <email>joan@cs.ru.nl</email>
</address> </address>
</author> </author>
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<!-- <author fullname="John Mattsson" initials="J" surname="Mattsson">
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<!-- 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, <date year="2025" month="October"/>
IETF is fine for non-WG IETF submissions -->
<workgroup>Crypto Forum</workgroup> <workgroup>Crypto Forum</workgroup>
<keyword>Keccak</keyword> <keyword>Keccak</keyword>
<keyword>Sakura</keyword> <keyword>Sakura</keyword>
<keyword>KangarooTwelve</keyword> <keyword>KangarooTwelve</keyword>
<keyword>TurboSHAKE</keyword> <keyword>TurboSHAKE</keyword>
<keyword>Cryptographic Hash</keyword> <keyword>Cryptographic Hash</keyword>
<keyword>eXtendable Output Function</keyword> <keyword>eXtendable Output Function</keyword>
<abstract> <abstract>
<t>This document defines four eXtendable Output Functions (XOF), <t>This document defines four eXtendable-Output Functions (XOFs),
hash functions with output of arbitrary length, named TurboSHAKE128, hash functions with output of arbitrary length, named TurboSHAKE128,
TurboSHAKE256, KT128 and KT256.</t> TurboSHAKE256, KT128, and KT256.</t>
<t>All four functions provide efficient and secure hashing primitives,
<t>All four functions provide efficient and secure hashing primitives,
and the last two are able to exploit the parallelism of the implementation and the last two are able to exploit the parallelism of the implementation
in a scalable way.</t> in a scalable way.</t>
<t>This document is a product of the Crypto Forum Research Group.
<t>This document is a product of the Crypto Forum Research Group.
It builds up on the definitions of the permutations and of the It builds up on the definitions of the permutations and of the
sponge construction in [FIPS 202], and is meant to serve as a stable reference sponge construction in NIST FIPS 202 and is meant to serve as a stable referen ce
and an implementation guide.</t> and an implementation guide.</t>
</abstract>
</abstract> </front>
</front> <middle>
<section numbered="true" toc="default">
<middle> <name>Introduction</name>
<section title="Introduction"> <t>This document defines the TurboSHAKE128, TurboSHAKE256 <xref target="TU
RBOSHAKE" format="default"/>,
<t>This document defines the TurboSHAKE128, TurboSHAKE256 <xref target="TURB KT128, and KT256 <xref target="KT" format="default"/> eXtendable-Output Func
OSHAKE"></xref>, tions (XOFs),
KT128 and KT256 <xref target="KT"></xref> eXtendable Output Functions (XOF), i.e., hash function generalizations that can return an output of arbitrary l
i.e., a hash function generalization that can return an output of arbitrary ength.
length. Both TurboSHAKE128 and TurboSHAKE256 are based on a Keccak-p permutation s
Both TurboSHAKE128 and TurboSHAKE256 are based on a Keccak-p permutation spe pecified in <xref target="FIPS202" format="default"/> and have a higher speed th
cified in <xref an the SHA-3 and SHAKE functions.</t>
target="FIPS202"></xref> and have a higher speed than the SHA-3 and SHAKE fu <t>TurboSHAKE is a sponge function family that makes use of Keccak-p[n_r=1
nctions.</t> 2,b=1600], a round-reduced
version of the permutation used in SHA-3. Similarly to the SHAKE's security,
<t>TurboSHAKE is a sponge function family that makes use of Keccak-p[n_r=12, it proposes two security strengths:
b=1600], a round-reduced
version of the permutation used in SHA-3. Similarly to the SHAKE's, it propo
ses two security strengths:
128 bits for TurboSHAKE128 and 256 bits for TurboSHAKE256. 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 Halving the number of rounds compared to the original SHAKE functions makes TurboSHAKE roughly two times
faster.</t> faster.</t>
<t>
<t>
KangarooTwelve applies tree hashing on top of TurboSHAKE and comprises two f unctions, KT128 and KT256. KangarooTwelve applies tree hashing on top of TurboSHAKE and comprises two f unctions, KT128 and KT256.
Note that <xref target="KT"></xref> only defined KT128 under the name Kangar ooTwelve. Note that <xref target="KT" format="default"/> only defined KT128 under the name KangarooTwelve.
KT256 is defined in this document. KT256 is defined in this document.
</t> </t>
<t>
<t>
The SHA-3 and SHAKE functions process data in a serial manner and are strong ly The SHA-3 and SHAKE functions process data in a serial manner and are strong ly
limited in exploiting available parallelism in modern CPU architectures. limited in exploiting available parallelism in modern CPU architectures.
Similar to ParallelHash <xref target="SP800-185"></xref>, KangarooTwelve spl its Similar to ParallelHash <xref target="SP800-185" format="default"/>, Kangaro oTwelve splits
the input message into fragments. It then applies TurboSHAKE on each of them the input message into fragments. It then applies TurboSHAKE on each of them
separately before applying TurboSHAKE again on the combination of the first separately before applying TurboSHAKE again on the combination of the first
fragment and the digests. fragment and the digests.
More precisely, KT128 uses TurboSHAKE128 and KT256 uses TurboSHAKE256. More precisely, KT128 uses TurboSHAKE128 and KT256 uses TurboSHAKE256.
They make use of Sakura coding for ensuring soundness of the tree hashing They make use of Sakura coding for ensuring soundness of the tree hashing
mode <xref target="SAKURA"/>. mode <xref target="SAKURA" format="default"/>.
The use of TurboSHAKE in KangarooTwelve makes it faster than ParallelHash.</ t> The use of TurboSHAKE in KangarooTwelve makes it faster than ParallelHash.</ t>
<t>The security of TurboSHAKE128, TurboSHAKE256, KT128, and KT256 builds o
<t>The security of TurboSHAKE128, TurboSHAKE256, KT128 and KT256 builds on t n the public
he public
scrutiny that Keccak has received since its scrutiny that Keccak has received since its
publication <xref target="KECCAK_CRYPTANALYSIS"/><xref target="TURBOSHAKE"/> publication <xref target="KECCAK_CRYPTANALYSIS" format="default"/> <xref tar
.</t> get="TURBOSHAKE" format="default"/>.</t>
<t>With respect to functions defined in <xref target="FIPS202" format="def
<t>With respect to <xref target="FIPS202"></xref> and <xref target="SP800-18 ault"/> and <xref target="SP800-185" format="default"/>, TurboSHAKE128, TurboSHA
5"></xref> KE256, KT128, and KT256 feature the following advantages:</t>
functions, TurboSHAKE128, TurboSHAKE256, KT128 and KT256 feature the followi <ul spacing="normal">
ng advantages:</t> <li>
<t>Unlike SHA3-224, SHA3-256, SHA3-384, and SHA3-512, the TurboSHAKE a
<t><list style="symbols"> nd
<t>Unlike SHA3-224, SHA3-256, SHA3-384, SHA3-512, the TurboSHAKE and
KangarooTwelve functions have an extendable output.</t> KangarooTwelve functions have an extendable output.</t>
</li>
<t>Unlike any <xref target="FIPS202"></xref> defined function, similarly to <li>
functions defined in <xref target="SP800-185"></xref>, KT128 and KT256 <t>Unlike any functions in <xref target="FIPS202" format="default"/>,
and similar to
functions in <xref target="SP800-185" format="default"/>, KT128 and KT256
allow the use of a customization string.</t> allow the use of a customization string.</t>
</li>
<t>Unlike any <xref target="FIPS202"></xref> and <xref target="SP800-185"></ <li>
xref> <t>Unlike any functions in <xref target="FIPS202" format="default"/> a
functions but ParallelHash, KT128 and KT256 exploit available parallelism.</ nd <xref target="SP800-185" format="default"/> except for ParallelHash, KT128 an
t> d KT256 exploit available parallelism.</t>
</li>
<t>Unlike ParallelHash, KT128 and KT256 do not have overhead when <li>
<t>Unlike ParallelHash, KT128 and KT256 do not have overhead when
processing short messages.</t> processing short messages.</t>
</li>
<t>The permutation in the TurboSHAKE functions has half <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, the number of rounds compared to the one in the SHA-3 and SHAKE functions,
making them faster than any function defined in <xref target="FIPS202"></xre f>. making them faster than any function defined in <xref target="FIPS202" forma t="default"/>.
