ISO IEC 9796-3-2006 Information technology - Security techniques - Digital signature schemes giving message recovery - Part 3 Discrete logarithm based mechanism.pdf

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1、 Reference number ISO/IEC 9796-3:2006(E) ISO/IEC 2006INTERNATIONAL STANDARD ISO/IEC 9796-3 Second edition 2006-09-15 Corrected version 2013-09-15 Information technology Security techniques Digital signature schemes giving message recovery Part 3: Discrete logarithm based mechanisms Technologies de l

2、information Techniques des scurit Schmas de signature numrique rtablissant le message Partie 3: Mcanismes bass sur les logarithmes discrets ISO/IEC 9796-3:2006(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or view

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5、or 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. ISO/IEC 2006 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any m

6、eans, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail cop

7、yrightiso.org Web www.iso.org Published in Switzerland ii ISO/IEC 2006 All rights reservedISO/IEC 9796-3:2006(E) ISO/IEC 2006 All rights reserved iiiContents Foreword v Introduction . vi 1 Scope . 1 2 Normative references . 1 3 Terms and definitions 1 4 Symbols, notation and conventions . 4 4.1 Symb

8、ols and notation 4 4.2 Conversion functions and mask generation functions 6 4.3 Legend for figures 6 5 Binding between signature mechanisms and hash-functions 7 6 Framework for digital signatures giving message recovery . 7 6.1 Processes 7 6.2 Parameter generation process 8 6.3 Signature generation

9、process . 8 6.4 Signature verification process 9 7 General model for digital signatures giving message recovery . 9 7.1 Requirements 9 7.2 Summary of functions and procedures . 10 7.3 User key generation process 11 7.4 Signature generation process . 11 7.5 Signature verification process 14 8 NR (Nyb

10、erg-Rueppel message recovery signature) . 17 8.1 Domain parameter and user keys . 17 8.2 Signature generation process . 17 8.3 Signature verification process 18 9 ECNR (Elliptic Curve Nyberg-Rueppel message recovery signature) 19 9.1 Domain parameter and user keys . 19 9.2 Signature generation proce

11、ss . 19 9.3 Signature verification process 20 10 ECMR (Elliptic Curve Miyaji message recovery signature) 21 10.1 Domain parameter and user keys . 21 10.2 Signature generation process . 22 10.3 Signature verification process 23 11 ECAO (Elliptic Curve Abe-Okamoto message recovery signature) 23 11.1 D

12、omain parameter 23 11.2 User keys . 24 11.3 Signature generation process . 24 11.4 Signature verification process 26 12 ECPV (Elliptic Curve Pintsov-Vanstone message recovery signature) 27 12.1 Domain and user parameters 27 12.2 Signature generation process . 28 12.3 Signature verification process 2

13、9 13 ECKNR (Elliptic Curve KCDSA/Nyberg-Rueppel message recovery signature) 31 13.1 Domain parameter and user keys . 31 13.2 Signature generation process . 31 13.3 Signature verification process 32 ISO/IEC 9796-3:2006(E) iv ISO/IEC 2006 All rights reservedAnnex A (informative) Mathematical conventio

14、ns . 34 A.1 Bit strings . 34 A.2 Octet strings . 34 A.3 Finite fields . 34 A.4 Elliptic curves . 35 Annex B (normative) Conversion functions . 36 B.1 Octet string / bit string conversion: OS2BSP and BS2OSP 36 B.2 Bit string / integer conversion: BS2IP and I2BSP 36 B.3 Octet string / integer conversi

15、on: OS2IP and I2OSP . 36 B.4 Finite field element / integer conversion: FE2IP F. 36 B.5 Octet string / finite field element conversion: OS2FEP Fand FE2OSP F. 37 B.6 Elliptic curve / octet string conversion: EC2OSP Eand OS2ECP E37 Annex C (normative) Mask generation functions (Key derivation function

16、s) . 39 C.1 Allowable mask generation functions . 39 C.2 MGF1 . 39 C.3 MGF2 . 39 Annex D (informative) Example method for producing the data input 40 D.1 Splitting the message and producing the data input . 40 D.2 Checking the redundancy . 40 Annex E (normative) ASN.1 module 42 E.1 Formal definition

