1、BS ISO/IEC 18370-2:2016 Information technology Security techniques Blind digital signatures Part 2: Discrete logarithm based mechanisms BSI Standards Publication WB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS ISO/IEC 18370-2:2016 BRITISH STANDARD National foreword This British Standard i
2、s the UK implementation of ISO/IEC 18370-2:2016. The UK participation in its preparation was entrusted to Technical Committee IST/33/2, Cryptography and Security Mechanisms. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not p
3、urport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2016. Published by BSI Standards Limited 2016 ISBN 978 0 580 80110 5 ICS 35.040 Compliance with a British Standard cannot confer immunity from legal obli
4、gations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 July 2016. Amendments/corrigenda issued since publication Date T e x t a f f e c t e dBS ISO/IEC 18370-2:2016 Information technology Security techniques Blind digital signatures Part
5、 2: Discrete logarithm based mechanisms Technologie de linformation Techniques de scurit Signatures numriques en aveugle Partie 2: Mcanismes fonds sur le logarithme discret INTERNATIONAL STANDARD ISO/IEC 18370-2 Reference number ISO/IEC 18370-2:2016(E) First edition 2016-07-01 ISO/IEC 2016 BS ISO/IE
6、C 18370-2:2016ii ISO/IEC 2016 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO/IEC 2016, Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including
7、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 office Ch. de Blandonnet 8 CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +
8、41 22 749 01 11 Fax +41 22 749 09 47 copyrightiso.org www.iso.org ISO/IEC 18370-2:2016(E)BS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E)Foreword v Introduction vi 1 Scope . 1 2 Normative references 1 3 T erms and definitions . 1 4 Symbols 3 5 General requirements . 4 6 Blind signature mechanisms . 4
9、6.1 General . 4 6.2 Mechanism 1 . 4 6.2.1 Security parameters 4 6.2.2 Key generation process 5 6.2.3 Blind signature process 5 6.2.4 Verification process . 6 7 Blind signature mechanisms with partial disclosure 6 7.1 General . 6 7.2 Mechanism 2 . 6 7.2.1 Security parameters 6 7.2.2 Key generation pr
10、ocess 6 7.2.3 Blind signature process with partial disclosure . 7 7.2.4 Verification process . 8 7.3 Mechanism 3 . 8 7.3.1 Symbols 8 7.3.2 Key generation process 8 7.3.3 Blind signature process with partial disclosure . 9 7.3.4 Verification process . 9 8 Blind signature mechanisms with selective dis
11、closure 10 8.1 General 10 8.2 Mechanism 4 10 8.2.1 Security parameters .10 8.2.2 Key generation process .10 8.2.3 Blind signature process with selective disclosure .10 8.2.4 Presentation process .12 8.2.5 Verification process 12 9 Traceable blind signature mechanisms 13 9.1 General 13 9.2 Mechanism
12、5 13 9.2.1 Symbols .13 9.2.2 Key generation process .13 9.2.3 Traceable blind signature process .14 9.2.4 Verification process 16 9.2.5 Requestor tracing process 16 9.2.6 Signature tracing process 17 9.2.7 Requestor tracing evidence evaluation process 17 9.2.8 Signature tracing evidence evaluation p
13、rocess 17 Annex A (normative) Object identifiers .19 Annex B (normative) Conversion functions .20 Annex C (normative) Group description .21 Annex D (informative) Special hash-functions22 ISO/IEC 2016 All rights reserved iii Contents PageBS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E)Annex E (informat
14、ive) Security considerations and comparison of blind signature mechanisms 24 Annex F (informative) Numerical examples 26 Bibliography .78 iv ISO/IEC 2016 All rights reservedBS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E) Foreword ISO (the International Organization for Standardization) and IEC (the I
15、nternational 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 particula
16、r fields of technical activity. ISO and IEC technical committees collaborate in fields of mutual 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 establish
17、ed a joint technical 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 document should be noted. This d
18、ocument 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 and IEC shall not be held responsible for identifying a
19、ny or all such 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
20、users and does not constitute an endorsement. For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplem
21、entary information The committee responsible for this document is ISO/IEC JTC 1, Information technology, Subcommittee SC 27, IT Security techniques. ISO/IEC 18370 consists of the following parts, under the general title Information technology Security techniques Blind digital signatures: Part 1: Gen
22、eral Part 2: Discrete logarithm based mechanisms Further parts may follow. ISO/IEC 2016 All rights reserved vBS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E) Introduction Blind digital signature mechanisms are a special type of digital signature mechanism, as specified in ISO/IEC 9796 (all parts) and
23、ISO/IEC 14888, which allow a user (a requestor) to obtain a signature from a signer of the users choice, without giving the signer any information about the message that is signed or the resulting signature. In some mechanisms, the signer does not completely lose control over the signed message sinc
24、e the signer can include explicit information in the resulting signature under an agreement with the requestor. These types of blind signatures are called blind signatures with partial disclosure. Other mechanisms allow a requestor to receive a blind signature on a message not known to the signer bu
25、t the choice of the message is restricted and needs to conform to certain rules. Such mechanisms are called blind signature mechanisms with selective disclosure. Depending on the mechanism, it may be possible for an authorized entity to trace a signature to the requestor who requested it. Such an en
26、tity can either identify a signature that resulted from a given signature request (signature tracing), or link a signature to the receiver who requested it (requestor tracing). Blind signature mechanisms with tracing features are called traceable blind signature mechanisms. ISO/IEC 18370 specifies b
27、lind digital signature mechanisms, as well as three variants: blind digital signature mechanisms with partial disclosure, blind digital signature mechanisms with selective disclosure and traceable blind digital signature mechanisms. ISO/IEC 18370-1 specifies principles and requirements for these mec
28、hanisms. This part of ISO/IEC 18370 specifies several specific instances of these mechanisms. The security of blind digital signature mechanisms and their variants depends on computational problems believed to be intractable, i.e. problems for which, given current knowledge, finding a solution is co
29、mputationally infeasible, such as the integer factorization problem or the discrete logarithm problem in an appropriate group. The mechanisms specified in this part of ISO/IEC 18370 are based on the latter problem. ISO/IEC 18370 does not specify mechanisms for key management or for certification of
30、public keys. A variety of means are available for obtaining a reliable copy of the public verification key, e.g. a public key certificate. Techniques for managing keys and certificates are outside the scope of ISO/IEC 18370. For further information, see ISO/IEC 9594-8, ISO/IEC 11770-3 and ISO/IEC 15
31、945. This part of ISO/IEC 18370 specifies mechanisms that use a collision resistant hash-function to hash the message to be blindly signed. ISO/IEC 10118 specifies hash-functions. The generation of key pairs requires random bits and prime numbers. The generation of signatures requires random bits. T
32、echniques for producing random bits and prime numbers are outside the scope of ISO/IEC 18370. For further information, see ISO/IEC 18031 and ISO/IEC 18032.vi ISO/IEC 2016 All rights reservedBS ISO/IEC 18370-2:2016Information technology Security techniques Blind digital signatures Part 2: Discrete lo
33、garithm based mechanisms 1 Scope This part of ISO/IEC 18370 specifies blind digital signature mechanisms, together with mechanisms for three variants of blind digital signatures. The variants are blind digital signature mechanisms with partial disclosure, blind digital signature mechanisms with sele
34、ctive disclosure and traceable blind digital signature mechanisms. The security of all the mechanisms in this part of ISO/IEC 18370 is based on the discrete logarithm problem. For each mechanism, this part of ISO/IEC 18370 specifies the following: the process for generating the keys of the entities
35、involved in these mechanisms; the process for producing blind signatures; the process for verifying signatures. This part of ISO/IEC 18370 specifies another process specific to blind signature mechanisms with selective disclosure, namely, the following: the presentation process. Furthermore, this pa
