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Checking references for intended status: Proposed Standard ---------------------------------------------------------------------------- (See RFCs 3967 and 4897 for information about using normative references to lower-maturity documents in RFCs) No issues found here. Summary: 0 errors (**), 0 flaws (~~), 2 warnings (==), 1 comment (--). Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 TSVWG M. Saito 3 Internet-Draft M. Matsumoto 4 Intended status: Standards Track Hiroshima University 5 Expires: November 17, 2019 V. Roca (Ed.) 6 E. Baccelli 7 INRIA 8 May 16, 2019 10 TinyMT32 Pseudo Random Number Generator (PRNG) 11 draft-ietf-tsvwg-tinymt32-02 13 Abstract 15 This document describes the TinyMT32 Pseudo Random Number Generator 16 (PRNG) that produces 32-bit pseudo-random unsigned integers and aims 17 at having a simple-to-use and deterministic solution. This PRNG is a 18 small-sized variant of Mersenne Twister (MT) PRNG, also designed by 19 M. Saito and M. Matsumoto. The main advantage of TinyMT32 over MT 20 is the use of a small internal state, compatible with most target 21 platforms including embedded devices, while keeping a reasonably good 22 randomness. 24 Status of This Memo 26 This Internet-Draft is submitted in full conformance with the 27 provisions of BCP 78 and BCP 79. 29 Internet-Drafts are working documents of the Internet Engineering 30 Task Force (IETF). Note that other groups may also distribute 31 working documents as Internet-Drafts. The list of current Internet- 32 Drafts is at https://datatracker.ietf.org/drafts/current/. 34 Internet-Drafts are draft documents valid for a maximum of six months 35 and may be updated, replaced, or obsoleted by other documents at any 36 time. It is inappropriate to use Internet-Drafts as reference 37 material or to cite them other than as "work in progress." 39 This Internet-Draft will expire on November 17, 2019. 41 Copyright Notice 43 Copyright (c) 2019 IETF Trust and the persons identified as the 44 document authors. All rights reserved. 46 This document is subject to BCP 78 and the IETF Trust's Legal 47 Provisions Relating to IETF Documents 48 (https://trustee.ietf.org/license-info) in effect on the date of 49 publication of this document. Please review these documents 50 carefully, as they describe your rights and restrictions with respect 51 to this document. Code Components extracted from this document must 52 include Simplified BSD License text as described in Section 4.e of 53 the Trust Legal Provisions and are provided without warranty as 54 described in the Simplified BSD License. 56 Table of Contents 58 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 59 2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 3 60 3. TinyMT32 PRNG Specification . . . . . . . . . . . . . . . . . 3 61 3.1. TinyMT32 Source Code . . . . . . . . . . . . . . . . . . 3 62 3.2. TinyMT32 Usage . . . . . . . . . . . . . . . . . . . . . 7 63 3.3. Specific Implementation Validation and Deterministic 64 Behavior . . . . . . . . . . . . . . . . . . . . . . . . 8 65 4. Security Considerations . . . . . . . . . . . . . . . . . . . 9 66 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9 67 6. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 9 68 7. References . . . . . . . . . . . . . . . . . . . . . . . . . 9 69 7.1. Normative References . . . . . . . . . . . . . . . . . . 9 70 7.2. Informative References . . . . . . . . . . . . . . . . . 9 71 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 10 73 1. Introduction 75 This document specifies the TinyMT32 PRNG, as a specialization of the 76 reference implementation version 1.1 (2015/04/24) by Mutsuo Saito and 77 Makoto Matsumoto, from Hiroshima University: 79 o Official web site: 81 o Official github site and reference implementation: 82 84 This specialisation aims at having a simple-to-use and deterministic 85 PRNG, as explained below. 