17、 42 E.2 Use of subsequent object identifiers . 43 Annex F (informative) Numerical examples 44 F.1 Numerical examples for NR 44 F.2 Numerical examples for ECNR . 47 F.3 Numerical examples for ECMR . 51 F.4 Numerical examples for ECAO . 54 F.5 Numerical examples for ECPV . 59 F.6 Numerical examples fo

18、r ECKNR 62 Annex G (informative) Summary of properties of mechanisms . 66 Annex H (informative) Correspondence of schemes . 68 Bibliography 69 ISO/IEC 9796-3:2006(E) ISO/IEC 2006 All rights reserved vForeword ISO (the International Organization for Standardization) and IEC (the International Electro

19、technical 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 technica

20、l 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 established a joint technical

21、 committee, ISO/IEC JTC 1. International Standards are drafted in accordance 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 circul

22、ated to national bodies for voting. Publication as an International Standard requires approval by at least 75 % of the national bodies casting a vote. ISO/IEC 9796-3 was prepared by Joint Technical Committee ISO/IEC /JTC 1, Information technology, Subcommittee SC 27, IT Security techniques. This sec

23、ond edition cancels and replaces the first edition (ISO/IEC 9796-3:2000), which has been technically revised. New mechanisms and object identifiers have been specified. ISO/IEC 9796 consists of the following parts, under the general title Information technology Security techniques Digital signature

24、schemes giving message recovery: Part 2: Integer factorization based mechanisms Part 3: Discrete logarithm based mechanisms This corrected version of ISO/IEC 9796-3:2006 incorporates the following corrections: The year of publication has been removed from references to ISO/IEC 15946-1. The last para

25、graph of 6.2.1 has been modified and ISO/IEC 15946-5 has been added to Clause 2. ISO/IEC 9796-3:2006(E) vi ISO/IEC 2006 All rights reservedIntroduction Digital signature mechanisms can be used to provide services such as entity authentication, data origin authentication, non-repudiation, and integri

26、ty of data. A digital signature mechanism satisfies the following requirements: given only the public verification key and not the private signature key, it is computationally infeasible to produce a valid signature for any given message; the signatures produced by a signer can neither be used for p

27、roducing a valid signature for any new message nor for recovering the signature key; it is computationally infeasible, even for the signer, to find two different messages with the same signature. Most digital signature mechanisms are based on asymmetric cryptographic techniques and involve three bas

28、ic operations: a process for generating pairs of keys, where each pair consists of a private signature key and the corresponding public verification key; a process using the private signature key, called the signature generation process; a process using the public verification key, called the signat

29、ure verification process. There are two types of digital signature mechanisms: when, for each given private signature key, the signatures produced for the same message are the same, the mechanism is said to be non-randomized (or deterministic) see ISO/IEC 14888-1; when, for a given message and a giv

30、en private signature key, each application of the signature process produces a different signature, the mechanism is said to be randomized. This part of ISO/IEC 9796 specifies randomized mechanisms. Digital signature schemes can also be divided into the following two categories: when the whole messa

31、ge has to be stored and/or transmitted along with the signature, the mechanism is named a signature mechanism with appendix see ISO/IEC 14888; when the whole message or a part of it is recovered from the signature, the mechanism is named a signature mechanism giving message recovery. If the message

32、is short enough, then the entire message can be included in the signature, and recovered from the signature in the signature verification process. Otherwise, a part of the message can be included in the signature and the rest of it is stored and/or transmitted along with the signature. The mechanism

33、s specified in ISO/IEC 9796 give either total or partial recovery, aiming at reducing storage and transmission overhead. This part of ISO/IEC 9796 includes six mechanisms, one of which was in ISO/IEC 9796-3:2000 and five of which are in ISO/IEC 15946-4:2004. The mechanisms specified in this part of

34、ISO/IEC 9796 use a hash- function to hash the entire message. ISO/IEC 10118 specifies hash-functions. Some of the mechanisms specified in this part of ISO/IEC 9796 use a group on an elliptic curve over finite field. ISO/IEC 15946-1 describes the mathematical background and general techniques necessa