36、rt of ISO/IEC 18370 specifies other processes specific to traceable blind signature mechanisms, namely, the following: a) the process for tracing requestors; b) the process for tracing signatures; c) the requestor tracing evidence evaluation process (optional); d) the signature tracing evidence eval
37、uation process (optional). 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced do
38、cument (including any amendments) applies. ISO/IEC 10118 (all parts), Information technology Security techniques Hash-functions 3 T erms a nd definiti ons For the purposes of this document, the terms and definitions given in ISO/IEC 18370-1 and the following apply. 3.1 abelian group group (G, *) suc
39、h that a * b = b * a for every a and b in G INTERNATIONAL ST ANDARD ISO/IEC 18370-2:2016(E) ISO/IEC 2016 All rights reserved 1BS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E) 3.2 cyclic group group G of n elements that contains an element a in G, called the generator, of order n SOURCE: ISO/IEC 14888-
40、3:2006, 3.2 3.3 e l l i p t i c c u r v e o v e r a f i n i t e f i e l d set E of points P = (x, y), where x and y are elements of the finite field (3.6), that satisfy a certain equation, together with an extra point referred to as the point at infinity Note 1 to entry: In this part of ISO/IEC 1837
41、0, only finite fields containing exactly q elements for a prime q 3 are considered. In this case, the equation that every point P = (x, y) of E (other than the point at infinity) should satisfy is of the form y 2= x 3+ ax + b. The finite field elements a and b should satisfy 4a 3+ 27b 2 0 F(where 0
42、Fis the additive identity element of the finite field). Note 2 to entry: The set of points E, together with an appropriately defined operation, forms a finite commutative group (3.5), where the point at infinity is the identity element. 3.4 f ie ld set of elements S and a pair of operations (+,*) de
43、fined on S, such that: i) a * (b + c) = a * b + a * c for every a, b and c in S, ii) S together with + forms an abelian group (3.1) (with identity element 0), and iii) S excluding 0 together with * forms an abelian group 3.5 f i n i t e c o m m u t a t i v e g r o u p abelian group (3.1) (G, *) with
44、 a finite number of elements Note 1 to entry: If a 0= e, and a n+1= a * a n(for n 0) is defined recursively, the order of a G is the least positive integer n, such that a n= e. Note 2 to entry: In some cases, such as when G is the set of points on an elliptic curve, arithmetic in the finite set G is
45、 described using additive notation. 3.6 f i n i t e f ie ld field (3.4) such that the underlying set of elements is finite Note 1 to entry: For any positive integer, m and a prime p, there exists a finite field containing exactly q = p melements. This field is unique up to an isomorphism and is deno
46、ted by F q . SOURCE: ISO/IEC 18033-2:2006, 3.21 3.7 group set of elements G and an operation * defined on the set of elements such that: i) (a * b) * c = a * (b * c) for every a, b and c in G, ii) there exists an identity element, e in G, such that a * e = e * a = a for every a in G, and iii) for ev
47、ery a in G, there exists an inverse element, a -1in G, such that a * a -1= a -1* a = e 3.8 security parameters variables that determine the security strength of a mechanism2 ISO/IEC 2016 All rights reservedBS ISO/IEC 18370-2:2016ISO/IEC 18370-2:2016(E) 4 Symbols a A indicates that element a is in se
48、t A a b concatenation of data items a and b in the order specified. In cases where the result of concatenating two or more data items is input to a cryptographic algorithm as part of one of the mechanisms specified in this part of ISO/IEC 18370, this result shall be composed so that it can be unique
49、ly resolved into its constituent data strings, i.e. so that there is no possibility of ambiguity in interpretation. This latter property could be achieved in a vari- ety of different ways, depending on the application. For example, it could be guaranteed by a) fixing the length of each of the substrings throughout the domain of use of the mecha- nism, or b) encoding the sequence of concatenated strings using a method that guarantees unique decoding, e.g. us
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