rfc8682xml2.original.xml   rfc8682.xml 
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]> <link href="https://dx.doi.org/10.17487/rfc8682" rel="alternate"/>
<link href="urn:issn:2070-1721" rel="alternate"/>
<?rfc toc="yes" ?> <front>
<?rfc compact="yes" ?> <title abbrev="TinyMT32 PRNG">TinyMT32 Pseudorandom Number Generator (PRNG)<
<?rfc subcompact="yes" ?> /title>
<?rfc symrefs="yes" ?> <seriesInfo name="RFC" value="8682" stream="IETF"/>
<?rfc sortrefs="yes" ?> <author fullname="Mutsuo Saito" initials="M" surname="Saito">
<?rfc rfcedstyle="yes" ?> <organization showOnFrontPage="true">Hiroshima University</organization>
<address>
<rfc category="std" docName="draft-ietf-tsvwg-tinymt32-06" ipr="trust200902"> <postal>
<street/>
<front> <city/>
<title abbrev="TinyMT32 PRNG">TinyMT32 Pseudo Random Number Generator (PR <country>Japan</country>
NG)</title> </postal>
<email>saito@math.sci.hiroshima-u.ac.jp</email>
<author fullname="Mutsuo Saito" initials="M" surname="Saito"> </address>
<organization>Hiroshima University</organization> </author>
<address> <author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto">
<postal> <organization showOnFrontPage="true">Hiroshima University</organization>
<street></street> <address>
<city></city> <postal>
<country>Japan</country> <street/>
</postal> <city/>
<email>saito@math.sci.hiroshima-u.ac.jp</email> <country>Japan</country>
</address> </postal>
</author> <email>m-mat@math.sci.hiroshima-u.ac.jp</email>
</address>
<author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto"> </author>
<organization>Hiroshima University</organization> <author fullname="Vincent Roca" initials="V" surname="Roca" role="editor">
<address> <organization showOnFrontPage="true">INRIA</organization>
<postal> <address>
<street></street> <postal>
<city></city> <street/>
<country>Japan</country> <city/>
</postal> <code/>
<email>m-mat@math.sci.hiroshima-u.ac.jp</email> <extaddr>Univ. Grenoble Alpes</extaddr>
</address> <country>France</country>
</author> </postal>
<email>vincent.roca@inria.fr</email>
<author fullname="Vincent Roca" initials="V" surname="Roca (Ed.)"> </address>
<organization>INRIA</organization> </author>
<address> <author fullname="Emmanuel Baccelli" initials="E" surname="Baccelli">
<postal> <organization showOnFrontPage="true">INRIA</organization>
<street></street> <address>
<city>Univ. Grenoble Alpes</city> <postal>
<code></code> <street/>
<country>France</country> <city/>
</postal> <code/>
<email>vincent.roca@inria.fr</email> <country>France</country>
</address> </postal>
</author> <email>emmanuel.baccelli@inria.fr</email>
</address>
<author fullname="Emmanuel Baccelli" initials="E" surname="Baccelli"> </author>
<organization>INRIA</organization> <date month="01" year="2020"/>
<address> <workgroup>TSVWG</workgroup>
<postal> <abstract pn="section-abstract">
<street></street> <t pn="section-abstract-1">
<city></city> This document describes the TinyMT32 Pseudorandom Number Generator (PRNG), which
<code></code> produces 32-bit pseudorandom unsigned integers and aims at having a simple-to-u
<country>France</country> se and deterministic solution.
</postal> This PRNG is a small-sized variant of the Mersenne Twister (MT) PRNG.
<email>emmanuel.baccelli@inria.fr</email> The main advantage of TinyMT32 over MT is the use of a small internal state, com
</address> patible with most target platforms that include embedded devices, while keeping
</author> reasonably good randomness that represents a significant improvement compared to
<!-- <date month="February" year="2017" /> --> the Park-Miller Linear Congruential PRNG.
<date/> However, neither the TinyMT nor MT PRNG is meant to be used for cryptographic ap
plications.
<workgroup>TSVWG</workgroup>
<abstract>
<t>
This document describes the TinyMT32 Pseudo Random Number Generator (PRNG) that
produces 32-bit pseudo-random unsigned integers and aims at having a simple-to-u
se and deterministic solution.
This PRNG is a small-sized variant of Mersenne Twister (MT) PRNG.
The main advantage of TinyMT32 over MT is the use of a small internal state, com
patible with most target platforms that include embedded devices, while keeping
a reasonably good randomness that represents a sigificant improvement compared t
o the Park-Miller Linear Congruential PRNG.
However, neither the TinyMT nor MT PRNG are meant to be used for cryptographic a
pplications.
</t> </t>
</abstract> </abstract>
<boilerplate>
</front> <section anchor="status-of-memo" numbered="false" removeInRFC="false" toc=
"exclude" pn="section-boilerplate.1">
<middle> <name slugifiedName="name-status-of-this-memo">Status of This Memo</name
>
<section anchor="introduction" title="Introduction"> <t pn="section-boilerplate.1-1">
<!-- ====================== --> This is an Internet Standards Track document.
</t>
<t> <t pn="section-boilerplate.1-2">
This document specifies the TinyMT32 PRNG, as a specialization of the reference This document is a product of the Internet Engineering Task Force
implementation version 1.1 (2015/04/24) by Mutsuo Saito and Makoto Matsumoto, fr (IETF). It represents the consensus of the IETF community. It has
om Hiroshima University, that can be found at <xref target="TinyMT-web"/> (TinyM received public review and has been approved for publication by
T web site) and <xref target="TinyMT-dev"/> (Github site). the Internet Engineering Steering Group (IESG). Further
This specialisation aims at having a simple-to-use and deterministic PRNG, as ex information on Internet Standards is available in Section 2 of
plained below. RFC 7841.
</t>
<t pn="section-boilerplate.1-3">
Information about the current status of this document, any
errata, and how to provide feedback on it may be obtained at
<eref target="https://www.rfc-editor.org/info/rfc8682" brackets="non
e"/>.
</t>
</section>
<section anchor="copyright" numbered="false" removeInRFC="false" toc="excl
ude" pn="section-boilerplate.2">
<name slugifiedName="name-copyright-notice">Copyright Notice</name>
<t pn="section-boilerplate.2-1">
Copyright (c) 2020 IETF Trust and the persons identified as the
document authors. All rights reserved.
</t>
<t pn="section-boilerplate.2-2">
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(<eref target="https://trustee.ietf.org/license-info" brackets="none
"/>) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with
respect to this document. Code Components extracted from this
document must include Simplified BSD License text as described in
Section 4.e of the Trust Legal Provisions and are provided without
warranty as described in the Simplified BSD License.