The KangarooTwelve functions immediately benefit from the same speedup, impr oving over The KangarooTwelve functions immediately benefit from the same speedup, impr oving over
<xref target="FIPS202"></xref> and <xref target="SP800-185"></xref>.</t> <xref target="FIPS202" format="default"/> and <xref target="SP800-185" forma
</list></t> t="default"/>.</t>
</li>
<t>With respect to SHA-256 and SHA-512 and other <xref target="FIPS180"/> fu </ul>
nctions, TurboSHAKE128, TurboSHAKE256, KT128 and KT256 feature the following adv <t>With respect to SHA-256, SHA-512, and other functions defined in <xref
antages:</t> target="FIPS180" format="default"/>, TurboSHAKE128, TurboSHAKE256, KT128, and KT
256 feature the following advantages:</t>
<t><list style="symbols"> <ul spacing="normal">
<t>Unlike <xref target="FIPS180"/> functions, the TurboSHAKE and KangarooTwe <li>
lve functions have an extendable output.</t> <t>Unlike any functions in <xref target="FIPS180" format="default"/>,
the TurboSHAKE and KangarooTwelve functions have an extendable output.</t>
<t>The TurboSHAKE functions produce output at the same rate as they process </li>
input, whereas SHA-256 and SHA-512, when used in a mask generation function (MGF <li>
) construction, produce output half as fast as they process input.</t> <t>The TurboSHAKE functions produce output at the same rate as they pr
ocess input, whereas SHA-256 and SHA-512, when used in a mask generation functio
<t>Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE256, K n (MGF) construction, produce output half as fast as they process input.</t>
T128 and KT256 do not suffer from the length extension weakness.</t> </li>
<li>
<t>Unlike any <xref target="FIPS180"></xref> functions, TurboSHAKE128, Turbo <t>Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE
SHAKE256, KT128 and KT256 use a round function with algebraic degree 2, which ma 256, KT128, and KT256 do not suffer from the length extension weakness.</t>
kes them more suitable to masking techniques for protections against side-channe </li>
l attacks.</t> <li>
</list></t> <t>Unlike any functions in <xref target="FIPS180" format="default"/>,
TurboSHAKE128, TurboSHAKE256, KT128, and KT256 use a round function with algebra
<t>This document represents the consensus of the Crypto Forum Research Group ic degree 2, which makes them more suitable to masking techniques for protection
(CFRG) s against side-channel attacks.</t>
in the IRTF. It is not an IETF product and is not a standard.</t> </li>
</ul>
<section title="Conventions"> <t>This document represents the consensus of the Crypto Forum Research Gro
<t>The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", up
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this (CFRG) in the IRTF. It has been reviewed by two members of the Crypto Review
document are to be interpreted as described in BCP 14 <xref target="RFC211 Panel, as well as by several members of the CFRG. It is not an IETF product
9"></xref> <xref target="RFC8174"></xref> and is not a standard.
when, and only when, they appear in all capitals, as shown here.</t> </t>
<section numbered="true" toc="default">
<t>The following notations are used throughout the document:</t> <name>Conventions</name>
<t>
<t><list style="hanging"> The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14>REQU
<t hangText="`...`">denotes a string of bytes given in IRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL
hexadecimal. For example, `0B 80`.</t> NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>
RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
<t hangText="|s|">denotes the length of a byte string `s`. "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
For example, |`FF FF`| = 2.</t> be interpreted as
described in BCP&nbsp;14 <xref target="RFC2119"/> <xref target="RFC8174"/>
<t hangText="`00`^b">denotes a byte string consisting of the concatenati when, and only when, they appear in all capitals, as shown here.
on </t>
of b bytes `00`. For example, `00`^7 = `00 00 00 00 00 00 00`.</t> <t>The following notations are used throughout the document:</t>
<ul spacing="normal">
<t hangText="`00`^0">denotes the empty byte-string.</t> <li>`...` denotes a string of bytes given in
hexadecimal. For example, `0B 80`.</li>
<t hangText="a||b">denotes the concatenation of two strings a and b. <li>|s| denotes the length of a byte string `s`.
For example, `10`||`F1` = `10 F1`</t> For example, |`FF FF`| = 2.</li>
<li>`00`^b denotes a byte string consisting of the concatenation
<t hangText="s[n:m]">denotes the selection of bytes from n (inclusive) t of b bytes `00`. For example, `00`^7 = `00 00 00 00 00 00 00`.</li>
o m <li>`00`^0 denotes the empty byte string.</li>
(exclusive) of a string s. The indexing of a byte-string starts at 0. <li>a||b denotes the concatenation of two strings, a and b.
For example, for s = `A5 C6 D7`, s[0:1] = `A5` and s[1:3] = `C6 D7`.</t> For example, `10`||`F1` = `10 F1`.</li>
<li>s[n:m] denotes the selection of bytes from n (inclusive) to m
<t hangText="s[n:]">denotes the selection of bytes from n to the end of (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`.</li
>
<li>s[n:] denotes the selection of bytes from n to the end of
a string s. a string s.
For example, for s = `A5 C6 D7`, s[0:] = `A5 C6 D7` and s[2:] = `D7`.</t For example, for s = `A5 C6 D7`, s[0:] = `A5 C6 D7` and s[2:] = `D7`.</l
> i>
</list></t> </ul>
<t>In the following, x and y are byte strings of equal length:</t>
<t>In the following, x and y are byte strings of equal length:</t> <ul spacing="normal">
<li>x^=y denotes x takes the value x XOR y.</li>
<t><list style="hanging"> <li>x &amp; y denotes x AND y.</li>
<t hangText="x^=y"> denotes x takes the value x XOR y.</t> </ul>
<t>In the following, x and y are integers:</t>
<t hangText="x &amp; y"> denotes x AND y.</t> <ul spacing="normal">
</list></t> <li>x+=y denotes x takes the value x + y.</li>
<li>x-=y denotes x takes the value x - y.</li>
<t>In the following, x and y are integers:</t> <li>x**y denotes the exponentiation of x by y.</li>
<li>x mod y denotes the remainder of the division of x by y.</li>
<t><list style="hanging"> <li>x / y denotes the integer dividend of the division of x by y.</li>
<t hangText="x+=y"> denotes x takes the value x + y.</t> </ul>
</section>
<t hangText="x-=y"> denotes x takes the value x - y.</t>
<t hangText="x**y"> denotes the exponentiation of x by y.</t>
<t hangText="x mod y"> denotes the remainder of the division of x by y.<
/t>
<t hangText="x / y"> denotes the integer dividend of the division of x b
y y.</t>
</list></t>
</section> </section>
</section> <section numbered="true" toc="default">
<name>TurboSHAKE</name>
<section title="TurboSHAKE"> <section anchor="TurboSHAKE_Interface" numbered="true" toc="default">
<section anchor="TurboSHAKE_Interface" title="Interface"> <name>Interface</name>
<t>TurboSHAKE is a family of eXtendable Output Functions (XOF). <t>TurboSHAKE is a family of eXtendable-Output Functions (XOFs).
Internally, it makes use of the sponge construction, parameterized by tw o integers, the rate and the capacity, that sum to the permutation width (here, 1600 bits). Internally, it makes use of the sponge construction, parameterized by tw o 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 The rate gives the number of bits processed or produced per call to the
permutation, whereas the capacity determines the security level, see <xref targe permutation, whereas the capacity determines the security level; see <xref targe
t="FIPS202"/> for more details. t="FIPS202" format="default"/> for more details.
This document focuses on only two instances, namely, TurboSHAKE128 and T This document focuses on only two instances, namely TurboSHAKE128 and Tu
urboSHAKE256. rboSHAKE256.
(Note that the original definition includes a wider range of instances p (Note that the original definition includes a wider range of instances p
arameterized by their capacity <xref target="TURBOSHAKE"/>.) arameterized by their capacity <xref target="TURBOSHAKE" format="default"/>.)
</t> </t>
<t>
<t> A TurboSHAKE instance takes a byte string M, an <bcp14>OPTIONAL</bcp14> by
An instance of TurboSHAKE takes as input parameters a byte-string M, an OP te D, and a positive integer L as input parameters, where:</t>
TIONAL byte D and a positive integer L <ul spacing="normal">
where<list style="hanging"> <li>M byte string is the message,</li>
<t hangText="M"> byte-string, is the Message and</t> <li>D byte in the range [`01`, `02`, .. , `7F`] is an <bcp14>OPTIONAL<
<t hangText="D"> byte in the range [`01`, `02`, .. , `7F`], is an OPTION /bcp14> domain separation byte, and</li>
AL Domain separation byte and</t> <li>L positive integer is the requested number of output bytes.</li>
<t hangText="L"> positive integer, is the requested number of output byt </ul>
es.</t> <t>
</list></t> Conceptually, an XOF can be viewed as a hash function with an infinitely l
ong output truncated to L bytes.
<t> This means that calling an XOF with the same input parameters but two diff
Conceptually, a XOF can be viewed as a hash function with an infinitely lo erent lengths yields outputs such that the shorter one is a prefix of the longer
ng output truncated to L bytes. one.
This means that calling a XOF with the same input parameters but two diffe
rent lengths yields outputs such that the shorter one is a prefix of the longer
one.
Specifically, if L1 &lt; L2, then TurboSHAKE(M, D, L1) is the same as the first L1 bytes of TurboSHAKE(M, D, L2). Specifically, if L1 &lt; L2, then TurboSHAKE(M, D, L1) is the same as the first L1 bytes of TurboSHAKE(M, D, L2).
