1、Information technology Security techniques Random bit generation AMENDMENT 1: Deterministic random bit generation Technologies de linformation Techniques de scurit Gnration de bits alatoires AMENDEMENT 1: Gnration dterministe de bits alatoires INTERNATIONAL STANDARD ISO/IEC 18031 Second edition 2011
2、-11-15 Reference number ISO/IEC 18031:2011/Amd.1:2017(E) AMENDMENT 1 2017-02 ISO/IEC 2017 ii ISO/IEC 2017 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO/IEC 2017, Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized
3、 otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright o
4、ffice Ch. de Blandonnet 8 CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 copyrightiso.org www.iso.org ISO/IEC 18031:2011/Amd.1:2017(E) ISO/IEC 18031:2011/Amd.1:2017(E) Foreword ISO (the International Organization for Standardization) and IEC (the International
5、 Electrotechnical Commission) form the specialized system for worldwide standardization. National bodies that are members of ISO or IEC participate in the development of International Standards through technical committees established by the respective organization to deal with particular fields of
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7、echnical committee, ISO/IEC JTC 1. The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document
8、 was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives). Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all su
9、ch patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www .iso .org/ patents). Any trade name used in this document is information given for the convenience of users and
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11、Trade (TBT) see the following URL: w w w . i s o .org/ iso/ foreword .html. Amendment 1 to ISO/IEC 18031-1:2011 was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology, Subcommittee SC 27, IT Security techniques. ISO/IEC 2017 All rights reserved iii Information technology Sec
12、urity techniques Random bit generation AMENDMENT 1: Deterministic random bit generation Page 141 Add a new Annex K. Annex K (informative) Example cases for MQ_DRBG K.1 General Annex K and its supporting files provides example cases for 14 settings listed in ISO/IEC 18031:2011, Table C.5. The support
13、ing files are available at the following URL: h t t p :/ standards .iso .org/ iso/ 18031/ In each of the 14 settings described in Annex K, the bitstring P provides a randomly selected system of multivariate quadratic equations that complies with the selection rules of C.5.2.5. The rank distribution
14、resulting from the verification of rank conditions is detailed for each setting. P is given in the format described in C.5.2.4 which is recalled below. Each example case also includes a sequence of consecutive input-output pairs for the Evaluate_MQ() function. K.1.1 Format for representing field ele
15、ments Each system coefficient is an element of the binary field GF(2 field_size ) and is a univariate polynomial over GF(2) modulo the irreducible polynomial given in Table C.6. A field element is handled as a bitstring of field_size bits composed of its GF(2) coefficients ordered by decreasing degr
16、ee. For example, the polynomial x 3+ x + 1 in GF(2 4 ) is represented as the bitstring 1011. K.1.2 Format for representing a single multivariate quadratic equation The quadratic system used in MQ_DRBG operates on n = state_length / field_size variables and contains n + m equations where m = block_le