87 TinyMT is a new small-sized variant of Mersenne Twister (MT) 88 introduced by Mutsuo Saito and Makoto Matsumoto in 2011. This 89 document focusses on the TinyMT32 variant (rather than TinyMT64) of 90 the PRNG, which outputs 32-bit unsigned integers. 92 The purpose of TinyMT is not to replace Mersenne Twister: TinyMT has 93 a far shorter period (2^^127 - 1) than MT. The merit of TinyMT is in 94 its small size of the internal state of 127 bits, far smaller than 95 the 19937 bits of MT. According to statistical tests (BigCrush in 96 TestU01 and 97 AdaptiveCrush ) the quality of the outputs of TinyMT seems pretty good in 99 terms of randomnes (in particular the uniformity of generated 100 numbers), taking the small size of the internal state into 101 consideration (see ). From this point of view, TinyMT32 103 represents a major improvement with respect to the Park-Miler Linear 104 Congruential PRNG (e.g., as specified in [RFC5170]) that suffers 105 several known limitations. However, neither TinyMT nor MT are meant 106 to be used for cryptographic applications. 108 The TinyMT32 PRNG initialization depends, among other things, on a 109 parameter set -- namely (mat1, mat2, tmat) -- that needs to be well 110 chosen (pre-calculated values are available in the official web 111 site). In order to facilitate the use of this PRNG and make the 112 sequence of pseudo-random numbers depend only on the seed value, this 113 specification requires the use of a specific parameter set (see 114 Section 3.1). This is a first difference with respect to the 115 implementation version 1.1 (2015/04/24) by Mutsuo Saito and Makoto 116 Matsumoto that leaves this parameter set unspecified. A second 117 difference is the removal of the tinymt32_init_by_array() alternative 118 initialization function, to only keep the simple initialisation 119 through a seed value (see Section 3.2). 121 Finally, the determinism of this PRNG, for a given seed, has been 122 carefully checked (see Section 3.3). It means that the same sequence 123 of pseudo-random numbers should be generated, no matter the target 124 execution platform and compiler, for a given initial seed value. 125 This determinism can be a key requirement as it the case with 126 [RLC-ID] that normatively depends on this specification. 128 2. Definitions 130 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 131 "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and 132 "OPTIONAL" in this document are to be interpreted as described in BCP 133 14 [RFC2119] [RFC8174] when, and only when, they appear in all 134 capitals, as shown here. 136 3. TinyMT32 PRNG Specification 138 3.1. TinyMT32 Source Code 140 The TinyMT32 PRNG requires to be initialized with a parameter set 141 that needs to be well chosen. In this specification, for the sake of 142 simplicity, the following parameter set MUST be used: 144 o mat1 = 0x8f7011ee = 2406486510 145 o mat2 = 0xfc78ff1f = 4235788063 146 o tmat = 0x3793fdff = 932445695 148 This parameter set is the first entry of the precalculated parameter 149 sets in file tinymt32dc/tinymt32dc.0.1048576.txt, by Kenji Rikitake, 150 and available at . 151 This is also the parameter set used in [KR12]. 153 The TinyMT32 PRNG reference implementation is reproduced in Figure 1, 154 with the following differences with respect to the original source 155 code: 157 o the original copyright and licence have been removed, in 158 accordance with BCP 78 and the IETF Trust's Legal Provisions 159 Relating to IETF Documents (http://trustee.ietf.org/license-info); 160 o the source code initially spread over the tinymt32.h and 161 tinymt32.c files has been merged; 162 o the unused parts of the original source code have been removed. 