</t> </t>
<t>By default, the domain separation byte is `1F`. For an API that
<t>By default, the Domain separation byte is `1F`. For an API that does not support a domain separation byte, D <bcp14>MUST</bcp14> be the `1
does not support a domain separation byte, D MUST be the `1F`.</t> F`.</t>
<t> <t>
The TurboSHAKE instance produces output that is a hash of the (M, D) coupl e. The TurboSHAKE instance produces output that is a hash of the (M, D) coupl e.
If D is fixed, this becomes a hash of the Message M. If D is fixed, this becomes a hash of the message M.
However, a protocol that requires a number of independent hash functions c an choose different values for D to implement these. However, a protocol that requires a number of independent hash functions c an choose different values for D to implement these.
Specifically, for any distinct values D1 and D2, TurboSHAKE(M, D1, L1) and Specifically, for distinct values D1 and D2, TurboSHAKE(M, D1, L1) and Tur
TurboSHAKE(M, D2, L2) yield independent hashes of M. boSHAKE(M, D2, L2) yield independent hashes of M.
</t> </t>
<t>
<t> Note that an implementation <bcp14>MAY</bcp14> propose an incremental inpu
Note that an implementation MAY propose an incremental input interface whe t interface where the input string M is given in pieces.
re the input string M is given in pieces. If so, the output <bcp14>MUST</bcp14> be the same as if the function was c
If so, the output MUST be the same as if the function was called with M eq alled with M equal to the concatenation of the different pieces in the order the
ual to the concatenation of the different pieces in the order they were given. y were given.
Independently, an implementation MAY propose an incremental output interfa Independently, an implementation <bcp14>MAY</bcp14> propose an incremental
ce where the output string is requested in pieces of given lengths. output interface where the output string is requested in pieces of given length
When the output is formed by concatenating the pieces in the requested ord s.
er, it MUST be the same as if the function was called with L equal to the sum of When the output is formed by concatenating the pieces in the requested ord
the given lengths. er, it <bcp14>MUST</bcp14> be the same as if the function was called with L equa
</t> l to the sum of the given lengths.
</t>
</section> </section>
<section numbered="true" toc="default">
<section title="Specifications"> <name>Specifications</name>
<t>TurboSHAKE makes use of the permutation Keccak-p[1600,n_r=12], <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 i.e., the permutation used in SHAKE and SHA-3 functions reduced
to its last n_r=12 rounds and specified in FIPS 202, Sections to its last n_r=12 rounds as specified in FIPS 202; see Sections
3.3 and 3.4 <xref target="FIPS202"></xref>. 3.3 and 3.4 of <xref target="FIPS202" format="default"/>.
KP denotes this permutation.</t> KP denotes this permutation.</t>
<t>Similarly to SHAKE128, TurboSHAKE128 is a sponge function
<t>Similarly to SHAKE128, TurboSHAKE128 is a sponge function
calling this permutation KP with a rate of 168 bytes calling this permutation KP with a rate of 168 bytes
or 1344 bits. It follows that TurboSHAKE128 has a capacity of or 1344 bits. It follows that TurboSHAKE128 has a capacity of
1600 - 1344 = 256 bits or 32 bytes. Respectively to SHAKE256, TurboSHAKE25 6 makes use 1600 - 1344 = 256 bits or 32 bytes. Respectively to SHAKE256, TurboSHAKE25 6 makes use
of a rate of 136 bytes or 1088 bits, and has a capacity of 512 bits or 64 of a rate of 136 bytes or 1088 bits and has a capacity of 512 bits or 64 b
bytes.</t> ytes.</t>
<t><figure><artwork><![CDATA[
+-------------+--------------+
| Rate | Capacity |
+----------------+-------------+--------------+
| TurboSHAKE128 | 168 Bytes | 32 Bytes |
| | | |
| TurboSHAKE256 | 136 Bytes | 64 Bytes |
+----------------+-------------+--------------+]]></artwork>
</figure></t>
<t>We now describe the operations inside TurboSHAKE128.<list style="symbol <table>
s"> <thead>
<t>First the input M' is formed by appending the domain separation byte <tr>
D to the message M.</t> <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> <t>We now describe the operations inside TurboSHAKE128.</t>
If the length of M' is not a multiple of 168 bytes then it is padded w <ul spacing="normal">
ith zeros at the end to make it a multiple of 168 bytes. <li>
If M' is already a multiple of 168 bytes then no padding is added. <t>First, the input M' is formed by appending the domain separation
Then a byte `80` is XORed to the last byte of the padded input M' byte D to the message M.</t>
</li>
<li>
<t>
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. and the resulting string is split into a sequence of 168-byte blocks.
</t> </t>
</li>
<t>M' never has a length of 0 bytes due to the presence of the domain se <li>
paration byte.</t> <t>M' never has a length of 0 bytes due to the presence of the domai
n separation byte.</t>
<t>As defined by the sponge construction, the process operates on a stat </li>
e <li>
and consists of two phases: the absorbing phase that processes the padde <t>As defined by the sponge construction, the process operates on a
d input M' state
and the squeezing phase that produces the output.</t> and consists of two phases: the absorbing phase, which processes the pad
ded input M',
<t>In the absorbing phase the state is initialized to all-zero. The and the squeezing phase, which produces the output.</t>
</li>
<li>
<t>In the absorbing phase, the state is initialized to all zero. The
message blocks are XORed into the first 168 bytes of the state. 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> Each block absorbed is followed with an application of KP to the state.< /t>
</li>
<t> In the squeezing phase the output is formed by taking the first 168 <li>
bytes of the state, <t> 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. </t> 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 wi <t>TurboSHAKE256 performs the same steps but makes use of 136-byte block
th respect s with respect
to the padding, absorbing, and squeezing phases.</t> to the padding, absorbing, and squeezing phases.</t>
<t>
<t> The definition of the TurboSHAKE functions equivalently implements the pad10
The definition of the TurboSHAKE functions equivalently implements the pad10 *1 rule; see Section 5.1 of <xref target="FIPS202" format="default"/> for a defi
*1 rule; see Section 5.1 of <xref target="FIPS202"/> for a definition of pad10*1 nition of pad10*1.
.
While M can be empty, the D byte is always present and is in the `01`-`7F` r ange. While M can be empty, the D byte is always present and is in the `01`-`7F` r ange.
This last byte serves as domain separation and integrates the first bit of p adding This last byte serves as domain separation and integrates the first bit of p adding
of the pad10*1 rule (hence it cannot be `00`). of the pad10*1 rule (hence, it cannot be `00`).
Additionally, it must leave room for the second bit of padding Additionally, it must leave room for the second bit of padding
(hence it cannot have the MSB set to 1), should it be the last byte of the b (hence, it cannot have the most significant bit (MSB) set to 1), should it b
lock. e the last byte of the block.
For more details, refer to Section 6.1 of <xref target="KT"></xref> and Sect For more details, refer to Section 6.1 of <xref target="KT" format="default"
ion 3 of <xref target="TURBOSHAKE"></xref>.</t> /> and Section 3 of <xref target="TURBOSHAKE" format="default"/>.</t>
<t>The pseudocode versions of TurboSHAKE128 and TurboSHAKE256 are provid
<t>The pseudocode versions of TurboSHAKE128 and TurboSHAKE256 are provided r ed in Appendices <xref target="TSHK128_PC" format="counter"/> and <xref target="
espectively in <xref target="TSHK128_PC"/> and <xref target="TSHK256_PC"/>.</t> TSHK256_PC" format="counter"/>, respectively.</t>
</section>
</section> </section>
</section> <section numbered="true" toc="default">
<name>KangarooTwelve: Tree Hashing over TurboSHAKE</name>
<section title="KangarooTwelve: Tree hashing over TurboSHAKE"> <section numbered="true" toc="default">
<name>Interface</name>
<section title="Interface"> <t>KangarooTwelve is a family of eXtendable-Output Functions (XOFs) cons
<t>KangarooTwelve is a family of eXtendable Output Functions (XOF) consist isting of the KT128 and KT256 instances.
ing of the KT128 and KT256 instances. A KangarooTwelve instance takes two byte strings (M, C) and a positive int
A KangarooTwelve instance takes as input parameters two byte-strings (M, C eger L as input parameters, where:</t>
) and a positive integer L <ul spacing="normal">
where <list style="hanging"> <li>M byte string is the message,</li>
<t hangText="M"> byte-string, is the Message and</t> <li>C byte string is an <bcp14>OPTIONAL</bcp14> customization string,
<t hangText="C"> byte-string, is an OPTIONAL Customization string and</t> and</li>
<t hangText="L"> positive integer, the requested number of output bytes.</ <li>L positive integer is the requested number of output bytes.</li>
t> </ul>
</list></t> <t>The customization string <bcp14>MAY</bcp14> serve as domain separatio
n.
<t>The Customization string MAY serve as domain separation. It is typically a short string such as a name or an identifier (e.g., UR
It is typically a short string such as a name or an identifier (e.g. URI I,
, Object Identifier (OID), etc.).