</t>
</section>
</boilerplate>
<toc>
<section anchor="toc" numbered="false" removeInRFC="false" toc="exclude" p
n="section-toc.1">
<name slugifiedName="name-table-of-contents">Table of Contents</name>
<ul bare="true" empty="true" indent="2" spacing="compact" pn="section-to
c.1-1">
<li pn="section-toc.1-1.1">
<t keepWithNext="true" pn="section-toc.1-1.1.1"><xref derivedContent
="1" format="counter" sectionFormat="of" target="section-1"/>.  <xref derivedCon
tent="" format="title" sectionFormat="of" target="name-introduction">Introductio
n</xref></t>
<ul bare="true" empty="true" indent="2" spacing="compact" pn="sectio
n-toc.1-1.1.2">
<li pn="section-toc.1-1.1.2.1">
<t keepWithNext="true" pn="section-toc.1-1.1.2.1.1"><xref derive
dContent="1.1" format="counter" sectionFormat="of" target="section-1.1"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-requirements-
language">Requirements Language</xref></t>
</li>
</ul>
</li>
<li pn="section-toc.1-1.2">
<t keepWithNext="true" pn="section-toc.1-1.2.1"><xref derivedContent
="2" format="counter" sectionFormat="of" target="section-2"/>.  <xref derivedCon
tent="" format="title" sectionFormat="of" target="name-tinymt32-prng-specificati
on">TinyMT32 PRNG Specification</xref></t>
<ul bare="true" empty="true" indent="2" spacing="compact" pn="sectio
n-toc.1-1.2.2">
<li pn="section-toc.1-1.2.2.1">
<t keepWithNext="true" pn="section-toc.1-1.2.2.1.1"><xref derive
dContent="2.1" format="counter" sectionFormat="of" target="section-2.1"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-tinymt32-sour
ce-code">TinyMT32 Source Code</xref></t>
</li>
<li pn="section-toc.1-1.2.2.2">
<t keepWithNext="true" pn="section-toc.1-1.2.2.2.1"><xref derive
dContent="2.2" format="counter" sectionFormat="of" target="section-2.2"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-tinymt32-usag
e">TinyMT32 Usage</xref></t>
</li>
<li pn="section-toc.1-1.2.2.3">
<t keepWithNext="true" pn="section-toc.1-1.2.2.3.1"><xref derive
dContent="2.3" format="counter" sectionFormat="of" target="section-2.3"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-specific-impl
ementation-val">Specific Implementation Validation and Deterministic Behavior</x
ref></t>
</li>
</ul>
</li>
<li pn="section-toc.1-1.3">
<t keepWithNext="true" pn="section-toc.1-1.3.1"><xref derivedContent
="3" format="counter" sectionFormat="of" target="section-3"/>.  <xref derivedCon
tent="" format="title" sectionFormat="of" target="name-security-considerations">
Security Considerations</xref></t>
</li>
<li pn="section-toc.1-1.4">
<t keepWithNext="true" pn="section-toc.1-1.4.1"><xref derivedContent
="4" format="counter" sectionFormat="of" target="section-4"/>.  <xref derivedCon
tent="" format="title" sectionFormat="of" target="name-iana-considerations">IANA
Considerations</xref></t>
</li>
<li pn="section-toc.1-1.5">
<t keepWithNext="true" pn="section-toc.1-1.5.1"><xref derivedContent
="5" format="counter" sectionFormat="of" target="section-5"/>.  <xref derivedCon
tent="" format="title" sectionFormat="of" target="name-references">References</x
ref></t>
<ul bare="true" empty="true" indent="2" spacing="compact" pn="sectio
n-toc.1-1.5.2">
<li pn="section-toc.1-1.5.2.1">
<t keepWithNext="true" pn="section-toc.1-1.5.2.1.1"><xref derive
dContent="5.1" format="counter" sectionFormat="of" target="section-5.1"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-normative-ref
erences">Normative References</xref></t>
</li>
<li pn="section-toc.1-1.5.2.2">
<t keepWithNext="true" pn="section-toc.1-1.5.2.2.1"><xref derive
dContent="5.2" format="counter" sectionFormat="of" target="section-5.2"/>.  <xre
f derivedContent="" format="title" sectionFormat="of" target="name-informative-r
eferences">Informative References</xref></t>
</li>
</ul>
</li>
<li pn="section-toc.1-1.6">
<t keepWithNext="true" pn="section-toc.1-1.6.1"><xref derivedContent
="" format="none" sectionFormat="of" target="section-appendix.a"/><xref derivedC
ontent="" format="title" sectionFormat="of" target="name-acknowledgments">Acknow
ledgments</xref></t>
</li>
<li pn="section-toc.1-1.7">
<t keepWithNext="true" pn="section-toc.1-1.7.1"><xref derivedContent
="" format="none" sectionFormat="of" target="section-appendix.b"/><xref derivedC
ontent="" format="title" sectionFormat="of" target="name-authors-addresses">Auth
ors' Addresses</xref></t>
</li>
</ul>
</section>
</toc>
</front>
<middle>
<section anchor="introduction" numbered="true" toc="include" removeInRFC="fa
lse" pn="section-1">
<name slugifiedName="name-introduction">Introduction</name>
<t pn="section-1-1">
This document specifies the TinyMT32 PRNG as a specialization of the
reference implementation version 1.1 (2015/04/24) by Mutsuo Saito and Makoto
Matsumoto from Hiroshima University, which can be found at <xref target="TinyMT-
web" format="default" sectionFormat="of" derivedContent="TinyMT-web"/> (the Tiny
MT website) and <xref target="TinyMT-dev" format="default" sectionFormat="of" de
rivedContent="TinyMT-dev"/>
(the GitHub site).
This specialization aims at having a simple-to-use and deterministic PRNG, as ex
plained below.
However, the TinyMT32 PRNG is not meant to be used for cryptographic application s. However, the TinyMT32 PRNG is not meant to be used for cryptographic application s.
</t> </t>
<t pn="section-1-2">
<t> TinyMT is a new, small-sized variant of the Mersenne
TinyMT is a new small-sized variant introduced in 2011 of the Mersenne Twister ( Twister (MT) PRNG introduced in 2011 <xref target="MT98" format="default" sectio
MT) PRNG <xref target="MT98"/>. nFormat="of" derivedContent="MT98"/>.
This document focusses on the TinyMT32 variant (rather than TinyMT64) of the Tin This document focuses on the TinyMT32 variant (rather than TinyMT64) of the Tiny
yMT PRNG, which outputs 32-bit unsigned integers. MT PRNG, which outputs 32-bit unsigned integers.
</t> </t>
<t pn="section-1-3">
<t> The purpose of TinyMT is not to replace the Mersenne Twister: TinyMT has a far s
The purpose of TinyMT is not to replace Mersenne Twister: TinyMT has a far short horter period (2<sup>127</sup> - 1) than MT.
er period (2^^127 - 1) than MT. The merit of TinyMT is in the small size of the 127-bit internal state, far smal
The merit of TinyMT is in the small size of the internal state of 127 bits, far ler than the 19937 bits of MT.
smaller than the 19937 bits of MT.
The outputs of TinyMT satisfy several statistical tests for non-cryptographic ra ndomness, including BigCrush The outputs of TinyMT satisfy several statistical tests for non-cryptographic ra ndomness, including BigCrush
in TestU01 <xref target="TestU01"/> and AdaptiveCrush <xref target="AdaptiveCrus h"/>, leaving it well-placed in TestU01 <xref target="TestU01" format="default" sectionFormat="of" derivedCon tent="TestU01"/> and AdaptiveCrush <xref target="AdaptiveCrush" format="default" sectionFormat="of" derivedContent="AdaptiveCrush"/>, leaving it well placed
for non-cryptographic usage, especially given the small size of its internal sta te for non-cryptographic usage, especially given the small size of its internal sta te
(see <xref target="TinyMT-web"/>). (see <xref target="TinyMT-web" format="default" sectionFormat="of" derivedConten
From this point of view, TinyMT32 represents a major improvement with respect to t="TinyMT-web"/>).
the Park-Miller Linear Congruential PRNG (e.g., as specified in <xref target="R
FC5170"/>) that suffers several known limitations (see for instance <xref target
="PTVF92"/>, section 7.1, p. 279, and <xref target="RLC-ID"/>, Appendix B).
