Internet DRAFT - draft-ietf-tsvwg-tinymt32
draft-ietf-tsvwg-tinymt32
TSVWG M. Saito
Internet-Draft M. Matsumoto
Intended status: Standards Track Hiroshima University
Expires: December 19, 2019 V. Roca (Ed.)
E. Baccelli
INRIA
June 17, 2019
TinyMT32 Pseudo Random Number Generator (PRNG)
draft-ietf-tsvwg-tinymt32-06
Abstract
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-use 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,
compatible with most target platforms that include embedded devices,
while keeping a reasonably good randomness that represents a
sigificant improvement compared to the Park-Miller Linear
Congruential PRNG. However, neither the TinyMT nor MT PRNG are meant
to be used for cryptographic applications.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on December 19, 2019.
Copyright Notice
Copyright (c) 2019 IETF Trust and the persons identified as the
document authors. All rights reserved.
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This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(https://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. 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.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. TinyMT32 PRNG Specification . . . . . . . . . . . . . . . . . 3
3.1. TinyMT32 Source Code . . . . . . . . . . . . . . . . . . 3
3.2. TinyMT32 Usage . . . . . . . . . . . . . . . . . . . . . 7
3.3. Specific Implementation Validation and Deterministic
Behavior . . . . . . . . . . . . . . . . . . . . . . . . 8
4. Security Considerations . . . . . . . . . . . . . . . . . . . 9
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9
6. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 9
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
7.1. Normative References . . . . . . . . . . . . . . . . . . 10
7.2. Informative References . . . . . . . . . . . . . . . . . 10
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 11
1. Introduction
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, that can be found at
[TinyMT-web] (TinyMT web site) and [TinyMT-dev] (Github site). This
specialisation aims at having a simple-to-use and deterministic PRNG,
as explained below. However, the TinyMT32 PRNG is not meant to be
used for cryptographic applications.
TinyMT is a new small-sized variant introduced in 2011 of the
Mersenne Twister (MT) PRNG [MT98]. This document focusses on the
TinyMT32 variant (rather than TinyMT64) of the TinyMT PRNG, which
outputs 32-bit unsigned integers.
The purpose of TinyMT is not to replace Mersenne Twister: TinyMT has
a far shorter period (2^^127 - 1) than MT. The merit of TinyMT is in
the small size of the internal state of 127 bits, far smaller than
the 19937 bits of MT. The outputs of TinyMT satisfy several
statistical tests for non-cryptographic randomness, including
BigCrush in TestU01 [TestU01] and AdaptiveCrush [AdaptiveCrush],
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leaving it well-placed for non-cryptographic usage, especially given
the small size of its internal state (see [TinyMT-web]). From this
point of view, TinyMT32 represents a major improvement with respect
to the Park-Miller Linear Congruential PRNG (e.g., as specified in
[RFC5170]) that suffers several known limitations (see for instance
[PTVF92], section 7.1, p. 279, and [RLC-ID], Appendix B).
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-random numbers
depend only on the seed value, this specification requires the use of
a specific parameter set (see Section 3.1). This is a major
difference with respect to the implementation version 1.1
(2015/04/24) that leaves this parameter set unspecified.
Finally, the determinism of this PRNG, for a given seed, has been
carefully checked (see Section 3.3). It means that the same sequence
of pseudo-random numbers should be generated, no matter the target
execution platform and compiler, for a given initial seed value.
This determinism can be a key requirement as it the case with
[RLC-ID] that normatively depends on this specification.
2. Definitions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in BCP
14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
3. TinyMT32 PRNG Specification
3.1. TinyMT32 Source Code
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 MUST be used:
o mat1 = 0x8f7011ee = 2406486510
o mat2 = 0xfc78ff1f = 4235788063
o tmat = 0x3793fdff = 932445695
This parameter set is the first entry of the precalculated parameter
sets in file tinymt32dc/tinymt32dc.0.1048576.txt, by Kenji Rikitake,
and available at [TinyMT-params]. This is also the parameter set
used in [KR12].
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The TinyMT32 PRNG reference implementation is reproduced in Figure 1.
This is a C language implementation, written for C99 [C99]. This
reference implementation differs from the original source code as
follows:
o the original copyright and license have been removed by the
original authors who are now authors of this document, in
accordance with BCP 78 and the IETF Trust's Legal Provisions
Relating to IETF Documents (http://trustee.ietf.org/license-info);
o the source code initially spread over the tinymt32.h and
tinymt32.c files has been merged;
o the unused parts of the original source code have been removed.