ODI...). It can serve the same purpose as TurboSHAKE's D input parameter (see <xr
It can serve the same purpose as TurboSHAKE's D input parameter (see <xr ef target="TurboSHAKE_Interface" format="default"/>) but with a larger range.
ef target="TurboSHAKE_Interface"/>), but with a larger range.
</t> </t>
<t>By default, the customization string is the empty string. For an API
<t>By default, the Customization string is the empty string. For an API that
that does not support a customization string parameter, C <bcp14>MUST</bcp14>
does not support a customization string parameter, C MUST be the empty s be the empty string.</t>
tring.</t> <t>Note that an implementation <bcp14>MAY</bcp14> propose an interface w
ith the input and/or output provided incrementally, as specified in <xref target
<t>Note that an implementation MAY propose an interface with the input a ="TurboSHAKE_Interface" format="default"/>.</t>
nd/or output provided incrementally as specified in <xref target="TurboSHAKE_Int </section>
erface"/>.</t> <section numbered="true" toc="default">
</section> <name>Specification of KT128</name>
<section title="Specification of KT128">
<t>On top of the sponge function TurboSHAKE128, KT128 uses a <t>On top of the sponge function TurboSHAKE128, KT128 uses a
Sakura-compatible tree hash mode <xref target="SAKURA"></xref>. Sakura-compatible tree hash mode <xref target="SAKURA" format="default"/
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 First, merge M and the <bcp14>OPTIONAL</bcp14> C to a single input strin
byte-string. g S in a
See <xref target="RE"/>.</t> reversible way. length_encode( |C|&nbsp;) gives the length in bytes of C
as a
byte string.
See <xref target="RE" format="default"/>.</t>
<t><figure><artwork><![CDATA[ <artwork name="" type="" align="left" alt=""><![CDATA[
S = M || C || length_encode( |C| ) ]]></artwork></figure></t> S = M || C || length_encode( |C| )]]></artwork>
<t>Then, split S into n chunks of 8192 bytes.</t> <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 = S_0 || .. || S_(n-1)
|S_0| = .. = |S_(n-2)| = 8192 bytes |S_0| = .. = |S_(n-2)| = 8192 bytes
|S_(n-1)| <= 8192 bytes ]]></artwork></figure></t> |S_(n-1)| <= 8192 bytes]]></artwork>
<t>From S_1 .. S_(n-1), compute the 32-byte Chaining Values CV_1 .. CV_( <t>From S_1 .. S_(n-1), compute the 32-byte chaining values CV_1 .. CV_(
n-1). n-1).
In order to be optimally efficient, this computation MAY exploit the In order to be optimally efficient, this computation <bcp14>MAY</bcp14>
parallelism available on the platform such as SIMD instructions.</t> exploit the
parallelism available on the platform, such as single instruction, multi
ple 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> CV_i = TurboSHAKE128( S_i, `0B`, 32 )]]></artwork>
<t>Compute the final node: FinalNode. <t>Compute the final node: FinalNode.</t>
<list style="symbols">
<t>If |S| &lt;= 8192 bytes, FinalNode = S</t>
<t>Otherwise compute FinalNode as follows:</t>
</list></t>
<t><figure><artwork><![CDATA[ <ul spacing="normal">
<li>
<t>If |S| &lt;= 8192 bytes, FinalNode = S.</t>
</li>
<li>
<t>Otherwise, compute FinalNode as follows:</t>
</li>
</ul>
<artwork name="" type="" align="left" alt=""><![CDATA[
FinalNode = S_0 || `03 00 00 00 00 00 00 00` FinalNode = S_0 || `03 00 00 00 00 00 00 00`
FinalNode = FinalNode || CV_1 FinalNode = FinalNode || CV_1
.. ..
FinalNode = FinalNode || CV_(n-1) FinalNode = FinalNode || CV_(n-1)
FinalNode = FinalNode || length_encode(n-1) FinalNode = FinalNode || length_encode(n-1)
FinalNode = FinalNode || `FF FF`]]></artwork></figure></t> FinalNode = FinalNode || `FF FF`]]></artwork>
<t>Finally, the KT128 output is retrieved: <t>Finally, the KT128 output is retrieved:</t>
<list style="symbols"> <ul spacing="normal">
<t>If |S| &lt;= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L ) <li><t>If |S| &lt;= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L
</t> )</t>
</list></t>
<t><figure> <artwork name="" type="" align="left" alt=""><![CDATA[
<artwork><![CDATA[ KT128( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )]]></artwork>
KT128( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )]]> </li>
</artwork></figure></t>
<t><list style="symbols"> <li><t>Otherwise, from TurboSHAKE128( FinalNode, `06`, L )</t>
<t>Otherwise from TurboSHAKE128( FinalNode, `06`, L )</t>
</list></t>
<t><figure> <artwork name="" type="" align="left" alt=""><![CDATA[
<artwork><![CDATA[ KT128( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L )]]></artwork>
KT128( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L )]]> </li>
</artwork></figure></t> </ul>
<t>The following figure illustrates the computation flow of KT128 <t>The following figure illustrates the computation flow of KT128
for |S| &lt;= 8192 bytes:</t> for |S| &lt;= 8192 bytes:</t>
<t><figure><artwork><![CDATA[ <artwork name="" type="" align="left" alt=""><![CDATA[
+--------------+ TurboSHAKE128(.., `07`, L) +--------------+ TurboSHAKE128(.., `07`, L)
| S |-----------------------------> output | S |-----------------------------> output
+--------------+]]></artwork></figure></t> +--------------+]]></artwork>
<t>The following figure illustrates the computation flow of KT128
<t>The following figure illustrates the computation flow of KT128 for |S| &gt; 8192 bytes and where TurboSHAKE128 and length_encode(&nbsp;x&
for |S| &gt; 8192 bytes and where TurboSHAKE128 and length_encode(&#160;x& nbsp;) are
#160;) are abbreviated as TSHK128 and l_e(&nbsp;x&nbsp;), respectively:</t>
abbreviated as respectively TSHK128 and l_e(&#160;x&#160;) :</t> <artwork name="" type="" align="left" alt=""><![CDATA[
<t><figure><artwork><![CDATA[
+--------------+ +--------------+
| S_0 | | S_0 |
+--------------+ +--------------+
|| ||
+--------------+ +--------------+
| `03`||`00`^7 | | `03`||`00`^7 |
+--------------+ +--------------+
|| ||
+---------+ TSHK128(..,`0B`,32) +--------------+ +---------+ TSHK128(..,`0B`,32) +--------------+
| S_1 |---------------------->| CV_1 | | S_1 |---------------------->| CV_1 |
skipping to change at line 470 skipping to change at line 430
+---------+ +--------------+ +---------+ +--------------+
|| ||
+--------------+ +--------------+
| l_e( n-1 ) | | l_e( n-1 ) |
+--------------+ +--------------+
|| ||
+--------------+ +--------------+
| `FF FF` | | `FF FF` |
+--------------+ +--------------+
| TSHK128(.., `06`, L) | TSHK128(.., `06`, L)
+--------------------> output]]></artw +--------------------> output]]></artw
ork></figure></t> ork>
<t>A pseudocode version is provided in <xref target="KT128_PC"/>.</t>
<t>The table below gathers the values of the domain separation <t>A pseudocode version is provided in <xref target="KT128_PC" format="d
efault"/>.</t>
<t>The table below gathers the values of the domain separation
bytes used by the tree hash mode:</t> bytes used by the tree hash mode:</t>
<t><figure><artwork><![CDATA[ <table>
+--------------------+------------------+ <thead>
| Type | Byte | <tr>
+--------------------+------------------+ <th>Type</th>
| SingleNode | `07` | <th>Byte</th>
| | | </tr>
| IntermediateNode | `0B` | </thead>
| | | <tbody>
| FinalNode | `06` | <tr>
+--------------------+------------------+]]></artwork> <td>SingleNode</td>
</figure></t> <td>`07`</td>
</section> </tr>
<tr>
<section anchor="RE" title="length_encode( x )"> <td>IntermediateNode</td>
<td>`0B`</td>
</tr>
<tr>
<td>FinalNode</td>
<td>`06`</td>
</tr>
</tbody>
</table>
<t>The function length_encode takes as inputs a non-negative integer x </section>
<section anchor="RE" numbered="true" toc="default">
<name>length_encode( x )</name>
<t>The function length_encode takes as inputs a non-negative integer x
&lt; 256**255 and outputs a string of bytes x_(n-1) || .. || x_0 || n wher e</t> &lt; 256**255 and outputs a string of bytes x_(n-1) || .. || x_0 || n wher e</t>
<artwork name="" type="" align="left" alt=""><![CDATA[
<t><figure> x = sum of 256**i * x_i for i from 0 to n-1]]></artwork>
<artwork><![CDATA[ <t>and where n is the smallest non-negative integer such that x &lt; 256
x = sum of 256**i * x_i for i from 0 to n-1]]></artwork></figure></t> **n.