</t>
<t> From this point of view, TinyMT32 represents a major improvement with respect
to the Park-Miller Linear Congruential PRNG (e.g., as specified in <xref target=
"RFC5170" format="default" sectionFormat="of" derivedContent="RFC5170"/>), which
suffers from several known
limitations (see, for instance, <xref target="PTVF92" format="default" sectionFo
rmat="of" derivedContent="PTVF92"/>,
Section 7.1, p. 279 and <xref target="RFC8681" sectionFormat="comma" section="B"
format="default" derivedLink="https://rfc-editor.org/rfc/rfc8681#appendix-B" de
rivedContent="RFC8681"/>).
</t>
<t pn="section-1-4">
The TinyMT32 PRNG initialization depends, among other things, on a parameter set , namely (mat1, mat2, tmat). The TinyMT32 PRNG initialization depends, among other things, on a parameter set , namely (mat1, mat2, tmat).
In order to facilitate the use of this PRNG and make the sequence of pseudo-rand In order to facilitate the use of this PRNG and to make the sequence of pseudora
om numbers depend only on the seed value, this specification requires the use of ndom numbers depend only on the seed value, this specification requires the use
a specific parameter set (see <xref target="tinymt32_source_code"/>). of a specific parameter set (see <xref target="tinymt32_source_code" format="def
This is a major difference with respect to the implementation version 1.1 (2015/ ault" sectionFormat="of" derivedContent="Section 2.1"/>).
04/24) that leaves this parameter set unspecified. This is a major difference with respect to the implementation version 1.1
(2015/04/24), which leaves this parameter set unspecified.
</t> </t>
<t pn="section-1-5">
<t> Finally, the determinism of this PRNG for a given seed has been carefully checke
Finally, the determinism of this PRNG, for a given seed, has been carefully chec d (see <xref target="tinymt32_validation" format="default" sectionFormat="of" de
ked (see <xref target="tinymt32_validation"/>). rivedContent="Section 2.3"/>).
It means that the same sequence of pseudo-random numbers should be generated, no This means that the same sequence of pseudorandom numbers should be generated, n
matter the target execution platform and compiler, for a given initial seed val o matter the target execution platform and compiler, for a given initial seed va
ue. lue.
This determinism can be a key requirement as it the case with <xref target="RLC- This determinism can be a key requirement, as is the case with <xref target="RFC
ID"/> that normatively depends on this specification. 8681" format="default" sectionFormat="of" derivedContent="RFC8681"/>, which norm
atively depends on this specification.
</t> </t>
<section anchor="definitionsAndAbbreviations" numbered="true" toc="include
</section> " removeInRFC="false" pn="section-1.1">
<name slugifiedName="name-requirements-language">Requirements Language</
<!-- <section anchor="definitionsAndAbbreviations" title="Definitions and Abbrev name>
iations"> --> <t pn="section-1.1-1">
<section anchor="definitionsAndAbbreviations" title="Definitions"> The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
<!-- ====================== --> "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>
",
<t> "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
"MAY", and "OPTIONAL" in this document are to be interpreted as be
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> interpreted as described in BCP 14 <xref target="RFC2119" format="default" s
when, and only when, they appear in all capitals, as shown here. ectionFormat="of" derivedContent="RFC2119"/> <xref target="RFC8174" format="defa
ult" sectionFormat="of" derivedContent="RFC8174"/> when, and only when, they app
ear in all capitals, as
shown here.
</t>
</section>
</section>
<section anchor="tinymt32_specs" numbered="true" toc="include" removeInRFC="
false" pn="section-2">
<name slugifiedName="name-tinymt32-prng-specification">TinyMT32 PRNG Speci
fication</name>
<section anchor="tinymt32_source_code" numbered="true" toc="include" remov
eInRFC="false" pn="section-2.1">
<name slugifiedName="name-tinymt32-source-code">TinyMT32 Source Code</na
me>
<t pn="section-2.1-1">
The TinyMT32 PRNG must be initialized with a parameter set that needs to be well
chosen.
In this specification, for the sake of simplicity, the following parameter set <
bcp14>MUST</bcp14> be used:
</t> </t>
<ul spacing="normal" bare="false" empty="false" pn="section-2.1-2">
<!-- <li pn="section-2.1-2.1">mat1 = 0x8f7011ee = 2406486510</li>
<t>This document uses the following definitions and abbreviations: <list style=" <li pn="section-2.1-2.2">mat2 = 0xfc78ff1f = 4235788063</li>
hanging"> <li pn="section-2.1-2.3">tmat = 0x3793fdff = 932445695</li>
</ul>
<t hangText="PRNG:"> pseudo-random number generator</t> <t pn="section-2.1-3">
</list></t> This parameter set is the first entry of the precalculated parameter sets in tin
ymt32dc/tinymt32dc.0.1048576.txt by Kenji Rikitake, available at <xref target="T
</section> inyMT-params" format="default" sectionFormat="of" derivedContent="TinyMT-params"
/>.
<!-- =========================================================================== This is also the parameter set used in <xref target="KR12" format="default" sect
================ --> ionFormat="of" derivedContent="KR12"/>.
<section anchor="tinymt32_specs" title="TinyMT32 PRNG Specification">
<!-- ====================== -->
<section anchor="tinymt32_source_code" title="TinyMT32 Source Code">
<!-- ====================== -->
<t>
The TinyMT32 PRNG requires to be initialized with a parameter set that needs to
be well chosen.
In this specification, for the sake of simplicity, the following parameter set M
UST be used:
<list style="symbols">
<t>mat1 = 0x8f7011ee = 2406486510</t>
<t>mat2 = 0xfc78ff1f = 4235788063</t>
<t>tmat = 0x3793fdff = 932445695</t>
</list>
This parameter set is the first entry of the precalculated parameter sets in fil
e tinymt32dc/tinymt32dc.0.1048576.txt, by Kenji Rikitake, and available at <xref
target="TinyMT-params"/>.
This is also the parameter set used in <xref target="KR12"/>.
</t> </t>
<t pn="section-2.1-4">
<t> The TinyMT32 PRNG reference implementation is reproduced in <xref target="fig_ti
The TinyMT32 PRNG reference implementation is reproduced in <xref target="fig_ti nymt32" format="default" sectionFormat="of" derivedContent="Figure 1"/>.
nymt32"/>. This is a C language implementation written for C99 <xref target="C99" format="d
This is a C language implementation, written for C99 <xref target="C99"/>. efault" sectionFormat="of" derivedContent="C99"/>.
This reference implementation differs from the original source code as follows: This reference implementation differs from the original source code as follows:
<list style="symbols">
<t>the original copyright and license have been removed by the original a
uthors who are now authors of this document, in accordance with BCP 78 and the I
ETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org
/license-info);</t>
<t>the source code initially spread over the tinymt32.h and tinymt32.c fi
les has been merged;</t>
<t>the unused parts of the original source code have been removed.
This is the case of the tinymt32_init_by_array() alternative initialis
ation function.