17、ngth / field_size. A quadratic equation is written as the concatenation of its coefficients in lexicographic order and by decreasing degree. Therefore the coefficient of the monomial x 1 x 1appears first, followed by that of x 1 x 2and so forth, up to the coefficient of x 1 x n . The coefficient of
18、the monomial x 2 x 2appears next, followed by that of x 2 x 3and so forth, until the last quadratic coefficient x n-1 x nis reached. Then linear coefficients appear, starting with the coefficient of the monomial x 1and ending with that of x n . When field_size = 1, the linear coefficients are omitte
19、d since the underlying field is GF(2) and x i x i= x i . The string ends with the constant coefficient of the quadratic equation. K.1.3 Format for representing a complete system of quadratic equations The quadratic system encoded into the bitstring P contains its n + m quadratic equations concatenat
20、ed in sequential order, starting with the coefficients of the first equation and ending with those of the (n+m)-th equation. P is formed by the resulting bit string of length system_length. K.1.4 Format for representing inputs and outputs ISO/IEC 18031:2011/Amd.1:2017(E) ISO 2017 All rights reserved
21、 1 ISO/IEC 18031:2011/Amd.1:2017(E) The input x to Evaluate_MQ(P, x) is a vector of n field elements and is given as a bitstring formed by concatenating their bitstring representations, starting with x 1and ending with x n . Similarly, the output y | z is a vector of n + m field elements represented
22、 in the same format. K.1.5 Summary of example cases Table K.1 summarizes the 14 example cases. Table K.1 Summary of example cases requested_strength block_length 112 128 192 256 80 K.2 Binary field GF(2) n = 112 m = 112 min_weight = 4 min_rank 106 K.4 Binary field GF(2 4 ) n = 32 m = 32 min_weight =
23、 5 min_rank 30 K.7 Binary field GF(2 6 ) n = 32 m = 32 min_weight = 5 min_rank 30 K.11 Binary field GF(2 8 ) n = 32 m = 32 min_weight = 5 min_rank 30 112 K.3 Binary field GF(2) n = 120 m = 112 min_weight = 4 min_rank 114 K.5 Binary field GF(2) n = 128 m = 128 min_weight = 4 min_rank 122 K.8 Binary f
24、ield GF(2 4 ) n = 48 m = 48 min_weight = 5 min_rank 44 K.12 Binary field GF(2 4 ) n = 64 m = 64 min_weight = 5 min_rank 60 128 K.6 Same as K.5 K.9 Binary field GF(2 3 ) n = 64 m = 64 min_weight = 5 min_rank 60 K.13 Same as K.12 192 K.10 Binary field GF(2) n = 200 m = 192 min_weight = 4 min_rank 192
25、K.14 Binary field GF(2 2 ) n = 128 m = 128 min_weight = 5 min_rank 124 256 K.15 Binary field GF(2) n = 272 m = 256 min_weight = 4 min_rank 264 K.2 Example case for requested_strength = 80 and block_length = 1122 ISO 2017 All rights reserved ISO/IEC 18031:2011/Amd.1:2017(E) K.2.1 System of multivaria
26、te quadratic equations The bitstring P containing the system coefficients is provided in digital form in the file “coefficients-BL- 112-Sec-80-F2.bin” in accordance with the format described in K.1.3. The file contains 177212 bytes and its SHA-1 checksum in hexadecimal form is 95d78546df132777af9328
27、86a887da96aa9afa46 The ranks are distributed as follows: 106: 4561 108: 2213145 110: 58156950 112: 43613144 Sum: 103987800 K.2.2 Inputs and outputs The bitstrings x, y and z are provided in digital form in accordance with the format described in K.1.4. Their hexadecimal values are: x = 0000000000000