<t>and where n is the smallest non-negative integer such that x &lt; 256**
n.
n is also the length of x_(n-1) || .. || x_0.</t> n is also the length of x_(n-1) || .. || x_0.</t>
<t>For example, length_encode(0) = `00`, length_encode(12) = `0C 01`, an
<t>As example, length_encode(0) = `00`, length_encode(12) = `0C 01` and d
length_encode(65538) = `01 00 02 03`</t> length_encode(65538) = `01 00 02 03`.</t>
<t>A pseudocode version is as follows, where { b } denotes the byte of n
<t>A pseudocode version is as follows where { b } denotes the byte of nume umerical value b.</t>
rical value b.</t> <sourcecode type="pseudocode"><![CDATA[
<t><figure><artwork><![CDATA[
length_encode(x): length_encode(x):
S = `00`^0 S = `00`^0
while x > 0 while x > 0
S = { x mod 256 } || S S = { x mod 256 } || S
x = x / 256 x = x / 256
S = S || { |S| } S = S || { |S| }
return S return S
end]]></artwork></figure></t> end]]></sourcecode>
</section>
</section> <section numbered="true" toc="default">
<name>Specification of KT256</name>
<section title="Specification of KT256"> <t>KT256 is specified exactly like KT128, with two differences:</t>
<t>KT256 is specified exactly like KT128, with two differences:</t> <ul spacing="normal">
<list style="symbols"> <li>
<t>All the calls to TurboSHAKE128 in KT128 are replaced with calls to Tu <t>All the calls to TurboSHAKE128 in KT128 are replaced with calls t
rboSHAKE256 in KT256.</t> o TurboSHAKE256 in KT256.</t>
<t>The chaining values CV_1 to CV_(n-1) are 64-byte long in KT256 and ar </li>
e computed as follows:</t> <li>
</list> <t>The chaining values CV_1 to CV_(n-1) are 64 bytes long in KT256 a
<t><figure><artwork><![CDATA[ nd are computed as follows:</t>
CV_i = TurboSHAKE256( S_i, `0B`, 64 )]]></artwork></figure></t> <artwork name="" type="" align="left" alt=""><![CDATA[
CV_i = TurboSHAKE256( S_i, `0B`, 64 )]]></artwork>
<t>A pseudocode version is provided in <xref target="KT256_PC"/>.</t> </li>
</ul>
<t>A pseudocode version is provided in <xref target="KT256_PC" format="d
efault"/>.</t>
</section>
</section> </section>
</section> <section numbered="true" toc="default">
<name>Message Authentication Codes</name>
<section title="Message authentication codes"> <t>Implementing a Message Authentication Code (MAC) with KT128 or KT256 <b
<t>Implementing a MAC with KT128 or KT256 MAY use a hash-then-MAC constructi cp14>MAY</bcp14> use a hash-then-MAC construction.
on.
This document defines and recommends a method called HopMAC:</t> This document defines and recommends a method called HopMAC:</t>
<artwork name="" type="" align="left" alt=""><![CDATA[
<t><figure>
<artwork><![CDATA[
HopMAC128(Key, M, C, L) = KT128(Key, KT128(M, C, 32), L) 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> HopMAC256(Key, M, C, L) = KT256(Key, KT256(M, C, 64), L)]]></artwork>
</figure></t> <t>Similarly to Hashed Message Authentication Code (HMAC), HopMAC consists
of two calls: an inner call compressing the
<t>Similarly to HMAC, HopMAC consists of two calls: an inner call compressin message M and the optional customization string C to a digest
g 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.</t> 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
<t>Unlike HMAC, the inner call to KangarooTwelve in HopMAC is keyless and does not require additional protection against side channel attacks (S
and does not require additional protection against side channel attacks (S CAs).
CA).
Consequently, in an implementation that has to protect the HopMAC key Consequently, in an implementation that has to protect the HopMAC key
against SCA only the outer call does need protection, against an SCA, only the outer call needs protection,
and this amounts to a single execution of the underlying permutation (assu ming the key length is at most 69 bytes).</t> and this amounts to a single execution of the underlying permutation (assu ming the key length is at most 69 bytes).</t>
<t>In any case, TurboSHAKE128, TurboSHAKE256, KT128, and KT256
<t>In any case, TurboSHAKE128, TurboSHAKE256, KT128 and KT256 <bcp14>MAY</bcp14> be used to compute a MAC with the key
MAY be used to compute a MAC with the key reversibly prepended or appended to the input. For instance, one <bcp14>MA
reversibly prepended or appended to the input. For instance, one MAY Y</bcp14>
compute a MAC on short messages simply calling KT128 with the compute a MAC on short messages simply calling KT128 with the
key as the customization string, i.e., MAC = KT128(M, Key, L).</t> key as the customization string, i.e., MAC = KT128(M, Key, L).</t>
</section> </section>
<section numbered="true" toc="default">
<section title="Test vectors"> <name>Test Vectors</name>
<t>Test vectors are based on the repetition of the pattern `00 01 02 .. F9
<t>Test vectors are based on the repetition of the pattern `00 01 02 .. F9 F FA`
A`
with a specific length. ptn(n) defines a string by repeating the pattern 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 e.g. `00 01 02 .. F9 FA` as many times as necessary and truncated to n bytes, for
</t> example:
</t>
<t><figure><artwork><![CDATA[ Pattern for a length of 17 bytes: <artwork name="" type="" align="left" alt=""><![CDATA[
Pattern for a length of 17 bytes:
ptn(17) = ptn(17) =
`00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10`]]></artwork></figure> `00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10`]]></artwork>
</t> <artwork name="" type="" align="left" alt=""><![CDATA[
Pattern for a length of 17**2 bytes:
<t><figure><artwork><![CDATA[ Pattern for a length of 17**2 bytes:
ptn(17**2) = ptn(17**2) =
`00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F `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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
20 21 22 23 24 25`]]></artwork></figure></t> 20 21 22 23 24 25`]]></artwork>
<t><figure><artwork><![CDATA[ <artwork name="" type="" align="left" alt=""><![CDATA[
TurboSHAKE128(M=`00`^0, D=`1F`, 32): TurboSHAKE128(M=`00`^0, D=`1F`, 32):
`1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53 `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` 8C D9 45 A3 97 DD EC 54 1F 1C E4 1A F2 C1 B7 4C`
TurboSHAKE128(M=`00`^0, D=`1F`, 64): TurboSHAKE128(M=`00`^0, D=`1F`, 64):
`1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53 `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 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 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` E8 19 3B DF 58 73 73 63 32 16 91 C0 54 62 C8 DF`
skipping to change at line 663 skipping to change at line 620
`8D EE AA 1A EC 47 CC EE 56 9F 65 9C 21 DF A8 E1 `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` 12 DB 3C EE 37 B1 81 78 B2 AC D8 05 B7 99 CC 37`
TurboSHAKE128(M=`FF`, D=`30`, 32): TurboSHAKE128(M=`FF`, D=`30`, 32):
`55 31 22 E2 13 5E 36 3C 32 92 BE D2 C6 42 1F A2 `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` 32 BA B0 3D AA 07 C7 D6 63 66 03 28 65 06 32 5B`
TurboSHAKE128(M=`FF FF FF`, D=`7F`, 32): TurboSHAKE128(M=`FF FF FF`, D=`7F`, 32):
`16 27 4C C6 56 D4 4C EF D4 22 39 5D 0F 90 53 BD `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` A6 D2 8E 12 2A BA 15 C7 65 E5 AD 0E 6E AF 26 F9`
]]></artwork></figure></t> ]]></artwork>
<t><figure><artwork><![CDATA[ <artwork name="" type="" align="left" alt=""><![CDATA[
TurboSHAKE256(M=`00`^0, D=`1F`, 64): TurboSHAKE256(M=`00`^0, D=`1F`, 64):
`36 7A 32 9D AF EA 87 1C 78 02 EC 67 F9 05 AE 13 `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 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 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` 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: 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 `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` 20 72 65 DC CF 2F 43 53 4E 9C 61 BA 0C 9D 1D 75`
skipping to change at line 753 skipping to change at line 710
`F3 FE 12 87 3D 34 BC BB 2E 60 87 79 D6 B7 0E 7F `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 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 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` 3B 5D DA B8 EE 25 5E 39 EE 38 90 72 96 2C 11 1A`
TurboSHAKE256(M=`FF FF FF`, D=`7F`, 64): TurboSHAKE256(M=`FF FF FF`, D=`7F`, 64):
`AB E5 69 C1 F7 7E C3 40 F0 27 05 E7 D3 7C 9A B7 `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 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 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` CF 7E D9 11 0B A9 7C E0 38 8D 07 4B AC 76 87 76`
]]></artwork></figure></t> ]]></artwork>
<t><figure><artwork><![CDATA[ KT128(M=`00`^0, C=`00`^0, 32): <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 `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` 3C 08 03 57 7A C7 16 7F 06 FE 2C E1 F0 EF 39 E5`
KT128(M=`00`^0, C=`00`^0, 64): KT128(M=`00`^0, C=`00`^0, 64):
`1A C2 D4 50 FC 3B 42 05 D1 9D A7 BF CA 1B 37 51 `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 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 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` 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: KT128(M=`00`^0, C=`00`^0, 10032), last 32 bytes:
skipping to change at line 827 skipping to change at line 785
KT128(M=ptn(8192 bytes), C=`00`^0, 32): 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 `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` 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): 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 `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` 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): 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 `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`]]></artwork></figure></t> 04 55 9A 2E A4 5F 78 57 0A 15 25 3D 67 BA 00 AE`]]></artwork>