This is also the case of the period_certification() function after hav
ing checked it is not required with the chosen parameter set;</t>
<t>the unused constants TINYMT32_MEXP and TINYMT32_MUL have been removed;
</t>
<t>the appropriate parameter set has been added to the initialization fun
ction;</t>
<t>the function order has been changed;</t>
<t>certain internal variables have been renamed for compactness purposes;
</t>
<t>the const qualifier has been added to the constant definitions;</t>
<t>the code that was dependant on the representation of negative integers
by 2's complements has been replaced by a more portable version;</t>
</list>
</t> </t>
<ul spacing="normal" bare="false" empty="false" pn="section-2.1-5">
<figure anchor="fig_tinymt32" title="TinyMT32 Reference Implementation"> <li pn="section-2.1-5.1">The original authors, who are coauthors of th
<artwork><![CDATA[ is document, have
<CODE BEGINS> granted IETF
the rights to publish this version with a license and copyright that are in
accordance with BCP 78 and the IETF Trust's Legal Provisions Relating to IETF
Documents (http://trustee.ietf.org/license-info).</li>
<li pn="section-2.1-5.2">The source code initially spread over the tin
ymt32.h and tinymt32.c files has been merged.</li>
<li pn="section-2.1-5.3">The unused parts of the original source code
have been removed.
This is the case of the tinymt32_init_by_array() alternative initializ
ation function.
This is also the case of the period_certification() function after hav
ing checked it is not required with the chosen parameter set.</li>
<li pn="section-2.1-5.4">The unused constants TINYMT32_MEXP and TINYMT
32_MUL have been removed.</li>
<li pn="section-2.1-5.5">The appropriate parameter set has been added
to the initialization function.</li>
<li pn="section-2.1-5.6">The function order has been changed.</li>
<li pn="section-2.1-5.7">Certain internal variables have been renamed
for compactness purposes.</li>
<li pn="section-2.1-5.8">The const qualifier has been added to the con
stant definitions.</li>
<li pn="section-2.1-5.9">The code that was dependent on the representa
tion of negative integers by 2's complements has been replaced by a more portabl
e version.</li>
</ul>
<figure anchor="fig_tinymt32" align="left" suppress-title="false" pn="fi
gure-1">
<name slugifiedName="name-tinymt32-reference-implemen">TinyMT32 Refere
nce Implementation</name>
<sourcecode name="" type="c" markers="true" pn="section-2.1-6.1">
/** /**
* Tiny Mersenne Twister only 127 bit internal state. * Tiny Mersenne Twister: only 127-bit internal state.
* Derived from the reference implementation version 1.1 (2015/04/24) * Derived from the reference implementation version 1.1 (2015/04/24)
* by Mutsuo Saito (Hiroshima University) and Makoto Matsumoto * by Mutsuo Saito (Hiroshima University) and Makoto Matsumoto
* (Hiroshima University). * (Hiroshima University).
*/ */
#include <stdint.h&gt; #include <stdint.h&gt;
/** /**
* tinymt32 internal state vector and parameters * tinymt32 internal state vector and parameters
*/ */
typedef struct { typedef struct {
uint32_t status[4]; uint32_t status[4];
uint32_t mat1; uint32_t mat1;
uint32_t mat2; uint32_t mat2;
uint32_t tmat; uint32_t tmat;
} tinymt32_t; } tinymt32_t;
static void tinymt32_next_state (tinymt32_t* s); static void tinymt32_next_state (tinymt32_t* s);
static uint32_t tinymt32_temper (tinymt32_t* s); static uint32_t tinymt32_temper (tinymt32_t* s);
/** /**
* Parameter set to use for this IETF specification. Don't change. * Parameter set to use for this IETF specification. Don't change.
* This parameter set is the first entry of the precalculated * This parameter set is the first entry of the precalculated
* parameter sets in file tinymt32dc/tinymt32dc.0.1048576.txt, by * parameter sets in tinymt32dc/tinymt32dc.0.1048576.txt by
* Kenji Rikitake, available at: * Kenji Rikitake, available at:
* https://github.com/jj1bdx/tinymtdc-longbatch/ * https://github.com/jj1bdx/tinymtdc-longbatch/.
* It is also the parameter set used: * It is also the parameter set used in:
* Rikitake, K., "TinyMT Pseudo Random Number Generator for * Rikitake, K., "TinyMT pseudo random number generator for
* Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12), * Erlang", Proceedings of the 11th ACM SIGPLAN Erlang Workshop,
* September, 2012. * September 2012.
*/ */
const uint32_t TINYMT32_MAT1_PARAM = UINT32_C(0x8f7011ee); const uint32_t TINYMT32_MAT1_PARAM = UINT32_C(0x8f7011ee);
const uint32_t TINYMT32_MAT2_PARAM = UINT32_C(0xfc78ff1f); const uint32_t TINYMT32_MAT2_PARAM = UINT32_C(0xfc78ff1f);
const uint32_t TINYMT32_TMAT_PARAM = UINT32_C(0x3793fdff); const uint32_t TINYMT32_TMAT_PARAM = UINT32_C(0x3793fdff);
/** /**
* This function initializes the internal state array with a * This function initializes the internal state array with a
* 32-bit unsigned integer seed. * 32-bit unsigned integer seed.
* @param s pointer to tinymt internal state. * @param s pointer to tinymt internal state.
* @param seed a 32-bit unsigned integer used as a seed. * @param seed a 32-bit unsigned integer used as a seed.
*/ */
void tinymt32_init (tinymt32_t* s, uint32_t seed) void tinymt32_init (tinymt32_t* s, uint32_t seed)
{ {
const uint32_t MIN_LOOP = 8; const uint32_t MIN_LOOP = 8;
const uint32_t PRE_LOOP = 8; const uint32_t PRE_LOOP = 8;
s->status[0] = seed; s-&gt;status[0] = seed;
s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM; s-&gt;status[1] = s-&gt;mat1 = TINYMT32_MAT1_PARAM;
s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM; s-&gt;status[2] = s-&gt;mat2 = TINYMT32_MAT2_PARAM;
s->status[3] = s->tmat = TINYMT32_TMAT_PARAM; s-&gt;status[3] = s-&gt;tmat = TINYMT32_TMAT_PARAM;
for (int i = 1; i < MIN_LOOP; i++) { for (int i = 1; i &lt; MIN_LOOP; i++) {
s->status[i & 3] ^= i + UINT32_C(1812433253) s-&gt;status[i &amp; 3] ^= i + UINT32_C(1812433253)
* (s->status[(i - 1) & 3] * (s-&gt;status[(i - 1) &amp; 3]
^ (s->status[(i - 1) & 3] >> 30)); ^ (s-&gt;status[(i - 1) &amp; 3] &gt;&gt; 30));
} }
/* /*
* NB: the parameter set of this specification warrants * NB: The parameter set of this specification warrants
* that none of the possible 2^^32 seeds leads to an * that none of the possible 2^^32 seeds leads to an
* all-zero 127-bit internal state. Therefore, the * all-zero 127-bit internal state. Therefore, the
* period_certification() function of the original * period_certification() function of the original
* TinyMT32 source code has been safely removed. If * TinyMT32 source code has been safely removed. If
* another parameter set is used, this function will * another parameter set is used, this function will
* have to be re-introduced here. * have to be reintroduced here.
*/ */
for (int i = 0; i < PRE_LOOP; i++) { for (int i = 0; i &lt; PRE_LOOP; i++) {
tinymt32_next_state(s); tinymt32_next_state(s);
} }
} }
/** /**
* This function outputs a 32-bit unsigned integer from * This function outputs a 32-bit unsigned integer from
* the internal state. * the internal state.
