1、INCITS/ISO/IEC 18033-2:20062008 (/ISO/IEC 18033-2:2006, IDT) Information technology Security techniques Encryption algorithms Part 2: Asymmetric ciphersINCITS/ISO/IEC 18033-2:20062008 (ISO/IEC 18033-2:2006, IDT)ITS/ISO/IEC 18033-2:20062008 ii ITIC 2008 All rights reserved PDF disclaimer This PDF fil
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4、eation parameters were optimized for printing. 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
5、Committee for Information Technology Standards) as an American National Standard. Date of ANSI Approval: 7/1/2008 Published by American National Standards Institute, 25 West 43rd Street, New York, New York 10036 Copyright 2008 by Information Technology Industry Council (ITI). All rights reserved. Th
6、ese materials are subject to copyright claims 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 repr
7、oduced in any form, including an electronic retrieval 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 iiiContentsPage1 Scope . . . . . . . . . .
8、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Deflnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Symbols and notation . . . . . . .
9、. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Mathematical conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.1 Functions and algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2 Bit strings and octet strings . . . . . . . . . . . . .
10、 . . . . . . . . . . . . . . . . 95.3 Finite Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.4 Elliptic curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.1 Cryptograp
11、hic hash functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.2 Key derivation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.3 MAC algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.4 Block ciphers . . . . . . . . . . .
12、 . . . . . . . . . . . . . . . . . . . . . . . . . . 166.5 Symmetric ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Asymmetric ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197.1 Plaintext length . . . . . . . . . . . . . . . . . . .
13、 . . . . . . . . . . . . . . . . 207.2 The use of labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217.3 Ciphertext format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217.4 Encryption options . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14、. . . . . . 217.5 Method of operation of an asymmetric cipher . . . . . . . . . . . . . . . . . . . 227.6 Allowable asymmetric ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Generic hybrid ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228.1 Key en
15、capsulation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 238.2 Data encapsulation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 248.3 HC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Constructions of data encapsulation me
16、chanisms . . . . . . . . . . . . . . . . . . . . 269.1 DEM1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.2 DEM2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279.3 DEM3 . . . . . . . . . . . . . . . . . . . . . . . . . . .
17、. . . . . . . . . . . . . . 2810 ElGamal-based key encapsulation mechanisms . . . . . . . . . . . . . . . . . . . . . 3010.1 Concrete groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3010.2 ECIES-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18、. 3210.3 PSEC-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3410.4 ACE-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3611 RSA-based asymmetric ciphers and key encapsulation mechanisms . . . . . . . . . . 3911.1 RSA key generation algo
19、rithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 3911.2 RSA Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4011.3 RSA encoding mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4011.4 RSAES . . . . . . . . . . . . . . . . . . . . . .
20、. . . . . . . . . . . . . . . . . . 4211.5 RSA-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4412 Ciphers based on modular squaring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Cryptographic transformationsINCITS/ISO/IEC 18033-2:20062008 ITIC 2008 All r
21、ights reservediv 12.1HIMEkeygenerationalgorithms4512.2 HIME encoding mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4612.3 HIME(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48AnnexA(normative)ASN.1syntaxforobjectidentiflers.51Annex B (informati
22、ve) Security considerations . . . . . . . . . . . . . . . . . . . . . . . 61B.1 MAC algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61B.2 Block ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62B.3 Symmetric ciphers . . . . . . . . .
23、 . . . . . . . . . . . . . . . . . . . . . . . . . 62B.4 Asymmetric ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63B.5 Key encapsulation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 65B.6 Data encapsulation mechanisms . . . . . . . . . . . . . . . . .
24、 . . . . . . . . . 66B.7 Security of HC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68B.8 Intractability assumptions related to concrete groups . . . . . . . . . . . . . . . 68B.9 Security of ECIES-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69B.10 Sec
25、urity of PSEC-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.11 Security of ACE-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.12 The RSA inversion problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72B.13 Security of RSAES . . . . . . .
26、 . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.14 Security of RSA-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.15 Security of HIME(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Annex C (informative) Test vectors . . . . . . . . . . . . .
27、. . . . . . . . . . . . . . . . . 75C.1 Test vectors for DEM1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75C.2 Test vectors for ECIES-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76C.3 Test vectors for PSEC-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28、 83C.4 Test vectors for ACE-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C.5 Test vectors for RSAES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100C.6 Test vectors for RSA-KEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105C.7 Test vectors for HC .