<t><figure><artwork><![CDATA[ KT256(M=`00`^0, C=`00`^0, 64): <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 `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 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 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` 3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9`
KT256(M=`00`^0, C=`00`^0, 128): KT256(M=`00`^0, C=`00`^0, 128):
`B2 3D 2E 9C EA 9F 49 04 E0 2B EC 06 81 7F C1 0C `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 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 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 3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9
skipping to change at line 939 skipping to change at line 898
KT256(M=ptn(8192 bytes), C=ptn(8189 bytes), 64): 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 `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 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 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` 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): 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 `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 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 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`]]></artwork></figure></t> B9 2D 1F C7 55 84 41 F1 83 2C 32 79 A4 24 1B 8B`]]></artwork>
</section> </section>
<section anchor="IANA" numbered="true" toc="default">
<section anchor="IANA" title="IANA Considerations"> <name>IANA Considerations</name>
<t> In the Named Information Hash Algorithm Registry, k12-256 refers to the <t> In the "Named Information Hash Algorithm Registry", k12-256 refers to
hash the hash
function obtained by evaluating KT128 on the input message with default C (t he empty string) function obtained by evaluating KT128 on the input message with default C (t he empty string)
and L = 32 bytes (256 bits). Similarly, k12-512 refers to the hash function obtained by evaluating 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 byt es (512 bits). </t> KT256 on the input message with default C (the empty string) and L = 64 byt es (512 bits). </t>
<t> In the "COSE Algorithms" registry, IANA has added the following entries for TurboSHAKE and KangarooTwelve:</t>
<t> In the COSE Algorithms registry, the following entries are assigned to T <table>
urboSHAKE and KangarooTwelve:</t> <thead>
<tr>
<t><figure><artwork><![CDATA[ <th>Name</th>
+---------------+-------+-------------------+--------------+ <th>Value</th>
| Name | Value | Description | Capabilities | <th>Description</th>
+---------------+-------+-------------------+--------------+ <th>Capabilities</th>
| TurboSHAKE128 | -261 | TurboSHAKE128 XOF | [kty] | </tr>
| | | | | </thead>
| TurboSHAKE256 | -262 | TurboSHAKE256 XOF | [kty] | <tbody>
| | | | | <tr>
| KT128 | -263 | KT128 XOF | [kty] | <td>TurboSHAKE128</td>
| | | | | <td>-261</td>
| KT256 | -264 | KT256 XOF | [kty] | <td>TurboSHAKE128 XOF</td>
+---------------+-------+-------------------+--------------+ ]]></artwor <td>[kty]</td>
k> </tr>
</figure></t> <tr>
</section> <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 anchor="Security" title="Security Considerations"> </section>
<t>This document is meant to serve as a stable reference and an <section anchor="Security" numbered="true" toc="default">
implementation guide for the KangarooTwelve and TurboSHAKE eXtendable Output <name>Security Considerations</name>
Functions. <t>This document is meant to serve as a stable reference and an
The security assurance of these functions relies on the cryptanalysis of red implementation guide for the KangarooTwelve and TurboSHAKE eXtendable-Output
uced-round versions of Keccak and they have the same claimed security strength a Functions.
s their corresponding SHAKE functions.</t> The security assurance of these functions relies on the cryptanalysis of red
uced-round versions of Keccak, and they have the same claimed security strength
as their corresponding SHAKE functions.</t>
<t><figure><artwork><![CDATA[ <table>
+-------------------------------+ <thead>
| security claim | <tr>
+-----------------+-------------------------------+ <td></td>
| TurboSHAKE128 | 128 bits (same as SHAKE128) | <th>Security Claim</th>
| | | </tr>
| KT128 | 128 bits (same as SHAKE128) | </thead>
| | | <tbody>
| TurboSHAKE256 | 256 bits (same as SHAKE256) | <tr>
| | | <th>TurboSHAKE128</th>
| KT256 | 256 bits (same as SHAKE256) | <td>128 bits (same as SHAKE128)</td>
+-----------------+-------------------------------+]]></artwork> </tr>
</figure></t> <tr>
<th>KT128</th>
<td>128 bits (same as SHAKE128)</td>
</tr>
<tr>
<th>TurboSHAKE256</th>
<td>256 bits (same as SHAKE256)</td>
</tr>
<tr>
<th>KT256</th>
<td>256 bits (same as SHAKE256)</td>
</tr>
</tbody>
</table>
<t> <t>To be more precise, KT128 is made of two layers:</t>
To be more precise, KT128 is made of two layers: <ul spacing="normal">
<list style="symbols"> <li>
<t>The inner function TurboSHAKE128. <t>The inner function TurboSHAKE128.
The security assurance of this layer relies on cryptanalysis. The security assurance of this layer relies on cryptanalysis.
The TurboSHAKE128 function is exactly Keccak[r=1344, c=256] (as in SHAKE128) The TurboSHAKE128 function is exactly Keccak[r=1344, c=256] (as in SHAKE128)
reduced to 12 rounds. reduced to 12 rounds.
Any cryptanalysis of reduced-round Keccak is also cryptanalysis of reduced-r ound TurboSHAKE128 Any cryptanalysis of reduced-round Keccak is also cryptanalysis of reduced-r ound TurboSHAKE128
(provided the number of rounds attacked is not higher than 12).</t> (provided the number of rounds attacked is not higher than 12).</t>
<t>The tree hashing over TurboSHAKE128. This layer is a mode on top </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 of TurboSHAKE128 that does not introduce any vulnerability thanks to
the use of Sakura coding proven secure in <xref target="SAKURA"/>.</t> the use of Sakura coding proven secure in <xref target="SAKURA" format="defa
</list></t> ult"/>.</t>
<t>This reasoning is detailed and formalized in <xref target="KT"/>.</t> </li>
</ul>
<t>KT256 is structured as KT128, except that it uses TurboSHAKE256 as inner <t>This reasoning is detailed and formalized in <xref target="KT" format="
function. 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) 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> reduced to 12 rounds, and the same reasoning on cryptanalysis applies.</t>
<t>TurboSHAKE128 and KT128 aim at 128-bit security.
<t>TurboSHAKE128 and KT128 aim at 128-bit security. To achieve 128-bit security strength, L, the chosen output length, <bcp14>MU
To achieve 128-bit security strength, the output L MUST be chosen long ST</bcp14> be large
enough so that there are no generic attacks that violate 128-bit security. 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 So for 128-bit (second) preimage security, the output should be at least 128
bits, bits;
for 128 bits of security against multi-target preimage attacks with T target for 128 bits of security against multi-target preimage attacks with T target
s s,
the output should be at least 128+log_2(T) bits 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. 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 Furthermore, when the output length is at least 256 bits, TurboSHAKE128 and
KT128 achieve NIST's post-quantum security level 2 <xref target="NISTPQ"/>.< KT128 achieve NIST's post-quantum security level 2 <xref target="NISTPQ" for
/t> mat="default"/>.</t>
<t>Similarly, TurboSHAKE256 and KT256 aim at 256-bit security.
<t>Similarly, TurboSHAKE256 and KT256 aim at 256-bit security. To achieve 256-bit security strength, L, the chosen output length, <bcp14>MU
To achieve 256-bit security strength, the output L MUST be chosen long ST</bcp14> be large
enough so that there are no generic attacks that violate 256-bit security. 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 So for 256-bit (second) preimage security, the output should be at least 256
bits, bits;
for 256 bits of security against multi-target preimage attacks with T target for 256 bits of security against multi-target preimage attacks with T target
s s,
the output should be at least 256+log_2(T) bits 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. 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 Furthermore, when the output length is at least 512 bits, TurboSHAKE256 and
KT256 achieve NIST's post-quantum security level 5 <xref target="NISTPQ"/>.< KT256 achieve NIST's post-quantum security level 5 <xref target="NISTPQ" for
/t> mat="default"/>.</t>
<t>
<t> Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE256, KT12
Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128, TurboSHAKE256, KT12 8, and KT256 do not suffer from the length extension weakness and therefore do n
8 and KT256 do not suffer from the length extension weakness, and therefore do n ot require the use of the HMAC construction, for instance, when used for MAC com
ot require the use of the HMAC construction for instance when used for MAC compu putation <xref target="FIPS198" format="default"/>.
tation <xref target="FIPS198"/>.
Also, they can naturally be used as a key derivation function. Also, they can naturally be used as a key derivation function.