* @param s pointer to tinymt internal state. * @param s pointer to tinymt internal state.
* @return 32-bit unsigned integer r (0 <= r < 2^32). * @return 32-bit unsigned integer r (0 &lt;= r &lt; 2^32).
*/ */
uint32_t tinymt32_generate_uint32 (tinymt32_t* s) uint32_t tinymt32_generate_uint32 (tinymt32_t* s)
{ {
tinymt32_next_state(s); tinymt32_next_state(s);
return tinymt32_temper(s); return tinymt32_temper(s);
} }
/** /**
* Internal tinymt32 constants and functions. * Internal tinymt32 constants and functions.
* Users should not call these functions directly. * Users should not call these functions directly.
*/ */
const uint32_t TINYMT32_SH0 = 1; const uint32_t TINYMT32_SH0 = 1;
const uint32_t TINYMT32_SH1 = 10; const uint32_t TINYMT32_SH1 = 10;
const uint32_t TINYMT32_SH8 = 8; const uint32_t TINYMT32_SH8 = 8;
const uint32_t TINYMT32_MASK = UINT32_C(0x7fffffff); const uint32_t TINYMT32_MASK = UINT32_C(0x7fffffff);
/** /**
* This function changes the internal state of tinymt32. * This function changes the internal state of tinymt32.
* @param s pointer to tinymt internal state. * @param s pointer to tinymt internal state.
*/ */
static void tinymt32_next_state (tinymt32_t* s) static void tinymt32_next_state (tinymt32_t* s)
{ {
uint32_t x; uint32_t x;
uint32_t y; uint32_t y;
y = s->status[3]; y = s-&gt;status[3];
x = (s->status[0] & TINYMT32_MASK) x = (s-&gt;status[0] &amp; TINYMT32_MASK)
^ s->status[1] ^ s-&gt;status[1]
^ s->status[2]; ^ s-&gt;status[2];
x ^= (x << TINYMT32_SH0); x ^= (x &lt;&lt; TINYMT32_SH0);
y ^= (y >> TINYMT32_SH0) ^ x; y ^= (y &gt;&gt; TINYMT32_SH0) ^ x;
s->status[0] = s->status[1]; s-&gt;status[0] = s-&gt;status[1];
s->status[1] = s->status[2]; s-&gt;status[1] = s-&gt;status[2];
s->status[2] = x ^ (y << TINYMT32_SH1); s-&gt;status[2] = x ^ (y &lt;&lt; TINYMT32_SH1);
s->status[3] = y; s-&gt;status[3] = y;
/* /*
* The if (y & 1) {...} block below replaces: * The if (y &amp; 1) {...} block below replaces:
* s->status[1] ^= -((int32_t)(y & 1)) & s->mat1; * s-&gt;status[1] ^= -((int32_t)(y &amp; 1)) &amp; s-&gt;mat1;
* s->status[2] ^= -((int32_t)(y & 1)) & s->mat2; * s-&gt;status[2] ^= -((int32_t)(y &amp; 1)) &amp; s-&gt;mat2;
* The adopted code is equivalent to the original code * The adopted code is equivalent to the original code
* but does not depend on the representation of negative * but does not depend on the representation of negative
* integers by 2's complements. It is therefore more * integers by 2's complements. It is therefore more
* portable, but includes an if-branch which may slow * portable but includes an if branch, which may slow
* down the generation speed. * down the generation speed.
*/ */
if (y & 1) { if (y &amp; 1) {
s->status[1] ^= s->mat1; s-&gt;status[1] ^= s-&gt;mat1;
s->status[2] ^= s->mat2; s-&gt;status[2] ^= s-&gt;mat2;
} }
} }
/** /**
* This function outputs a 32-bit unsigned integer from * This function outputs a 32-bit unsigned integer from
* the internal state. * the internal state.
* @param s pointer to tinymt internal state. * @param s pointer to tinymt internal state.
* @return 32-bit unsigned pseudo-random number. * @return 32-bit unsigned pseudorandom number.
*/ */
static uint32_t tinymt32_temper (tinymt32_t* s) static uint32_t tinymt32_temper (tinymt32_t* s)
{ {
uint32_t t0, t1; uint32_t t0, t1;
t0 = s->status[3]; t0 = s-&gt;status[3];
t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8); t1 = s-&gt;status[0] + (s-&gt;status[2] &gt;&gt; TINYMT32_SH8);
t0 ^= t1; t0 ^= t1;
/* /*
* The if (t1 & 1) {...} block below replaces: * The if (t1 &amp; 1) {...} block below replaces:
* t0 ^= -((int32_t)(t1 & 1)) & s->tmat; * t0 ^= -((int32_t)(t1 &amp; 1)) &amp; s-&gt;tmat;
* The adopted code is equivalent to the original code * The adopted code is equivalent to the original code
* but does not depend on the representation of negative * but does not depend on the representation of negative
* integers by 2's complements. It is therefore more * integers by 2's complements. It is therefore more
* portable, but includes an if-branch which may slow * portable but includes an if branch, which may slow
* down the generation speed. * down the generation speed.
*/ */
if (t1 & 1) { if (t1 &amp; 1) {
t0 ^= s->tmat; t0 ^= s-&gt;tmat;
} }
return t0; return t0;
} }
<CODE ENDS> </sourcecode>
]]></artwork> </figure>
</figure> </section>
<section anchor="tinymt32_usage" numbered="true" toc="include" removeInRFC
</section> ="false" pn="section-2.2">
<name slugifiedName="name-tinymt32-usage">TinyMT32 Usage</name>
<section anchor="tinymt32_usage" title="TinyMT32 Usage"> <t pn="section-2.2-1">
<!-- ====================== --> This PRNG <bcp14>MUST</bcp14> first be initialized with the following function:
</t>
<t> <ul empty="true" spacing="normal" bare="false" pn="section-2.2-2">
This PRNG MUST first be initialized with the following function: <li pn="section-2.2-2.1">void tinymt32_init (tinymt32_t* s, uint32_t
<list style="empty"> seed);</li>
<t>void tinymt32_init (tinymt32_t* s, uint32_t seed);</t> </ul>
</list> <t pn="section-2.2-3">
It takes as input a 32-bit unsigned integer used as a seed (note that value 0 is permitted by TinyMT32). It takes as input a 32-bit unsigned integer used as a seed (note that value 0 is permitted by TinyMT32).
This function also takes as input a pointer to an instance of a tinymt32_t struc This function also takes as input a pointer to an instance of a tinymt32_t
ture that needs to be allocated by the caller but left uninitialized. structure that needs to be allocated by the caller but is left uninitialized.
This structure will then be updated by the various TinyMT32 functions in order t o keep the internal state of the PRNG. This structure will then be updated by the various TinyMT32 functions in order t o keep the internal state of the PRNG.
The use of this structure admits several instances of this PRNG to be used in pa rallel, each of them having its own instance of the structure. The use of this structure admits several instances of this PRNG to be used in pa rallel, each of them having its own instance of the structure.