35、ry for implementing cryptosystems based on elliptic curves defined over finite fields. ISO/IEC 9796-3:2006(E) ISO/IEC 2006 All rights reserved viiThe International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC) draw attention to the fact that it is claimed

36、 that compliance with this document may involve the use of patents concerning the mechanisms NR, ECMR and ECAO given in Clause 8, 10 and 11, respectively. Area Patent no. Issue date Inventors NR see Clause 8 US 5 600 725, EP 0 639 907 1997-02-04 K. Nyberg and R. A. Rueppel ECMR see Clause 10 JP H09-

37、160492 (patent application) A. Miyaji ECAO see Clause 11 JP 3 434 251 2003-08-04 M. Abe and T. Okamoto ISO and IEC take no position concerning the evidence, validity and scope of these patent rights. The holders of these patent rights have assured the ISO and IEC that they are willing to negotiate l

38、icences under reasonable and non-discriminatory terms and conditions with applicants throughout the world. In this respect, the statement of the holders of these patent rights are registered with ISO and IEC. Information may be obtained from the following companies. Patent no. Name of holder of pate

39、nt right Contact address US 5 600 725, EP 0 639 907 Certicom Corp. 5520 Explorer Drive, 4th Floor, Mississauga, Ontario, Canada L4W 5L1 JP H09-160492 Matsushita Electric Industrial Co., Ltd. Matsushita IMP Building 19 thFloor, 1-3-7, Siromi, Chuo-ku, Osaka 540-6319, Japan JP 3 434 251 NTT Intellectu

40、al Property Center 9-11 Midori-Cho 3-chome, Musashino-shi, Tokyo 180-8585, Japan Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights other than those identified above. ISO and IEC shall not be held responsible for identifying any or al

41、l such patent rights. NOTE 1 Computational feasibility depends on the specific security requirements and environment. NOTE 2 Any signature mechanism giving message recovery for example, the mechanisms specified in this part of ISO/IEC 9796 can be converted for provision of digital signatures with ap

42、pendix. In this case, the signature is produced by application of the signature mechanism to a hash-token of the message. INTERNATIONAL STANDARD ISO/IEC 9796-3:2006(E) ISO/IEC 2006 All rights reserved 1Information technology Security techniques Digital signature schemes giving message recovery Part

43、3: Discrete logarithm based mechanisms 1 Scope This part of ISO/IEC 9796 specifies six digital signature schemes giving message recovery. The security of these schemes is based on the difficulty of the discrete logarithm problem, which is defined on a finite field or an elliptic curve over a finite

44、field. This part of ISO/IEC 9796 also defines an optional control field in the hash-token, which can provide added security to the signature. This part of ISO/IEC 9796 specifies randomized mechanisms. The mechanisms specified in this part of ISO/IEC 9796 give either total or partial message recovery

45、. NOTE For discrete logarithm based digital signature schemes with appendix, see ISO/IEC 14888-3. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest

46、 edition of the referenced document (including any amendments) applies. ISO/IEC 10118 (all parts), Information technology Security techniques Hash-functions ISO/IEC 15946-1, Information technology Security techniques Cryptographic techniques based on elliptic curves Part 1: General ISO/IEC 15946-5,

47、Information technology Security techniques Cryptographic techniques based on elliptic curves Part 5: Elliptic curve generation 3 Terms and definitions For the purposes of this document, the following terms and definitions apply. 3.1 data input octet string which depends on the entire message or a po

48、rtion of the message and which forms a part of the input to the signature generation process 3.2 domain parameter data item which is common to and known by or accessible to all entities within the domain ISO/IEC 14888-1:1998 ISO/IEC 9796-3:2006(E) 2 ISO/IEC 2006 All rights reservedNOTE The set of do

49、main parameters may contain data items such as hash-function identifier, length of the hash- token, maximum length of the recoverable part of the message, finite field parameters, elliptic curve parameters, or other parameters specifying the security policy in the domain. 3.3 elliptic curve set of points P = (x, y), where x and y are elements of an explicitly given finite field, that satisfy a cubic equation without any singular point, together with the “point at in