The input must be an injective encoding of secret and diversification mate rial, and the output can be taken as the derived key(s). The input must be an injective encoding of secret and diversification mate rial, 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 sha red secret produced by The input does not need to be uniformly distributed, e.g., it can be a sha red secret produced by
the Diffie-Hellman or ECDH protocol, but it needs to have sufficient min-e ntropy. the Diffie-Hellman or Elliptic Curve Diffie-Hellman (ECDH) protocol, but i t needs to have sufficient min-entropy.
</t> </t>
<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 TurboSHAKE
256
<bcp14>SHOULD</bcp14> avoid using these three values for D.</t>
</section>
<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 TurboSHAK
E256,
SHOULD avoid using these three values for D.</t>
</section>
<!--
<section title="Contributors">
<t><cref>[TEMPLATE TODO] This optional section can be used to mention cont
ributors to your internet draft.</cref></t>
</section> -->
</middle> </middle>
<back>
<back> <references>
<name>References</name>
<references>
<name>Normative References</name>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2
119.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8
174.xml"/>
<!-- References Section --> <reference anchor="FIPS202" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.
<references title="Normative References"> FIPS.202.pdf">
&rfc2119; <front>
&rfc8174; <title>SHA-3 Standard: Permutation-Based Hash and Extendable-Output Function
<reference anchor="FIPS202"> s</title>
<front> <author>
<title>FIPS PUB 202 - SHA-3 Standard: Permutation-Based Hash and <organization abbrev="NIST">National Institute of Standards and Technology
Extendable-Output Functions</title> </organization>
<author> </author>
<organization>National Institute of Standards and Technology <date month="August" year="2015"/>
</organization> </front>
</author> <seriesInfo name="NIST FIPS" value="202"/>
<date month="August" year="2015"></date> <seriesInfo name="DOI" value="10.6028/NIST.FIPS.202"/>
</front> </reference>
<seriesInfo name="WWW" value="http://dx.doi.org/10.6028/NIST.FIPS.202" />
</reference>
<reference anchor="SP800-185">
<front>
<title>NIST Special Publication 800-185 SHA-3 Derived Functions:
cSHAKE, KMAC, TupleHash and ParallelHash</title>
<author>
<organization>National Institute of Standards and Technology
</organization>
</author>
<date month="December" year="2016"></date>
</front>
<seriesInfo name="WWW" value="https://doi.org/10.6028/NIST.SP.800-185" />
</reference>
</references>
<references title="Informative References"> <reference anchor="SP800-185">
<front>
<title>SHA-3 Derived Functions:
cSHAKE, KMAC, TupleHash and ParallelHash</title>
<author fullname="John Kelsey" surname="Kelsey">
<organization>Information Technology 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"/>
</front>
<seriesInfo 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>
<reference anchor="TURBOSHAKE"> </references>
<front> <references>
<title>TurboSHAKE</title> <name>Informative References</name>
<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="Beno&icirc;t Viguier"/>
<date month="March" year="2023"/>
</front>
<seriesInfo name="WWW" value="http://eprint.iacr.org/2023/342"/>
</reference>
<reference anchor="KT"> <reference anchor="TURBOSHAKE" target="http://eprint.iacr.org/2023/342">
<front> <front>
<title>KangarooTwelve: fast hashing based on Keccak-p</title> <title>TurboSHAKE</title>
<author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/>
<author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/>
<author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="S." surname="Hoffert" fullname="Seth Hoffert"/>
<author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/>
<author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assc
<author initials="B." surname="Viguier" fullname="Beno&icirc;t Viguier"/> he"/>
<date month="July" year="2018"/> <author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/>
</front> <author initials="B." surname="Viguier" fullname="Benoît Viguier"/>
<seriesInfo name="WWW" value="https://link.springer.com/chapter/10.1007/978- <date month="March" year="2023"/>
3-319-93387-0_21"/> </front>
<seriesInfo name="WWW" value="http://eprint.iacr.org/2016/770.pdf"/> <refcontent>Cryptology ePrint Archive, Paper 2023/342</refcontent>
</reference> </reference>
<reference anchor="SAKURA"> <reference anchor="KT" target="https://link.springer.com/chapter/10.1007
<front> /978-3-319-93387-0_21">
<title>Sakura: a flexible coding for tree hashing</title> <front>
<author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <title>KangarooTwelve: Fast Hashing Based on Keccak-p</title>
<author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/>
<author initials="M." surname="Peeters" fullname="Michael Peeters"/> <author initials="J." surname="Daemen" fullname="Joan Daemen"/>
<author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/>
<date month="June" year="2014"/> <author initials="G." surname="Van Assche" fullname="Gilles Van Assc
</front> he"/>
<seriesInfo name="WWW" value="https://link.springer.com/chapter/10.1007/978- <author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/>
3-319-07536-5_14"/> <author initials="B." surname="Viguier" fullname="Benoît Viguier"/>
<seriesInfo name="WWW" value="http://eprint.iacr.org/2013/231.pdf"/> <date month="June" year="2018"/>
</reference> </front>
<refcontent>Applied Cryptography and Network Security (ACNS 2018), Lec
ture Notes in Computer Science, vol. 10892, pp. 400-418</refcontent>
<seriesInfo name="DOI" value="10.1007/978-3-319-93387-0_21"/>
</reference>
<reference anchor="KECCAK_CRYPTANALYSIS"> <reference anchor="SAKURA" target="https://link.springer.com/chapter/10.
<front> 1007/978-3-319-07536-5_14">
<title>Summary of Third-party cryptanalysis of Keccak</title> <front>
<author> <title>Sakura: a Flexible Coding for Tree Hashing</title>
<organization>Keccak Team</organization> <author initials="G." surname="Bertoni" fullname="Guido Bertoni"/>
</author> <author initials="J." surname="Daemen" fullname="Joan Daemen"/>
<date year="2022"/> <author initials="M." surname="Peeters" fullname="Michael Peeters"/>
</front> <author initials="G." surname="Van Assche" fullname="Gilles Van Assc
<seriesInfo name="WWW" value="https://www.keccak.team/third_party.html"/> he"/>
</reference> <date year="2014"/>
</front>
<refcontent>Applied Cryptography and Network Security (ACNS 2014), Lec
ture Notes in Computer Science, vol. 8479, pp. 217-234</refcontent>
<seriesInfo name="DOI" value="10.1007/978-3-319-07536-5_14"/>
</reference>
<reference anchor="XKCP"> <reference anchor="KECCAK_CRYPTANALYSIS" target="https://www.keccak.team
<front> /third_party.html">
<title>eXtended Keccak Code Package</title> <front>
<author initials="G." surname="Bertoni" fullname="Guido Bertoni"/> <title>Summary of Third-party cryptanalysis of Keccak</title>
<author initials="J." surname="Daemen" fullname="Joan Daemen"/> <author>
<author initials="M." surname="Peeters" fullname="Michael Peeters"/> <organization>Keccak Team</organization>
<author initials="G." surname="Van Assche" fullname="Gilles Van Assche"/ </author>
> </front>
<author initials="R." surname="Van Keer" fullname="Ronny Van Keer"/> </reference>
<date month="December" year="2022"/>
</front>
<seriesInfo name="WWW" value="https://github.com/XKCP/XKCP"/>
</reference>
<reference anchor="NISTPQ"> <reference anchor="XKCP" target="https://github.com/XKCP/XKCP">
<front> <front>
<title>Submission Requirements and Evaluation Criteria for the Post-Quantu <title>eXtended Keccak Code Package</title>
m Cryptography Standardization Process</title> <author/>
<author> <date month="December" year="2022"/>
<organization>National Institute of Standards and Technology </front>
</organization> <refcontent>commit 64404bee</refcontent>
</author> </reference>
<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>
<reference anchor="FIPS180"> <reference anchor="NISTPQ" target="https://csrc.nist.gov/CSRC/media/Proj
<front> ects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf">
<title>Secure Hash Standard (SHS)</title> <front>
<author> <title>Submission Requirements and Evaluation Criteria for the Post-
<organization>National Institute of Standards and Technology (NIST)</org Quantum Cryptography Standardization Process</title>
anization> <author>
</author> <organization abbrev="NIST">National Institute of Standards and Te
<date year="2015" month="August"/> chnology
</front> </organization>
<seriesInfo name="FIPS PUB" value="180-4"/> </author>
<seriesInfo name="WWW" value="https://doi.org/10.6028/NIST.FIPS.180-4"/> </front>
</reference> </reference>
<reference anchor="FIPS198"> <reference anchor="FIPS180" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.