28、000000000000001 y = bb8cf180cbc3a6002c19c770ed0d z = 7847b864cfadf70fb359203e06d8 x = bb8cf180cbc3a6002c19c770ed0d y = a1e0811b5b7733113ca8e22dd2b1 z = 57d27f7b0fc67aec0d5e8115cd93 x = a1e0811b5b7733113ca8e22dd2b1 y = 634ae5294dbc4cc79ce11cfeb1d7 z = c42c5cc5b5b61396df3fcf7a4e2b x = 634ae5294dbc4cc7
29、9ce11cfeb1d7 y = 36701faea23130a0407a44f5e420 z = bf3ddd3cbb141fcd96cbba66ebb9 x = 36701faea23130a0407a44f5e420 y = 74b5baa1095f61eb6b15d317d5ed ISO 2017 All rights reserved 3 ISO/IEC 18031:2011/Amd.1:2017(E) z = 7f4ad5787a0c5451bddcf2aef533 x = 74b5baa1095f61eb6b15d317d5ed y = 62804addbe9da290c38e9
30、de0fe71 z = 5f1f209b62cce21f75d9d03607a9 x = 62804addbe9da290c38e9de0fe71 y = 7d0892da52eed7facc377af1918f z = 69d5bef53c03fa33a0273cf44c21 x = 7d0892da52eed7facc377af1918f y = 8ee43a16842345d4cd182852cdea z = ed479a677e6c2a3cffbbada0e765 x = 8ee43a16842345d4cd182852cdea y = 2eb8cc9185445b2bab3f4b50
31、4aaf z = 9407f0fe9393fa335051ac2bf414 x = 2eb8cc9185445b2bab3f4b504aaf y = 8deb10cb70bc3818209a576fb5cb z = 6106cb8aa8e9a7de949a506b2278 K.3 Example case for requested_strength = 112 and block_length = 112 K.3.1 System of multivariate quadratic equations The bitstring P containing the system coeffic
32、ients is provided in digital form in the file “coefficients-BL- 112-Sec-112-F2.bin” in accordance with the format described in K.1.3. The file contains 210569 bytes and its SHA-1 checksum in hexadecimal form is ae1c4ea33afc96e3aa421f6456055a7c7ee33989 The ranks are distributed as follows: 114: 5239
33、116: 2551294 118: 66936700 120: 502002654 ISO 2017 All rights reserved ISO/IEC 18031:2011/Amd.1:2017(E) Sum: 119693498 K.3.2 Inputs and outputs The bitstrings x, y and z are provided in digital form in accordance with the format described in K.1.4. Their hexadecimal values are: x = 00000000000000000
34、0000000000001 y = 46609cda28057a917a08b60a1d969d z = a06fe3e456a8c24315dfde6088bd x = 46609cda28057a917a08b60a1d969d y = 37d12de7b69f2170ba8717e96f0f43 z = 8fb9899c9e2d4ef33056aadf946d x = 37d12de7b69f2170ba8717e96f0f43 y = 463860297cec60797650c4897563d4 z = 89745528548d7bd3a2c9e5afd3fc x = 46386029
35、7cec60797650c4897563d4 y = 6a4c5b16c156738e9b07c4c2c2818e z = 5f9f14194e601f48657164f34e34 x = 6a4c5b16c156738e9b07c4c2c2818e y = 289c50a28bb48a685703eb425597dd z = c9dae7a3c32a01648a32d91b8728 x = 289c50a28bb48a685703eb425597dd y = 4d96224af4aeaac54d8472374f645d z = cf7a6cc73793049241497ee26603 x =
36、 4d96224af4aeaac54d8472374f645d y = df5ac81223125d967056d5dcdba088 z = 3d9741ec702076fe8473b7181aa9 x = df5ac81223125d967056d5dcdba088 ISO 2017 All rights reserved 5 ISO/IEC 18031:2011/Amd.1:2017(E) y = 41a1df8cc57c402f520d671464b728 z = 285d6b741e417e417b9f8fa87356 x = 41a1df8cc57c402f520d671464b72
37、8 y = 0af3539a48bc07e3afb00d3c529ff5 z = e6d4d36dcc2cca4826b94e76be10 x = 0af3539a48bc07e3afb00d3c529ff5 y = e2f7d8f01d2ae145a643b9351ada76 z = 29bdd54840cf84027f20e48ce195 K.4 Example case for requested_strength = 80 and block_length = 128 K.4.1 System of multivariate quadratic equations The bitstr
38、ing P containing the system coefficients is provided in digital form in the file “coefficients-BL- 128-Sec-80-F16.bin” in accordance with the format described in K.1.3. The file contains 17952 bytes and its SHA-1 checksum in hexadecimal form is d6614e19bd953ca88ff49f016b80f5ac17b7dab1 The ranks are