This is the case of the tinymt32_init_by_array() alternative
initialisation function. This is also the case of the
period_certification() function after having checked it is not
required with the chosen parameter set;
o the unused constants TINYMT32_MEXP and TINYMT32_MUL have been
removed;
o the appropriate parameter set has been added to the initialization
function;
o the function order has been changed;
o certain internal variables have been renamed for compactness
purposes;
o the const qualifier has been added to the constant definitions;
o the code that was dependant on the representation of negative
integers by 2's complements has been replaced by a more portable
version;
<CODE BEGINS>
/**
* Tiny Mersenne Twister only 127 bit internal state.
* Derived from the reference implementation version 1.1 (2015/04/24)
* by Mutsuo Saito (Hiroshima University) and Makoto Matsumoto
* (Hiroshima University).
*/
#include <stdint.h>
/**
* tinymt32 internal state vector and parameters
*/
typedef struct {
uint32_t status[4];
uint32_t mat1;
uint32_t mat2;
uint32_t tmat;
} tinymt32_t;
static void tinymt32_next_state (tinymt32_t* s);
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static uint32_t tinymt32_temper (tinymt32_t* s);
/**
* Parameter set to use for this IETF specification. Don't change.
* This parameter set is the first entry of the precalculated
* parameter sets in file tinymt32dc/tinymt32dc.0.1048576.txt, by
* Kenji Rikitake, available at:
* https://github.com/jj1bdx/tinymtdc-longbatch/
* It is also the parameter set used:
* Rikitake, K., "TinyMT Pseudo Random Number Generator for
* Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
* September, 2012.
*/
const uint32_t TINYMT32_MAT1_PARAM = UINT32_C(0x8f7011ee);
const uint32_t TINYMT32_MAT2_PARAM = UINT32_C(0xfc78ff1f);
const uint32_t TINYMT32_TMAT_PARAM = UINT32_C(0x3793fdff);
/**
* This function initializes the internal state array with a
* 32-bit unsigned integer seed.
* @param s pointer to tinymt internal state.
* @param seed a 32-bit unsigned integer used as a seed.
*/
void tinymt32_init (tinymt32_t* s, uint32_t seed)
{
const uint32_t MIN_LOOP = 8;
const uint32_t PRE_LOOP = 8;
s->status[0] = seed;
s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM;
s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM;
s->status[3] = s->tmat = TINYMT32_TMAT_PARAM;
for (int i = 1; i < MIN_LOOP; i++) {
s->status[i & 3] ^= i + UINT32_C(1812433253)
* (s->status[(i - 1) & 3]
^ (s->status[(i - 1) & 3] >> 30));
}
/*
* NB: the parameter set of this specification warrants
* that none of the possible 2^^32 seeds leads to an
* all-zero 127-bit internal state. Therefore, the
* period_certification() function of the original
* TinyMT32 source code has been safely removed. If
* another parameter set is used, this function will
* have to be re-introduced here.
*/
for (int i = 0; i < PRE_LOOP; i++) {
tinymt32_next_state(s);
}
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}
/**
* This function outputs a 32-bit unsigned integer from
* the internal state.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned integer r (0 <= r < 2^32).
*/
uint32_t tinymt32_generate_uint32 (tinymt32_t* s)
{
tinymt32_next_state(s);
return tinymt32_temper(s);
}
/**
* Internal tinymt32 constants and functions.
* Users should not call these functions directly.
*/
const uint32_t TINYMT32_SH0 = 1;
const uint32_t TINYMT32_SH1 = 10;
const uint32_t TINYMT32_SH8 = 8;
const uint32_t TINYMT32_MASK = UINT32_C(0x7fffffff);
/**
* This function changes the internal state of tinymt32.
* @param s pointer to tinymt internal state.