163 This is the case of the tinymt32_init_by_array() alternative 164 initialisation function; 165 o the unused constants TINYMT32_MEXP and TINYMT32_MUL have been 166 removed; 167 o the appropriate parameter set has been added to the initialization 168 function; 169 o the function order has been changed; 170 o certain internal variables have been renamed for compactness 171 purposes; 172 o the const qualifier has been added to the constant definitions. 174 175 /** 176 * Tiny Mersenne Twister only 127 bit internal state. 177 * Derived from the reference implementation version 1.1 (2015/04/24) 178 * by Mutsuo Saito (Hiroshima University) and Makoto Matsumoto 179 * (Hiroshima University). 180 */ 181 #include 183 /** 184 * tinymt32 internal state vector and parameters 185 */ 186 typedef struct { 187 uint32_t status[4]; 188 uint32_t mat1; 189 uint32_t mat2; 190 uint32_t tmat; 191 } tinymt32_t; 192 static void tinymt32_next_state (tinymt32_t* s); 193 static uint32_t tinymt32_temper (tinymt32_t* s); 195 /** 196 * Parameter set to use for this IETF specification. Don't change. 197 * This parameter set is the first entry of the precalculated 198 * parameter sets in file tinymt32dc/tinymt32dc.0.1048576.txt, by 199 * Kenji Rikitake, available at: 200 * https://github.com/jj1bdx/tinymtdc-longbatch/ 201 * It is also the parameter set used: 202 * Rikitake, K., "TinyMT Pseudo Random Number Generator for 203 * Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12), 204 * September, 2012. 205 */ 206 const uint32_t TINYMT32_MAT1_PARAM = UINT32_C(0x8f7011ee); 207 const uint32_t TINYMT32_MAT2_PARAM = UINT32_C(0xfc78ff1f); 208 const uint32_t TINYMT32_TMAT_PARAM = UINT32_C(0x3793fdff); 210 /** 211 * This function initializes the internal state array with a 212 * 32-bit unsigned integer seed. 213 * @param s pointer to tinymt internal state. 214 * @param seed a 32-bit unsigned integer used as a seed. 215 */ 216 void tinymt32_init (tinymt32_t* s, uint32_t seed) 217 { 218 const uint32_t MIN_LOOP = 8; 219 const uint32_t PRE_LOOP = 8; 220 s->status[0] = seed; 221 s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM; 222 s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM; 223 s->status[3] = s->tmat = TINYMT32_TMAT_PARAM; 224 for (int i = 1; i < MIN_LOOP; i++) { 225 s->status[i & 3] ^= i + UINT32_C(1812433253) 226 * (s->status[(i - 1) & 3] 227 ^ (s->status[(i - 1) & 3] >> 30)); 228 } 229 /* 230 * NB: the parameter set of this specification warrants 231 * that none of the possible 2^^32 seeds leads to an 232 * all-zero 127-bit internal state. Therefore, the 233 * period_certification() function of the original 234 * TinyMT32 source code has been safely removed. If 235 * another parameter set is used, this function will 236 * have to be re-introduced here. 237 */ 238 for (int i = 0; i < PRE_LOOP; i++) { 239 tinymt32_next_state(s); 241 } 242 } 244 /** 245 * This function outputs a 32-bit unsigned integer from 246 * the internal state. 247 * @param s pointer to tinymt internal state. 248 * @return 32-bit unsigned integer r (0 <= r < 2^32). 249 */ 250 uint32_t tinymt32_generate_uint32 (tinymt32_t* s) 251 { 252 tinymt32_next_state(s); 253 return tinymt32_temper(s); 254 } 256 /** 257 * Internal tinymt32 constants and functions. 258 * Users should not call these functions directly. 259 */ 260 const uint32_t TINYMT32_SH0 = 1; 261 const uint32_t TINYMT32_SH1 = 10; 262 const uint32_t TINYMT32_SH8 = 8; 263 const uint32_t TINYMT32_MASK = UINT32_C(0x7fffffff); 265 /** 266 * This function changes the internal state of tinymt32. 267 * @param s pointer to tinymt internal state. 268 */ 269 static void tinymt32_next_state (tinymt32_t* s) 270 { 271 uint32_t x; 272 uint32_t y; 274 y = s->status[3]; 275 x = (s->status[0] & TINYMT32_MASK) 276 ^ s->status[1] 277 ^ s->status[2]; 278 x ^= (x << TINYMT32_SH0); 279 y ^= (y >> TINYMT32_SH0) ^ x; 280 s->status[0] = s->status[1]; 281 s->status[1] = s->status[2]; 282 s->status[2] = x ^ (y << TINYMT32_SH1); 283 s->status[3] = y; 284 /* 285 * The if (y & 1) {...