39、distributed as follows: 30: 520948 32: 7782684 Sum: 8303632 K.4.2 Inputs and outputs The bitstrings x, y and z are provided in digital form in accordance with the format described in K.1.4. Their hexadecimal values are: x = 00000000000000000000000000000001 y = f719e81ed992ca7c793258b5251d0534 z = 66
40、092272f74a85ecaef639d78ed9831f x = f719e81ed992ca7c793258b5251d0534 y = 37614b89b9bbd6eea4560ecb3bdb8807 z = 96b4c1aeb27aa47fbc7a3b14643437366 ISO 2017 All rights reserved ISO/IEC 18031:2011/Amd.1:2017(E) x = 37614b89b9bbd6eea4560ecb3bdb8807 y = 136bf7d8fbcbabd37a2baa321a5d94f7 z = 29141359d8099496e
41、af84ae3d863591a x = 136bf7d8fbcbabd37a2baa321a5d94f7 y = bc6316205ac244b4fc8dcee70f423874 z = d8005ccefa012118820cf02c9eb4328d x = bc6316205ac244b4fc8dcee70f423874 y = 64d8adbf03a6418fa549f235e5f84bcd z = 9c0aad312ef00336d0f055e81f2b3677 x = 64d8adbf03a6418fa549f235e5f84bcd y = 3ac1c733b68ca73455034
42、3d950649d5a z = 1f07210c4a6d4fd784ee0f9f9789c5ab x = 3ac1c733b68ca734550343d950649d5a y = 1a22cbbe771e641373700306718dbf6e z = ba8064102a7e8d714e92e0dfddfbe607 x = 1a22cbbe771e641373700306718dbf6e y = fa2eabf2c9794f6b9bac6561409aab0d z = 7e2bae34daaf284557bbe5ae48e54d26 x = fa2eabf2c9794f6b9bac65614
43、09aab0d y = 46f6f74d23504a64565b2c35cd0036df z = c6285e77cbf16150457d03bfc6015ef7 x = 46f6f74d23504a64565b2c35cd0036df y = 729bc30c32fd7fec1ccb95bc4aabfa27 z = 963bda8ab7dc84ee2dd5a60a9c4392cd K.5 Example case for requested_strength = 112 and block_length = 128 ISO 2017 All rights reserved 7 ISO/IEC
44、 18031:2011/Amd.1:2017(E) K.5.1 System of multivariate quadratic equations The bitstring P containing the system coefficients is provided in digital form in the file “coefficients-BL- 128-Sec-112-F2.bin” in accordance with the format described in K.1.3. The file contains 264224 bytes and its SHA-1 c
45、hecksum in hexadecimal form is fcd983e78ddd489a9425be58b8139e04c89fb6c6 The ranks are distributed as follows: 122: 7704 124: 3783524 126: 99303857 128: 74493971 Sum: 177589056 K.5.2 Inputs and outputs The bitstrings x, y and z are provided in digital form in accordance with the format described in K
46、.1.4. Their hexadecimal values are: x = 00000000000000000000000000000001 y = c04f664eb59219b1e6b0d0e0fc5ae660 z = 894f5e21cc208ce73ebb136c0c7b6e47 x = c04f664eb59219b1e6b0d0e0fc5ae660 y = 10da311bd87ba42fd89a17f45b0b0931 z = f3561e3a42a23037d04b7991e44f98d0 x = 10da311bd87ba42fd89a17f45b0b0931 y = c
47、42c14916632d8518f435796c069a381 z = 461593a9b73573772cf8f8a93020eada x = c42c14916632d8518f435796c069a381 y = 325ebb605c4037b6092a7952adedd16d z = 3f80f69b2f81f012994189125cba6b00 x = 325ebb605c4037b6092a7952adedd16d y = 596cdd4392413988fa7a15fa7fb5d74b8 ISO 2017 All rights reserved ISO/IEC 18031:20
48、11/Amd.1:2017(E) z = 8ec0f223da49f826f6faf8d25b54b231 x = 596cdd4392413988fa7a15fa7fb5d74b y = 17790ac47b8112312631c0e3b0066fd0 z = 8d98258ade35f74057a98542c0d7d937 x = 17790ac47b8112312631c0e3b0066fd0 y = d76a00f9e3318091e0f113b48f0cb752 z = 8b9664e30122848541b91743171b4812 x = d76a00f9e3318091e0f1
49、13b48f0cb752 y = 4ffffdf6def93bb391d90312a801ece5 z = d17acb75d2f57976df164061716601e0 x = 4ffffdf6def93bb391d90312a801ece5 y = 89b596d08123105f5994679f5e428136 z = 1de72c77e98fa45090197c81e4d2a3a3 x = 89b596d08123105f5994679f5e428136 y = 7294da76d6d2bf9dfb9d2c1d03ca4928 z = 96cea7ffad3bc8be151106cd4c067565 K.6 Example case for requested_strength = 128 and block_length = 128 The example case is the same as in K.5. K.7 Example case for requested_strength = 80 a