</t> </t>
<t pn="section-2.2-4">
<t> Then, each time a new 32-bit pseudorandom unsigned integer between 0 and 2<sup>3
Then, each time a new 32-bit pseudo-random unsigned integer between 0 and 2^32 - 2</sup> - 1 inclusive is needed, the following function is used:
1 inclusive is needed, the following function is used: </t>
<list style="empty"> <ul empty="true" spacing="normal" bare="false" pn="section-2.2-5">
<t>uint32_t tinymt32_generate_uint32 (tinymt32_t * s);</t> <li pn="section-2.2-5.1">uint32_t tinymt32_generate_uint32 (tinymt32_t
</list> * s);</li>
</ul>
<t pn="section-2.2-6">
Of course, the tinymt32_t structure must be left unchanged by the caller between successive calls to this function. Of course, the tinymt32_t structure must be left unchanged by the caller between successive calls to this function.
</t> </t>
</section>
</section> <section anchor="tinymt32_validation" numbered="true" toc="include" remove
InRFC="false" pn="section-2.3">
<section anchor="tinymt32_validation" title="Specific Implementation Vali <name slugifiedName="name-specific-implementation-val">Specific Implemen
dation and Deterministic Behavior"> tation Validation and Deterministic Behavior</name>
<!-- ====================== --> <t pn="section-2.3-1">
For a given seed, PRNG determinism can be a requirement (e.g., with <xref target
<t> ="RFC8681" format="default" sectionFormat="of" derivedContent="RFC8681"/>).
PRNG determinism, for a given seed, can be a requirement (e.g., with <xref targe Consequently, any implementation of the TinyMT32 PRNG in line with this specific
t="RLC-ID"/>). ation <bcp14>MUST</bcp14> have the same output as that provided by the reference
Consequently, any implementation of the TinyMT32 PRNG in line with this specific implementation of <xref target="fig_tinymt32" format="default" sectionFormat="o
ation MUST have the same output as that provided by the reference implementation f" derivedContent="Figure 1"/>.
of <xref target="fig_tinymt32"/>.
In order to increase the compliancy confidence, this document proposes the follo wing criteria. In order to increase the compliancy confidence, this document proposes the follo wing criteria.
Using a seed value of 1, the first 50 values returned by tinymt32_generate_uint3 2(s) as 32-bit unsigned integers Using a seed value of 1, the first 50 values returned by tinymt32_generate_uint3 2(s) as 32-bit unsigned integers
are equal to values provided in <xref target="fig_tinymt32_out"/>, to be read li are equal to the values provided in <xref target="fig_tinymt32_out" format="defa
ne by line. ult" sectionFormat="of" derivedContent="Figure 2"/>, which
are to be read line by line.
Note that these values come from the tinymt/check32.out.txt file provided by the PRNG authors to validate implementations Note that these values come from the tinymt/check32.out.txt file provided by the PRNG authors to validate implementations
of TinyMT32, as part of the MersenneTwister-Lab/TinyMT Github repository. of TinyMT32 as part of the MersenneTwister-Lab/TinyMT GitHub repository.
</t> </t>
<figure anchor="fig_tinymt32_out" align="left" suppress-title="false" pn
<figure anchor="fig_tinymt32_out" title="First 50 decimal values (to be read per ="figure-2">
line) returned by tinymt32_generate_uint32(s) as 32-bit unsigned integers, with <name slugifiedName="name-first-50-decimal-values-to-">First 50 decima
a seed value of 1."> l values (to be read per line) returned by tinymt32_generate_uint32(s) as 32-bit
<artwork><![CDATA[ unsigned integers, with a seed value of 1</name>
<artwork name="" type="" align="left" alt="" pn="section-2.3-2.1">
2545341989 981918433 3715302833 2387538352 3591001365 2545341989 981918433 3715302833 2387538352 3591001365
3820442102 2114400566 2196103051 2783359912 764534509 3820442102 2114400566 2196103051 2783359912 764534509
643179475 1822416315 881558334 4207026366 3690273640 643179475 1822416315 881558334 4207026366 3690273640
3240535687 2921447122 3984931427 4092394160 44209675 3240535687 2921447122 3984931427 4092394160 44209675
2188315343 2908663843 1834519336 3774670961 3019990707 2188315343 2908663843 1834519336 3774670961 3019990707
4065554902 1239765502 4035716197 3412127188 552822483 4065554902 1239765502 4035716197 3412127188 552822483
161364450 353727785 140085994 149132008 2547770827 161364450 353727785 140085994 149132008 2547770827
4064042525 4078297538 2057335507 622384752 2041665899 4064042525 4078297538 2057335507 622384752 2041665899
2193913817 1080849512 33160901 662956935 642999063 2193913817 1080849512 33160901 662956935 642999063
3384709977 1723175122 3866752252 521822317 2292524454 3384709977 1723175122 3866752252 521822317 2292524454
]]></artwork> </artwork>
</figure> </figure>
<t pn="section-2.3-3">
<t> In particular, the deterministic behavior of the <xref target="fig_tinymt32" for
In particular, the deterministic behavior of the <xref target="fig_tinymt32"/> s mat="default" sectionFormat="of" derivedContent="Figure 1"/> source code has bee
ource code has been checked across several platforms: n checked across several platforms:
high-end laptops running 64-bits Mac OSX and Linux/Ubuntu; high-end laptops running 64-bit Mac OS X and Linux/Ubuntu;
a board featuring a 32-bits ARM Cortex-A15 and running 32-bit Linux/Ubuntu; a board featuring a 32-bit ARM Cortex-A15 and running 32-bit Linux/Ubuntu;
several embedded cards featuring either an ARM Cortex-M0+, a Cortex-M3 or a Cort several embedded cards featuring either an ARM Cortex-M0+, a Cortex-M3, or a Cor
ex-M4 32-bit microcontroller, all of them running RIOT <xref target="Baccelli18" tex-M4 32-bit microcontroller, all of them running RIOT <xref target="Baccelli18
/>; " format="default" sectionFormat="of" derivedContent="Baccelli18"/>;
two low-end embedded cards featuring either a 16-bit microcontroller (TI MSP430) two low-end embedded cards featuring either a 16-bit microcontroller (TI MSP430)
or a 8-bit microcontroller (Arduino ATMEGA2560), both of them running RIOT. or an 8-bit microcontroller (Arduino ATMEGA2560), both of them running RIOT.
</t> </t>
<t pn="section-2.3-4">
<t> This specification only outputs 32-bit unsigned pseudorandom numbers and does no
This specification only outputs 32-bit unsigned pseudo-random numbers and does n t try to map this output to a smaller integer range (e.g., between 10 and 49 inc
ot try to map this output to a smaller integer range (e.g., between 10 and 49 in lusive).
clusive). If a specific use case needs such a mapping, it will have to provide its own fun
If a specific use-case needs such a mapping, it will have to provide its own fun ction.
ction. In that case, if PRNG determinism is also required, the use of a floating point
In that case, if PRNG determinism is also required, the use of floating point (s (single or double precision) to perform this mapping should probably be
ingle or double precision) to perform this mapping should probably be avoided, t avoided, as these calculations may lead to different rounding errors across diff
hese calculations leading potentially to different rounding errors across differ erent target platforms.
ent target platforms. Great care should also be taken to not introduce biases in the randomness of the
Great care should also be put on not introducing biases in the randomness of the mapped output (which may be the case with some mapping algorithms) incompatible
mapped output (it may be the case with some mapping algorithms) incompatible wi with the use-case requirements.
th the use-case requirements. The details of how to perform such a mapping are out of scope of this document.