*/
static void tinymt32_next_state (tinymt32_t* s)
{
uint32_t x;
uint32_t y;
y = s->status[3];
x = (s->status[0] & TINYMT32_MASK)
^ s->status[1]
^ s->status[2];
x ^= (x << TINYMT32_SH0);
y ^= (y >> TINYMT32_SH0) ^ x;
s->status[0] = s->status[1];
s->status[1] = s->status[2];
s->status[2] = x ^ (y << TINYMT32_SH1);
s->status[3] = y;
/*
* The if (y & 1) {...} block below replaces:
* s->status[1] ^= -((int32_t)(y & 1)) & s->mat1;
* s->status[2] ^= -((int32_t)(y & 1)) & s->mat2;
* The adopted code is equivalent to the original code
* but does not depend on the representation of negative
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* integers by 2's complements. It is therefore more
* portable, but includes an if-branch which may slow
* down the generation speed.
*/
if (y & 1) {
s->status[1] ^= s->mat1;
s->status[2] ^= s->mat2;
}
}
/**
* This function outputs a 32-bit unsigned integer from
* the internal state.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned pseudo-random number.
*/
static uint32_t tinymt32_temper (tinymt32_t* s)
{
uint32_t t0, t1;
t0 = s->status[3];
t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8);
t0 ^= t1;
/*
* The if (t1 & 1) {...} block below replaces:
* t0 ^= -((int32_t)(t1 & 1)) & s->tmat;
* The adopted code is equivalent to the original code
* but does not depend on the representation of negative
* integers by 2's complements. It is therefore more
* portable, but includes an if-branch which may slow
* down the generation speed.
*/
if (t1 & 1) {
t0 ^= s->tmat;
}
return t0;
}
<CODE ENDS>
Figure 1: TinyMT32 Reference Implementation
3.2. TinyMT32 Usage
This PRNG MUST first be initialized with the following function:
void tinymt32_init (tinymt32_t* s, uint32_t seed);
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
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a pointer to an instance of a tinymt32_t structure that needs to be
allocated by the caller but left uninitialized. This structure will
then be updated by the various TinyMT32 functions in order to keep
the internal state of the PRNG. The use of this structure admits
several instances of this PRNG to be used in parallel, each of them
having its own instance of the structure.
Then, each time a new 32-bit pseudo-random unsigned integer between 0
and 2^32 - 1 inclusive is needed, the following function is used:
uint32_t tinymt32_generate_uint32 (tinymt32_t * s);
Of course, the tinymt32_t structure must be left unchanged by the
caller between successive calls to this function.
3.3. Specific Implementation Validation and Deterministic Behavior
PRNG determinism, for a given seed, can be a requirement (e.g., with
[RLC-ID]). Consequently, any implementation of the TinyMT32 PRNG in
line with this specification MUST have the same output as that
provided by the reference implementation of Figure 1. In order to
increase the compliancy confidence, this document proposes the
following criteria. Using a seed value of 1, the first 50 values
returned by tinymt32_generate_uint32(s) as 32-bit unsigned integers
are equal to values provided in Figure 2, 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 of TinyMT32,
as part of the MersenneTwister-Lab/TinyMT Github repository.
2545341989 981918433 3715302833 2387538352 3591001365
3820442102 2114400566 2196103051 2783359912 764534509
643179475 1822416315 881558334 4207026366 3690273640
3240535687 2921447122 3984931427 4092394160 44209675
2188315343 2908663843 1834519336 3774670961 3019990707
4065554902 1239765502 4035716197 3412127188 552822483
161364450 353727785 140085994 149132008 2547770827
4064042525 4078297538 2057335507 622384752 2041665899
2193913817 1080849512 33160901 662956935 642999063
3384709977 1723175122 3866752252 521822317 2292524454
Figure 2: First 50 decimal values (to be read per line) returned by
tinymt32_generate_uint32(s) as 32-bit unsigned integers, with a seed
value of 1.
In particular, the deterministic behavior of the Figure 1 source code
has been checked across several platforms: high-end laptops running
64-bits Mac OSX and Linux/Ubuntu; a board featuring a 32-bits ARM
Cortex-A15 and running 32-bit Linux/Ubuntu; several embedded cards
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featuring either an ARM Cortex-M0+, a Cortex-M3 or a Cortex-M4 32-bit
microcontroller, all of them running RIOT [Baccelli18]; 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.
