ANSI INCITS ISO IEC 18032-2005 Information technology Security techniques Prime number generation.pdf
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1、INCITS/ISO/IEC 18032-2005 (ISO/IEC 18032:2005, IDT) Information technology Security techniques Prime numbergenerationIINCITS/ISO/IEC 18032-2005 (ISO/IEC 18032:2005, IDT)INCITS/ISO/IEC 18032-2005ii ITIC 2005 All rights reserved PDF disclaimer This PDF file may contain embedded typefaces. In accordanc
2、e with Adobes licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobes licens
3、ing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing.
4、 Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. Adopted by INCITS (InterNational Committee for Information Technology Standards
5、) as an American National Standard. Date of ANSI Approval: 8/29/2005 Published by American National Standards Institute, 25 West 43rd Street, New York, New York 10036 Copyright 2005 by Information Technology Industry Council (ITI). All rights reserved. These materials are subject to copyright claims
6、 of International Standardization Organization (ISO), International Electrotechnical Commission (IEC), American National Standards Institute (ANSI), and Information Technology Industry Council (ITI). Not for resale. No part of this publication may be reproduced in any form, including an electronic r
7、etrieval system, without the prior written permission of ITI. All requests pertaining to this standard should be submitted to ITI, 1250 Eye Street NW, Washington, DC 20005. Printed in the United States of America INCITS/ISO/IEC 18032-2005 ITIC 2005 All rights reserved iii Contents Page Foreword . iv
8、 1 Scope . 1 2 Normative references 1 3 Terms and definitions . 2 4 Symbols . 2 5 Trial division 3 6 Probabilistic primality tests 4 6.1 Miller-Rabin primality test . 4 6.2 Frobenius-Grantham primality test. 5 6.3 Lehmann primality test . 5 7 Deterministic primality verification methods . 6 7.1 Elli
9、ptic curve primality certificate . 6 7.2 Primality certificate based on Maurers algorithm . 7 8 Prime number generation . 8 8.1 Requirements 8 8.2 Using probabilistic tests . 9 8.3 Using deterministic methods 10 9 Candidate prime testing 11 Annex A (informative) Error probabilities 13 Annex B (infor
10、mative) Generating primes with side conditions . 16 Bibliography . 18 INCITS/ISO/IEC 18032-2005 iv ITIC 2005 All rights reserved Foreword ISO (the International Organization for Standardization) and IEC (the International Electrotechnical Commission) form the specialized system for worldwide standar
11、dization. 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 technical activity. ISO and IEC technical committees collaborate in fields of m
12、utual interest. Other international organizations, governmental and non-governmental, in liaison with ISO and IEC, also take part in the work. In the field of information technology, ISO and IEC have established a joint technical committee, ISO/IEC JTC 1. International Standards are drafted in accor
13、dance with the rules given in the ISO/IEC Directives, Part 2. The main task of the joint technical committee is to prepare International Standards. Draft International Standards adopted by the joint technical committee are circulated to national bodies for voting. Publication as an International Sta
14、ndard requires approval by at least 75 % of the national bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO and IEC shall not be held responsible for identifying any or all such patent rights. ISO/IEC 18032
15、 was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology, Subcommittee SC 27, IT Security techniques. AMERICAN NATIONAL STANDARD INCITS/ISO/IEC 18032-2005 ITIC 2005 All rights reserved 1 Information technology Security techniques Prime number generation 1 Scope This Internati
16、onal Standard specifies methods for generating and testing prime numbers as required in cryptographic protocols and algorithms. Firstly, this International Standard specifies methods for testing whether a given number is prime. The testing methods included in this International Standard can be divid
17、ed into two groups: Probabilistic primality tests, which have a small error probability. All probabilistic tests described here may declare a composite to be a prime. One test described here may declare a prime to be composite. Deterministic methods, which are guaranteed to give the right verdict. T
18、hese methods use so-called primality certificates. Secondly, this International Standard specifies methods to generate prime numbers. Again, both probabilistic and deterministic methods are presented. NOTE Readers with a background in algorithm theory may have had previous encounters with probabilis
19、tic and deterministic algorithms. We stress that the deterministic methods in this International Standard internally still make use of random bits, and “deterministic” only refers to the fact that the output is correct with probability one. Annex B describes variants of the methods for generating pr
20、imes so that particular cryptographic requirements can be met. The methods for generating, proving and verifying primality defined by this International Standard are applicable to cryptographic systems based on the properties of the primes. NOTE The specifications of the tests given in this Internat
21、ional Standard define the properties to be tested in the simplest possible form. Following these specifications directly will not necessarily produce the most efficient implementations. This is especially the case for the Frobenius-Grantham test. 2 Normative references The following referenced docum
22、ents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO/IEC 9796-2:2002, Information technology Security techniques Digital signatu
23、re schemes giving message recovery Part 2: Integer factorization based mechanisms ISO/IEC 15946-1:2002, Information technology Security techniques Cryptographic techniques based on elliptic curves Part 1: General INCITS/ISO/IEC 18032-2005 2 ITIC 2005 All rights reserved 3 Terms and definitions For t
24、he purposes of this document, the following terms and definitions apply. 3.1 composite number composite Integer N 1 is composite if it is not prime, i.e. there exist divisors of N that are not trivial divisors. 3.2 entropy Total amount of information yielded by a set of bits. It is representative of
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