The details of how to perform such a mapping are out-of-scope of this document.
</t> </t>
</section>
</section> </section>
<section anchor="SecurityConsiderations" numbered="true" toc="include" remov
</section> eInRFC="false" pn="section-3">
<name slugifiedName="name-security-considerations">Security Considerations
<!-- =========================================================================== </name>
================ --> <t pn="section-3-1">
The authors do not believe the present specification generates specific
<section anchor="SecurityConsiderations" title="Security Considerations"> security risks per se. However, the TinyMT and MT PRNG must not be used for
<!-- ====================== --> cryptographic applications.
<t>
The authors do not believe the present specification generates specific security
risks per se.
However, neither the TinyMT nor MT PRNG are meant to be used for cryptographic a
pplications.
</t> </t>
</section>
</section> <section anchor="iana" numbered="true" toc="include" removeInRFC="false" pn=
"section-4">
<section anchor="iana" title="IANA Considerations"> <name slugifiedName="name-iana-considerations">IANA Considerations</name>
<!-- ====================== --> <t pn="section-4-1">
This document has no IANA actions.
<t>
This document does not require any IANA action.
</t> </t>
</section>
</section> </middle>
<back>
<section title="Acknowledgments"> <references pn="section-5">
<!-- ====================== --> <name slugifiedName="name-references">References</name>
<references pn="section-5.1">
<t> <name slugifiedName="name-normative-references">Normative References</na
The authors would like to thank Belkacem Teibi with whom we explored TinyMT32 sp me>
ecificities when looking to an alternative to the Park-Miller Linear Congruentia <reference anchor="C99" quoteTitle="true" derivedAnchor="C99">
l PRNG. <front>
The authors would like to thank <title>Programming languages - C: C99, correction 3:2007</title>
Carl Wallace, Stewart Bryant, Greg Skinner, Mike Heard, the three TSVWG chairs, <seriesInfo name="ISO/IEC" value="9899:1999/Cor 3:2007"/>
Wesley Eddy, our shepherd, David Black and Gorry Fairhurst, as well as Spencer D <author>
awkins and Mirja Kuhlewind. <organization showOnFrontPage="true">International Organization fo
Last but not least, the authors are really grateful to the IESG members, in part r Standardization</organization>
icular Benjamin Kaduk, Eric Rescorla, Adam Roach, Roman Danyliw, Barry Leiba, Ma </author>
rtin Vigoureux, Eric Vyncke for their highly valuable feedbacks that greatly con <date month="November" year="2007"/>
tributed to improve this specification. </front>
</reference>
<reference anchor="RFC2119" target="https://www.rfc-editor.org/info/rfc2
119" quoteTitle="true" derivedAnchor="RFC2119">
<front>
<title>Key words for use in RFCs to Indicate Requirement Levels</tit
le>
<author initials="S." surname="Bradner" fullname="S. Bradner">
<organization showOnFrontPage="true"/>
</author>
<date year="1997" month="March"/>
<abstract>
<t>In many standards track documents several words are used to sig
nify the requirements in the specification. These words are often capitalized.
This document defines these words as they should be interpreted in IETF document
s. This document specifies an Internet Best Current Practices for the Internet
Community, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174" target="https://www.rfc-editor.org/info/rfc8
174" quoteTitle="true" derivedAnchor="RFC8174">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author initials="B." surname="Leiba" fullname="B. Leiba">
<organization showOnFrontPage="true"/>
</author>
<date year="2017" month="May"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying tha
t only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
</references>
<references pn="section-5.2">
<name slugifiedName="name-informative-references">Informative References
</name>
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u.ac.jp/~m-mat/MT/ADAPTIVE" quoteTitle="true" derivedAnchor="AdaptiveCrush">
<front>
<title>Automation of Statistical Tests on Randomness to Obtain Clear
er Conclusion</title>
<seriesInfo name="DOI" value="10.1007/978-3-642-04107-5_26"/>
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<organization showOnFrontPage="true"/>
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<date month="November" year="2009"/>
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<refcontent>Monte Carlo and Quasi-Monte Carlo Methods 2008</refcontent
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<title>RIOT: An Open Source Operating System for Low-End Embedded De
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<seriesInfo name="DOI" value="10.1109/JIOT.2018.2815038"/>
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<author initials="C." surname="Gundogan">
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<author initials="O." surname="Hahm">
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<author initials="P." surname="Kietzmann">
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<date year="1992"/>
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<refcontent>Cambridge University Press</refcontent>
</reference>
<reference anchor="RFC5170" target="https://www.rfc-editor.org/info/rfc5
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<front>
<title>Low Density Parity Check (LDPC) Staircase and Triangle Forwar
d Error Correction (FEC) Schemes</title>
<author initials="V." surname="Roca" fullname="V. Roca">
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<abstract>
<t>This document describes two Fully-Specified Forward Error Corre
ction (FEC) Schemes, Low Density Parity Check (LDPC) Staircase and LDPC Triangle
, and their application to the reliable delivery of data objects on the packet e
rasure channel (i.e., a communication path where packets are either received wit
hout any corruption or discarded during transmission). These systematic FEC cod
es belong to the well- known class of "Low Density Parity Check" codes, and are
large block FEC codes in the sense of RFC 3453. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5170"/>
<seriesInfo name="DOI" value="10.17487/RFC5170"/>
</reference>
<reference anchor="RFC8681" target="https://www.rfc-editor.org/info/rfc8
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<front>
<title>Sliding Window Random Linear Code (RLC) Forward Erasure Corre
ction (FEC) Schemes for FECFRAME</title>
<seriesInfo name="RFC" value="8681"/>
<seriesInfo name="DOI" value="10.17487/RFC8681"/>
<author initials="V" surname="Roca" fullname="Vincent Roca">
<organization showOnFrontPage="true"/>
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r-Lab/TinyMT" quoteTitle="true" derivedAnchor="TinyMT-dev">
<front>
<title>Tiny Mersenne Twister (TinyMT)</title>
<seriesInfo name="commit" value="9d7ca3c"/>
<author/>
<date month="March" year="2018"/>
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</reference>
<reference anchor="TinyMT-params" target="https://github.com/jj1bdx/tiny
mtdc-longbatch" quoteTitle="true" derivedAnchor="TinyMT-params">
<front>
<title>TinyMT pre-calculated parameter list</title>
<seriesInfo name="commit" value="30079eb"/>
<author/>
<date month="March" year="2013"/>
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<reference anchor="TinyMT-web" target="http://www.math.sci.hiroshima-u.a
c.jp/~m-mat/MT/TINYMT/" quoteTitle="true" derivedAnchor="TinyMT-web">
<front>
<title>Tiny Mersenne Twister (TinyMT)</title>
<author fullname="Mutsuo Saito" initials="M" surname="Saito">
<organization showOnFrontPage="true"/>
</author>
<author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto"
>
<organization showOnFrontPage="true"/>
</author>
</front>
</reference>
</references>
</references>
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ndix.a">
<name slugifiedName="name-acknowledgments">Acknowledgments</name>
<t pn="section-appendix.a-1">
The authors would like to thank Belkacem Teibi, with whom we explored TinyMT32
specificities when looking to an alternative to the Park-Miller Linear
Congruential PRNG. The authors would also like to thank Carl Wallace; Stewart
Bryant; Greg Skinner; Mike Heard; the three TSVWG chairs, Wesley Eddy (our
shepherd), David Black, and Gorry Fairhurst; as well as Spencer Dawkins and
Mirja Kuehlewind. Last but not least, the authors are really grateful to the
IESG members, in particular Benjamin Kaduk, Eric Rescorla, Adam Roach, Roman
Danyliw, Barry Leiba, Martin Vigoureux, and Eric Vyncke for their highly
valuable feedback that greatly contributed to improving this specification.