<front> FIPS.180-4.pdf">
<title>The Keyed-Hash Message Authentication Code (HMAC)</title> <front>
<author> <title>Secure Hash Standard</title>
<organization>National Institute of Standards and Technology (NIST)</org <author>
anization> <organization abbrev="NIST">National Institute of Standards and Technology
</author> </organization>
<date year="2008" month="July"/> </author>
</front> <date month="August" year="2015"/>
<seriesInfo name="FIPS PUB" value="198-1"/> </front>
<seriesInfo name="WWW" value="https://doi.org/10.6028/NIST.FIPS.198-1"/> <seriesInfo name="NIST FIPS" value="180-4"/>
</reference> <seriesInfo name="DOI" value="10.6028/NIST.FIPS.180-4"/>
</reference>
</references> <reference 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 abbrev="NIST">National Institute of Standards and Technology
</organization>
</author>
<date month="July" year="2008"/>
</front>
<seriesInfo name="NIST FIPS" value="198-1"/>
<seriesInfo name="DOI" value="10.6028/NIST.FIPS.198-1"/>
</reference>
<section anchor="pseudocode" title="Pseudocode"> </references>
<t>The sub-sections of this appendix contain pseudocode definitions of </references>
TurboSHAKE128, TurboSHAKE256 and KangarooTwelve. <section anchor="pseudocode" numbered="true" toc="default">
<name>Pseudocode</name>
<t>The subsections of this appendix contain pseudocode definitions of
TurboSHAKE128, TurboSHAKE256, and KangarooTwelve.
Standalone Python versions are also available in the Keccak Code Package Standalone Python versions are also available in the Keccak Code Package
<xref target="XKCP"></xref> and in <xref target="KT"></xref> <xref target="XKCP" format="default"/> and in <xref target="KT" format="defa
</t> ult"/>
</t>
<section anchor="Keccak_PC" title="Keccak-p[1600,n_r=12]"> <section anchor="Keccak_PC" numbered="true" toc="default">
<name>Keccak-p[1600,n_r=12]</name>
<t><figure><artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
KP(state): KP(state):
RC[0] = `8B 80 00 80 00 00 00 00` RC[0] = `8B 80 00 80 00 00 00 00`
RC[1] = `8B 00 00 00 00 00 00 80` RC[1] = `8B 00 00 00 00 00 00 80`
RC[2] = `89 80 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[3] = `03 80 00 00 00 00 00 80`
RC[4] = `02 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[5] = `80 00 00 00 00 00 00 80`
RC[6] = `0A 80 00 00 00 00 00 00` RC[6] = `0A 80 00 00 00 00 00 00`
RC[7] = `0A 00 00 80 00 00 00 80` RC[7] = `0A 00 00 80 00 00 00 80`
RC[8] = `81 80 00 80 00 00 00 80` RC[8] = `81 80 00 80 00 00 00 80`
skipping to change at line 1249 skipping to change at line 1239
# iota # iota
lanes[0][0] ^= RC[round] lanes[0][0] ^= RC[round]
state = `00`^0 state = `00`^0
for y from 0 to 4 for y from 0 to 4
for x from 0 to 4 for x from 0 to 4
state = state || lanes[x][y] state = state || lanes[x][y]
return state return state
end end
]]></artwork></figure></t> ]]></sourcecode>
<t>where ROL64(x, y) is a rotation of the 'x' 64-bit word toward the bit
<t>where ROL64(x, y) is a rotation of the 'x' 64-bit word toward the bits s
with higher indexes by 'y' positions. The 8-bytes byte-string x is with higher indexes by 'y' positions. The 8-bytes byte string x is
interpreted as a 64-bit word in little-endian format. interpreted as a 64-bit word in little-endian format.
</t> </t>
</section> </section>
<section anchor="TSHK128_PC" numbered="true" toc="default">
<name>TurboSHAKE128</name>
<section anchor="TSHK128_PC" title="TurboSHAKE128"> <sourcecode type="pseudocode"><![CDATA[
<t><figure><artwork><![CDATA[
TurboSHAKE128(message, separationByte, outputByteLen): TurboSHAKE128(message, separationByte, outputByteLen):
offset = 0 offset = 0
state = `00`^200 state = `00`^200
input = message || separationByte input = message || separationByte
# === Absorb complete blocks === # === Absorb complete blocks ===
while offset < |input| - 168 while offset < |input| - 168
state ^= input[offset : offset + 168] || `00`^32 state ^= input[offset : offset + 168] || `00`^32
state = KP(state) state = KP(state)
offset += 168 offset += 168
skipping to change at line 1286 skipping to change at line 1276
# === Squeeze === # === Squeeze ===
output = `00`^0 output = `00`^0
while outputByteLen > 168 while outputByteLen > 168
output = output || state[0:168] output = output || state[0:168]
outputByteLen -= 168 outputByteLen -= 168
state = KP(state) state = KP(state)
output = output || state[0:outputByteLen] output = output || state[0:outputByteLen]
return output return output
]]></artwork></figure></t> ]]></sourcecode>
</section> </section>
<section anchor="TSHK256_PC" numbered="true" toc="default">
<section anchor="TSHK256_PC" title="TurboSHAKE256"> <name>TurboSHAKE256</name>
<t><figure><artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
TurboSHAKE256(message, separationByte, outputByteLen): TurboSHAKE256(message, separationByte, outputByteLen):
offset = 0 offset = 0
state = `00`^200 state = `00`^200
input = message || separationByte input = message || separationByte
# === Absorb complete blocks === # === Absorb complete blocks ===
while offset < |input| - 136 while offset < |input| - 136
state ^= input[offset : offset + 136] || `00`^64 state ^= input[offset : offset + 136] || `00`^64
state = KP(state) state = KP(state)
offset += 136 offset += 136
skipping to change at line 1318 skipping to change at line 1308
# === Squeeze === # === Squeeze ===
output = `00`^0 output = `00`^0
while outputByteLen > 136 while outputByteLen > 136
output = output || state[0:136] output = output || state[0:136]
outputByteLen -= 136 outputByteLen -= 136
state = KP(state) state = KP(state)
output = output || state[0:outputByteLen] output = output || state[0:outputByteLen]
return output return output
]]></artwork></figure></t> ]]></sourcecode>
</section> </section>
<section anchor="KT128_PC" numbered="true" toc="default">
<section anchor="KT128_PC" title="KT128"> <name>KT128</name>
<t><figure><artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
KT128(inputMessage, customString, outputByteLen): KT128(inputMessage, customString, outputByteLen):
S = inputMessage || customString S = inputMessage || customString
S = S || length_encode( |customString| ) S = S || length_encode( |customString| )
if |S| <= 8192 if |S| <= 8192
return TurboSHAKE128(S, `07`, outputByteLen) return TurboSHAKE128(S, `07`, outputByteLen)
else else
# === Kangaroo hopping === # === Kangaroo hopping ===
FinalNode = S[0:8192] || `03` || `00`^7 FinalNode = S[0:8192] || `03` || `00`^7
offset = 8192 offset = 8192
numBlock = 0 numBlock = 0
while offset < |S| while offset < |S|
blockSize = min( |S| - offset, 8192) blockSize = min( |S| - offset, 8192)
CV = TurboSHAKE128(S[offset : offset + blockSize], `0B`, 32) CV = TurboSHAKE128(S[offset : offset+blockSize], `0B`, 32)
FinalNode = FinalNode || CV FinalNode = FinalNode || CV
numBlock += 1 numBlock += 1
offset += blockSize offset += blockSize
FinalNode = FinalNode || length_encode( numBlock ) || `FF FF` FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`
return TurboSHAKE128(FinalNode, `06`, outputByteLen) return TurboSHAKE128(FinalNode, `06`, outputByteLen)
end end
]]></artwork></figure></t> ]]></sourcecode>
</section> </section>
<section anchor="KT256_PC" numbered="true" toc="default">
<section anchor="KT256_PC" title="KT256"> <name>KT256</name>
<t><figure><artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
KT256(inputMessage, customString, outputByteLen): KT256(inputMessage, customString, outputByteLen):
S = inputMessage || customString S = inputMessage || customString
S = S || length_encode( |customString| ) S = S || length_encode( |customString| )
if |S| <= 8192 if |S| <= 8192
return TurboSHAKE256(S, `07`, outputByteLen) return TurboSHAKE256(S, `07`, outputByteLen)
else else
# === Kangaroo hopping === # === Kangaroo hopping ===
FinalNode = S[0:8192] || `03` || `00`^7 FinalNode = S[0:8192] || `03` || `00`^7
offset = 8192 offset = 8192
numBlock = 0 numBlock = 0
while offset < |S| while offset < |S|
blockSize = min( |S| - offset, 8192) blockSize = min( |S| - offset, 8192)
CV = TurboSHAKE256(S[offset : offset + blockSize], `0B`, 64) CV = TurboSHAKE256(S[offset : offset+blockSize], `0B`, 64)
FinalNode = FinalNode || CV FinalNode = FinalNode || CV
numBlock += 1 numBlock += 1
offset += blockSize offset += blockSize
FinalNode = FinalNode || length_encode( numBlock ) || `FF FF` FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`
return TurboSHAKE256(FinalNode, `06`, outputByteLen) return TurboSHAKE256(FinalNode, `06`, outputByteLen)
end end
]]></artwork></figure></t> ]]></sourcecode>
</section> </section>
</section> </section>
</back> </back>
</rfc> </rfc>
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