} block below replaces: 286 * s->status[1] ^= -((int32_t)(y & 1)) & s->mat1; 287 * s->status[2] ^= -((int32_t)(y & 1)) & s->mat2; 288 * The adopted code is equivalent to the original code 289 * but does not depend on the representation of negative 290 * integers by 2's complements. It is therefore more 291 * portable, but includes an if-branch which may slow 292 * down the generation speed. 293 */ 294 if (y & 1) { 295 s->status[1] ^= s->mat1; 296 s->status[2] ^= s->mat2; 297 } 298 } 300 /** 301 * This function outputs a 32-bit unsigned integer from 302 * the internal state. 303 * @param s pointer to tinymt internal state. 304 * @return 32-bit unsigned pseudo-random number. 305 */ 306 static uint32_t tinymt32_temper (tinymt32_t* s) 307 { 308 uint32_t t0, t1; 309 t0 = s->status[3]; 310 t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8); 311 t0 ^= t1; 312 t0 ^= -((int32_t)(t1 & 1)) & s->tmat; 313 return t0; 314 } 315 317 Figure 1: TinyMT32 Reference Implementation 319 3.2. TinyMT32 Usage 321 This PRNG MUST first be initialized with the following function: 323 void tinymt32_init (tinymt32_t * s, uint32_t seed); 325 It takes as input a 32-bit unsigned integer used as a seed (note that 326 value 0 is authorized by TinyMT32). This function also takes as 327 input a pointer to an instance of a tinymt32_t structure that needs 328 to be allocated by the caller but left uninitialized. This structure 329 will then updated by the various TinyMT32 functions in order to keep 330 the internal state of the PRNG. The use of this structure authorizes 331 several instances of this PRNG to be used in parallel, each of them 332 having its own instance of the structure. 334 Then, each time a new 32-bit pseudo-random unsigned integer between 0 335 and 2^32 - 1 inclusive is needed, the following function is used: 337 uint32_t tinymt32_generate_uint32 (tinymt32_t * s); 339 Of course, the tinymt32_t structure must be left unchanged by the 340 caller between successive calls to this function. 342 3.3. Specific Implementation Validation and Deterministic Behavior 344 PRNG determinism, for a given seed, can be a requirement (e.g., with 345 [RLC-ID]). Consequently, any implementation of the TinyMT32 PRNG in 346 line with this specification MUST comply with the following criteria. 347 Using a seed value of 1, the first 50 values returned by 348 tinymt32_generate_uint32(s) as 32-bit unsigned integers MUST be equal 349 to values provided in Figure 2. Note that these values come from the 350 tinymt/check32.out.txt file provided by the PRNG authors to validate 351 implementations of TinyMT32, as part of the MersenneTwister-Lab/ 352 TinyMT Github repository. 354 2545341989 981918433 3715302833 2387538352 3591001365 355 3820442102 2114400566 2196103051 2783359912 764534509 356 643179475 1822416315 881558334 4207026366 3690273640 357 3240535687 2921447122 3984931427 4092394160 44209675 358 2188315343 2908663843 1834519336 3774670961 3019990707 359 4065554902 1239765502 4035716197 3412127188 552822483 360 161364450 353727785 140085994 149132008 2547770827 361 4064042525 4078297538 2057335507 622384752 2041665899 362 2193913817 1080849512 33160901 662956935 642999063 363 3384709977 1723175122 3866752252 521822317 2292524454 365 Figure 2: First 50 decimal values returned by 366 tinymt32_generate_uint32(s) as 32-bit unsigned integers, with a seed 367 value of 1. 