</t> </t>
</section>
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="include" pn="section-appendix.b">
</middle> <name slugifiedName="name-authors-addresses">Authors' Addresses</name>
<author fullname="Mutsuo Saito" initials="M" surname="Saito">
<back> <organization showOnFrontPage="true">Hiroshima University</organization>
<references title="Normative References"> <address>
<!-- ====================== --> <postal>
&rfc2119; <street/>
&rfc8174; <city/>
<country>Japan</country>
<reference anchor="C99"> </postal>
<front> <email>saito@math.sci.hiroshima-u.ac.jp</email>
<title>Programming languages - C: C99, correction 3:2007</title> </address>
<author /> </author>
<date month="November" year="2007" /> <author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto">
</front> <organization showOnFrontPage="true">Hiroshima University</organization>
<seriesInfo name="International Organization for Standardization," value <address>
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</reference> <street/>
<city/>
</references> <country>Japan</country>
</postal>
<references title="Informative References"> <email>m-mat@math.sci.hiroshima-u.ac.jp</email>
<!-- ====================== --> </address>
</author>
&rfc5170; <author fullname="Vincent Roca" initials="V" surname="Roca" role="editor">
<organization showOnFrontPage="true">INRIA</organization>
<reference anchor="TinyMT-web" target="http://www.math.sci.hiroshima-u.ac. <address>
jp/~m-mat/MT/TINYMT/"> <postal>
<front> <street/>
<title>Tiny Mersenne Twister (TinyMT) web site</title> <city/>
<author fullname="Mutsuo Saito" initials="M" surname="Saito"><organiza <code/>
tion /> </author> <extaddr>Univ. Grenoble Alpes</extaddr>
<author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto">< <country>France</country>
organization /> </author> </postal>
<date /> <email>vincent.roca@inria.fr</email>
</front> </address>
</reference> </author>
<author fullname="Emmanuel Baccelli" initials="E" surname="Baccelli">
<reference anchor="TinyMT-dev" target="https://github.com/MersenneTwister- <organization showOnFrontPage="true">INRIA</organization>
Lab/TinyMT"> <address>
<front> <postal>
<title>Tiny Mersenne Twister (TinyMT) github site</title> <street/>
<author fullname="Mutsuo Saito" initials="M" surname="Saito"><organiza <city/>
tion /> </author> <code/>
<author fullname="Makoto Matsumoto" initials="M" surname="Matsumoto">< <country>France</country>
organization /> </author> </postal>
<date /> <email>emmanuel.baccelli@inria.fr</email>
</front> </address>
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</section>
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dc-longbatch/">
<front>
<title>TinyMT pre-calculated parameter list github site</title>
<author fullname="Kenji Rikitake" initials="K" surname="Rikitake"><org
anization /> </author>
<date />
</front>
</reference>
<reference anchor="RLC-ID" target="https://tools.ietf.org/html/draft-ietf-
tsvwg-rlc-fec-scheme">
<front>
<title>Sliding Window Random Linear Code (RLC) Forward Erasure Correct
ion (FEC) Scheme for FECFRAME</title>
<author initials="V" surname="Roca" fullname="Vincent Roca"> <organiza
tion /> </author>
<author initials="B" surname="Teibi" fullname="Belkacem Teibi"> <organ
ization /> </author>
<date month="February" year="2019" />
</front>
<seriesInfo name='Work in' value='Progress' />
<seriesInfo name='Transport Area Working Group (TSVWG)' value='draft-iet
f-tsvwg-rlc-fec-scheme (Work in Progress)' />
</reference>
<reference anchor="MT98">
<front>
<title>Mersenne Twister: A 623-dimensionally equidistributed uniform ps
eudorandom number generator</title>
<author initials="M." surname="Matsumoto"> <organization /></author>
<author initials="T." surname="Nishimura"> <organization /></author>
<date month="January" year="1998" />
</front>
<seriesInfo name="" value="ACM Transactions on Modeling and Computer Sim
ulation (TOMACS), Volume 8 Issue 1, Jan. 1998, pp.3-30, January 1998, DOI:10.114
5/272991.272995" />
</reference>
<reference anchor="KR12">
<front>
<title>TinyMT Pseudo Random Number Generator for Erlang</title>
<author initials="K." surname="Rikitake">
<organization />
</author>
<date month="September" year="2012" />
</front>
<seriesInfo name="" value="ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
September 14, 2012, Copenhagen, Denmark, DOI: http://dx.doi.org/10.1145/2364489
.2364504" />
</reference>
<reference anchor="Baccelli18">
<front>
<title>RIOT: An Open Source Operating System for Low-End Embedded Devic
es in the IoT</title>
<author initials="E." surname="Baccelli"> <organization /> </author>
<author initials="C." surname="Gundogan"> <organization /> </author>
<author initials="O." surname=" Hahm"> <organization /> </author>
<author initials="P." surname=" Kietzmann"> <organization /> </author>
<author initials="M. S." surname=" Lenders"> <organization /> </author
>
<author initials="H." surname=" Petersen"> <organization /> </author>
<author initials="K." surname="Schleiser"> <organization /> </author>
<author initials="T. C." surname=" Schmidt"> <organization /> </author
>
<author initials="M." surname="Wahlisch"> <organization /> </author>
<date month="December" year="2018" />
</front>
<seriesInfo name="" value="IEEE Internet of Things Journal (Volume 5, Is
sue 6), DOI: 10.1109/JIOT.2018.2815038" />
</reference>
<reference anchor="PTVF92">
<front>
<title>Numerical Recipies in C; Second Edition</title>
<author initials="W." surname="Press"> <organization /> </author>
<author initials="S." surname="Teukolsky"> <organization /> </author>
<author initials="W." surname="Vetterling"> <organization /> </author>
<author initials="B." surname="Flannery"> <organization /> </author>
<date year="1992" />
</front>
<seriesInfo name="Cambridge University Press," value="ISBN: 0-521-43108-
5" />
</reference>
<reference anchor="TestU01" target="http://simul.iro.umontreal.ca/testu01/
tu01.html">
<front>
<title>TestU01: A C Library for Empirical Testing of Random Number Gene
rators</title>
<author initials="P." surname="L'Ecuyer"> <organization /> </author>
<author initials="R." surname="Simard"> <organization /> </author>
<date month="" year="2007" />
</front>
<seriesInfo name="" value="ACM Transactions on Mathematical Software, Vo
l. 33, article 22, 2007" />
</reference>
<reference anchor="AdaptiveCrush" target="http://www.math.sci.hiroshima-u.
ac.jp/~m-mat/MT/ADAPTIVE/">
<front>
<title>Automation of statistical tests on randomness to obtain clearer
conclusion</title>
<author initials="H." surname="Haramoto"> <organization /> </author>
<date month="November" year="2009" />
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8, DOI:10.1007/978-3-642-04107-5_26" />
</reference>
</references>
<!-- ====================== -->
</back>
</rfc> </rfc>
 End of changes. 47 change blocks. 
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