29、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109C.8 Test vectors for HIME(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123INCITS/ISO/IEC 18033-2:20062008 ITIC 20
30、08 All rights reservedvForewordISO (the International Organization for Standardization) and IEC (the International ElectrotechnicalCommission) form the specialized system for worldwide standardization. National bodies that aremembers of ISO or IEC participate in the development of International Stan
31、dards through technicalcommittees established by the respective organization to deal with particular fields of technicalactivity. ISO and IEC technical committees collaborate in fields of mutual interest. Otherinternational organizations, governmental and non-governmental, in liaison with ISO and IE
32、C, alsotake part in the work. In the field of information technology, ISO and IEC have established a jointtechnical 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 pr
33、epare International Standards. DraftInternational Standards adopted by the joint technical committee are circulated to national bodies forvoting. Publication as an International Standard requires approval by at least 75 % of the nationalbodies casting a vote.ISO/IEC 18033-2 was prepared by Joint Tec
34、hnical Committee ISO/IEC JTC 1, Informationtechnology, Subcommittee SC 27, IT Security techniques.ISO/IEC 18033 consists of the following parts, under the general title Information technology Security techniques Encryption algorithms: Part 1: General Part 2: Asymmetric ciphers Part 3: Block ciphers
35、Part 4: Stream ciphersINCITS/ISO/IEC 18033-2:20062008 ITIC 2008 All rights reservedvi The International Organization for Standardization (ISO) and International ElectrotechnicalCommission (IEC) draw attention to the fact that it is claimed that compliance with this InternationalStandard may involve
36、the use of patents.The ISO and IEC take no position concerning the evidence, validity and scope of this patent right.The holder of this patent right has assured the ISO and IEC that he is willing to negotiate licencesunder reasonable and non-discriminatory terms and conditions with applicants throug
37、hout the world.In this respect, the statement of the holder of this patent right is registered with the ISO and IEC.Information may be obtained from:ISO/IEC JTC 1/SC 27 Standing Document 8 (SD8) “Patent Information“Standing Document 8 (SD8) is publicly available at: http:/www.ni.din.de/sc27Attention
38、 is drawn to the possibility that some of the elements of this International Standard may bethe subject of patent rights other than those identified above. ISO and IEC shall not be heldresponsible for identifying any or all such patent rights.IntroductionINCITS/ISO/IEC 18033-2:20062008 ITIC 2008 All
39、 rights reserved1Information technology Security techniques Encryption algorithms Part 2: Asymmetric ciphers 1 Scope This part of ISO/IEC 18033 specifies several asymmetric ciphers. These specifications prescribe the functional interfaces and correct methods of use of such ciphers in general, as wel
40、l as the precise functionality and cipher text format for several specific asymmetric ciphers (although conforming systems may choose to use alternative formats for storing and transmitting cipher-texts). A normative annex (Annex A) gives ASN.1 syntax for object identifiers, public keys, and paramet
41、er structures to be associated with the algorithms specified in this part of ISO/IEC 18033. However, these specifications do not prescribe protocols for reliably obtaining a public key, for proof of possession of a private key, or for validation of either public or private keys; see ISO/IEC 11770-3
42、for guidance on such key management issues. The asymmetric ciphers that are specified in this part of ISO/IEC 18033 are indicated in Clause 7.6. NOTE Briefly, the asymmetric ciphers are: ECIES-HC; PSEC-HC; ACE-HC: generic hybrid ciphers based on ElGamal encryption; RSA-HC: a generic hybrid cipher ba
43、sed on the RSA transform; RSAES: the OAEP padding scheme applied to the RSA transform; HIME(R): a scheme based on the hardness of factoring. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited
44、applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO/IEC 9797-1:1999, Information technology Security techniques Message Authentication Codes (MACs) Part 1: Mechanisms using a block cipher ISO/IEC 9797-2:2002, Information technology S
45、ecurity techniques Message Authentication Codes (MACs) Part 2: Mechanisms using a dedicated hash-function ISO/IEC 10118-2:2000, Information technology Security techniques Hash-functions Part 2: Hash-functions using an n-bit block cipher ISO/IEC 10118-3:2004, Information technology Security technique
46、s Hash-functions Part 3: Dedicated hash-functions ISO/IEC 18033-3:2005, Information technology Security techniques Encryption algorithms Part 3: Block ciphers AAMERICAN NATIONAL STANDARD INCITS/ISO/IEC 18033-2:20062008 ITIC 2008 All rights reserved2 3 Definitions For the purposes of this document, t
47、he following terms and definitions apply.NOTE Where appropriate, forward references are given to clauses which contain more detailed definitions and/or further elaboration. 3.1 asymmetric cipher system based on asymmetric cryptographic techniques whose public transformation is used for encryption an
48、d whose private transformation is used for decryption ISO/IEC 18033-1 NOTE See Clause 7. 3.2 asymmetric cryptographic technique cryptographic technique that uses two related transformations, a public transformation (defined by the public key) and a private transformation (defined by the private key)
49、. The two transformations have the property that, given the public transformation, it is computationally infeasible to derive the private transformation. ISO/IEC 11770-1:1996 3.3 asymmetric key pair pair of related keys, a public key and a private key, where the private key defines the private transformation and the public key defines the public transformation ISO/IEC 9798-1:1997 NOTE See Clauses 7, 8.1. 3.4 bit one of the two symbols 0 or 1 NOTE See