369 In particular, the deterministic behavior of the Figure 1 source code 370 has been checked across several platforms: high-end laptops running 371 64-bits Mac OSX and Linux/Ubuntu; a board featuring a 32-bits ARM 372 Cortex-A15 and running 32-bit Linux/Ubuntu; several embedded cards 373 featuring either an ARM Cortex-M0+, a Cortex-M3 or a Cortex-M4 32-bit 374 microcontroller, all of them running RIOT [Baccelli18]; two low-end 375 embedded cards featuring either a 16-bit microcontroller (TI MSP430) 376 or a 8-bit microcontroller (Arduino ATMEGA2560), both of them running 377 RIOT. 379 This specification only outputs 32-bit unsigned pseudo-random numbers 380 and does not try to map this output to a smaller integer range (e.g., 381 between 10 and 49 inclusive). If a specific use-case needs such a 382 mapping, it will have to provide its own function. In that case, if 383 PRNG determinism is also required, the use of floating point (single 384 or double precision) to perform this mapping should probably be 385 avoided, these calculations leading potentially to different rounding 386 errors across different target platforms. Great care should also be 387 put on not introducing biases in the randomness of the mapped output 388 (it may be the case with some mapping algorithms) incompatible with 389 the use-case requirements. The details of how to perform such a 390 mapping are out-of-scope of this document. 392 4. Security Considerations 394 The authors do not believe the present specification generates 395 specific security risks per se. 397 5. IANA Considerations 399 This document does not require any IANA action. 401 6. Acknowledgments 403 The authors would like to thank Belkacem Teibi with whom we explored 404 TinyMT32 specificities when looking to an alternative to the Park- 405 Miler Linear Congruential PRNG. The authors would like to thank 406 Stewart Bryant, Greg Skinner, the three TSVWG chairs, Wesley Eddy, 407 our shepherd, David Black and Gorry Fairhurst, as well as Spencer 408 Dawkins and Mirja Kuhlewind. Last but not least, the authors are 409 really grateful to the IESG members, in particular Benjamin Kaduk, 410 Eric Rescorla, and Adam Roach for their highly valuable feedbacks 411 that greatly contributed to improve this specification. 413 7. References 415 7.1. Normative References 417 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 418 Requirement Levels", BCP 14, RFC 2119, 419 DOI 10.17487/RFC2119, March 1997, 420 . 422 [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 423 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, 424 May 2017, . 426 7.2. Informative References 428 [Baccelli18] 429 Baccelli, E., Gundogan, C., Hahm, O., Kietzmann, P., 430 Lenders, M., Petersen, H., Schleiser, K., Schmidt, T., and 431 M. Wahlisch, "RIOT: An Open Source Operating System for 432 Low-End Embedded Devices in the IoT", IEEE Internet of 433 Things Journal (Volume 5, Issue 6), DOI: 434 10.1109/JIOT.2018.2815038, December 2018. 436 [KR12] Rikitake, K., "TinyMT Pseudo Random Number Generator for 437 Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12), 438 September 14, 2012, Copenhagen, Denmark, DOI: 439 http://dx.doi.org/10.1145/2364489.2364504, September 2012. 441 [RFC5170] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity 442 Check (LDPC) Staircase and Triangle Forward Error 443 Correction (FEC) Schemes", RFC 5170, DOI 10.17487/RFC5170, 444 June 2008, . 446 [RLC-ID] Roca, V. and B. Teibi, "Sliding Window Random Linear Code 447 (RLC) Forward Erasure Correction (FEC) Scheme for 448 FECFRAME", Work in Progress, Transport Area Working Group 449 (TSVWG) draft-ietf-tsvwg-rlc-fec-scheme (Work in 450 Progress), February 2019, . 453 Authors' Addresses 455 Mutsuo Saito 456 Hiroshima University 457 Japan 459 EMail: saito@math.sci.hiroshima-u.ac.jp 461 Makoto Matsumoto 462 Hiroshima University 463 Japan 465 EMail: m-mat@math.sci.hiroshima-u.ac.jp 467 Vincent Roca 468 INRIA 469 Univ. Grenoble Alpes 470 France 472 EMail: vincent.roca@inria.fr 473 Emmanuel Baccelli 474 INRIA 475 France 477 EMail: emmanuel.baccelli@inria.fr