This specification only outputs 32-bit unsigned pseudo-random numbers
and does not try to map this output to a smaller integer range (e.g.,
between 10 and 49 inclusive). If a specific use-case needs such a
mapping, it will have to provide its own function. In that case, if
PRNG determinism is also required, the use of floating point (single
or double precision) to perform this mapping should probably be
avoided, these calculations leading potentially to different rounding
errors across different target platforms. Great care should also be
put on not introducing biases in the randomness of the mapped output
(it may be the case with some mapping algorithms) incompatible with
the use-case requirements. The details of how to perform such a
mapping are out-of-scope of this document.
4. Security Considerations
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 applications.
5. IANA Considerations
This document does not require any IANA action.
6. Acknowledgments
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 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 Kuhlewind. 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, Eric Vyncke for their highly valuable
feedbacks that greatly contributed to improve this specification.
7. References
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7.1. Normative References
[C99] "Programming languages - C: C99, correction 3:2007",
International Organization for Standardization, ISO/IEC
9899:1999/Cor 3:2007, November 2007.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
7.2. Informative References
[AdaptiveCrush]
Haramoto, H., "Automation of statistical tests on
randomness to obtain clearer conclusion", Monte Carlo and
Quasi-Monte Carlo Methods 2008,
DOI:10.1007/978-3-642-04107-5_26, November 2009,
<http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/
ADAPTIVE/>.
[Baccelli18]
Baccelli, E., Gundogan, C., Hahm, O., Kietzmann, P.,
Lenders, M., Petersen, H., Schleiser, K., Schmidt, T., and
M. Wahlisch, "RIOT: An Open Source Operating System for
Low-End Embedded Devices in the IoT", IEEE Internet of
Things Journal (Volume 5, Issue 6), DOI:
10.1109/JIOT.2018.2815038, December 2018.
[KR12] Rikitake, K., "TinyMT Pseudo Random Number Generator for
Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
September 14, 2012, Copenhagen, Denmark, DOI:
http://dx.doi.org/10.1145/2364489.2364504, September 2012.
[MT98] Matsumoto, M. and T. Nishimura, "Mersenne Twister: A
623-dimensionally equidistributed uniform pseudorandom
number generator", ACM Transactions on Modeling and
Computer Simulation (TOMACS), Volume 8 Issue 1, Jan. 1998,
pp.3-30, January 1998, DOI:10.1145/272991.272995, January
1998.
[PTVF92] Press, W., Teukolsky, S., Vetterling, W., and B. Flannery,
"Numerical Recipies in C; Second Edition", Cambridge
University Press, ISBN: 0-521-43108-5, 1992.
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[RFC5170] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity
Check (LDPC) Staircase and Triangle Forward Error
Correction (FEC) Schemes", RFC 5170, DOI 10.17487/RFC5170,
June 2008, <https://www.rfc-editor.org/info/rfc5170>.
[RLC-ID] Roca, V. and B. Teibi, "Sliding Window Random Linear Code
(RLC) Forward Erasure Correction (FEC) Scheme for
FECFRAME", Work in Progress, Transport Area Working Group
(TSVWG) draft-ietf-tsvwg-rlc-fec-scheme (Work in
Progress), February 2019, <https://tools.ietf.org/html/
draft-ietf-tsvwg-rlc-fec-scheme>.
[TestU01] L'Ecuyer, P. and R. Simard, "TestU01: A C Library for
Empirical Testing of Random Number Generators", ACM
Transactions on Mathematical Software, Vol. 33, article
22, 2007, 2007,
<http://simul.iro.umontreal.ca/testu01/tu01.html>.
[TinyMT-dev]
Saito, M. and M. Matsumoto, "Tiny Mersenne Twister
(TinyMT) github site",
<https://github.com/MersenneTwister-Lab/TinyMT>.
[TinyMT-params]
Rikitake, K., "TinyMT pre-calculated parameter list github
site", <https://github.com/jj1bdx/tinymtdc-longbatch/>.
[TinyMT-web]
Saito, M. and M. Matsumoto, "Tiny Mersenne Twister
(TinyMT) web site",
<http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/TINYMT/>.
Authors' Addresses
Mutsuo Saito
Hiroshima University
Japan
EMail: saito@math.sci.hiroshima-u.ac.jp
Makoto Matsumoto
Hiroshima University
Japan
EMail: m-mat@math.sci.hiroshima-u.ac.jp
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Vincent Roca
INRIA
Univ. Grenoble Alpes
France
EMail: vincent.roca@inria.fr
Emmanuel Baccelli
INRIA
France
EMail: emmanuel.baccelli@inria.fr
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