ISO/IEC 18031:2011

Information technology — Security techniques — Random bit generation

ISO/IEC 18031:2011 specifies a conceptual model for a random bit generator for cryptographic purposes, together with the elements of this model. ISO/IEC 18031:2011 specifies the characteristics of the main elements required for a non-deterministic random bit generator, specifies the characteristics of the main elements required for a deterministic random bit generator, establishes the security requirements for both the non-deterministic and the deterministic random bit generator. Where there is a requirement to produce sequences of random numbers from random bit strings, ISO/IEC 18031:2011 gives guidelines on how this can be performed. Techniques for statistical testing of random bit generators for the purposes of independent verification or validation, and detailed designs for such generators, are outside the scope of ISO/IEC 18031:2011.

Technologies de l'information — Techniques de sécurité — Génération de bits aléatoires

General Information

• Status: Published
• Publication Date: 07-Nov-2011
• ICS: 35.030 - IT Security
• ICS: 35.040 - Information coding
• Technical Committee: ISO/IEC JTC 1/SC 27 - Information security, cybersecurity and privacy protection
• Drafting Committee: ISO/IEC JTC 1/SC 27/WG 2 - Cryptography and security mechanisms
• Current Stage: 9092 - International Standard to be revised
• Completion Date: 21-Aug-2020

Relations

• Amended By: ISO/IEC 18031:2011/Amd 1:2017 - Information technology — Security techniques — Random bit generation — Amendment 1: Deterministic random bit generation
• Effective Date: 26-Nov-2021
• Revises: ISO/IEC 18031:2005 - Information technology — Security techniques — Random bit generation
• Effective Date: 08-Aug-2009

Standards Content (Sample)

INTERNATIONAL ISO/IEC
STANDARD 18031
Second edition
2011-11-15


Information technology — Security
techniques — Random bit generation
Technologies de l'information — Techniques de sécurité — Génération
de bits aléatoires





Reference number
ISO/IEC 18031:2011(E)
©
ISO/IEC 2011

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ISO/IEC 18031:2011(E)

COPYRIGHT PROTECTED DOCUMENT


© ISO/IEC 2011
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
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ii © ISO/IEC 2011 – All rights reserved

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ISO/IEC 18031:2011(E)
Contents Page
Foreword . vi
Introduction . vii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols . 5
5 Properties and requirements of an RBG . 6
5.1 Properties of an RBG . 6
5.2 Requirements of an RBG . 7
5.3 Optional requirements for an RBG . 8
6 RBG model . 8
6.1 Conceptual functional model for random bit generation . 8
6.2 RBG basic components . 9
6.2.1 Introduction to the RBG basic components . 9
6.2.2 Entropy source . 10
6.2.3 Additional inputs . 10
6.2.4 Internal state . 11
6.2.5 Internal state transition functions . 12
6.2.6 Output generation function . 13
6.2.7 Support functions . 13
7 Types of RBGs . 14
7.1 Introduction to the types of RBGs . 14
7.2 Non-deterministic random bit generators . 14
7.3 Deterministic random bit generators . 15
7.4 The RBG spectrum . 15
8 Overview and requirements for an NRBG . 16
8.1 NRBG overview . 16
8.2 Functional model of an NRBG . 16
8.3 NRBG entropy sources . 18
8.3.1 Primary entropy source for an NRBG . 18
8.3.2 Physical entropy sources for an NRBG . 20
8.3.3 NRBG non-physical entropy sources . 20
8.3.4 NRBG additional entropy sources . 21
8.3.5 Hybrid NRBGs . 22
8.4 NRBG additional inputs . 22
8.4.1 NRBG additional inputs overview . 22
8.4.2 Requirements for NRBG additional inputs . 22
8.5 NRBG internal state . 23
8.5.1 NRBG internal state overview . 23
8.5.2 Requirements for the NRBG internal state . 23
8.5.3 Optional requirements for the NRBG internal state . 24
8.6 NRBG internal state transition functions . 24
8.6.1 NRBG internal state transition functions overview . 24
8.6.2 Requirements for the NRBG internal state transition functions . 25
8.6.3 Optional requirements for the NRBG internal state transition functions . 25
8.7 NRBG output generation function . 26
8.7.1 NRBG output generation function overview. 26
8.7.2 Requirements for the NRBG output generation function . 26
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ISO/IEC 18031:2011(E)
8.7.3 An optional requirement for the NRBG output generation function .26
8.8 NRBG health tests .26
8.8.1 NRBG health tests overview .26
8.8.2 General NRBG health test requirements .27
8.8.3 NRBG health test on deterministic components .27
8.8.4 NRBG health tests on entropy sources .28
8.8.5 NRBG health tests on random output .29
8.9 NRBG component interaction .31
8.9.1 NRBG component interaction overview .31
8.9.2 Requirements for NRBG component interaction .31
8.9.3 Optional requirements for NRBG component interaction .31
9 Overview and requirements for a DRBG .31
9.1 DRBG overview .31
9.2 Functional model of a DRBG .32
9.3 DRBG entropy source .34
9.3.1 Primary entropy source for a DRBG .34
9.3.2 Generating seed values for a DRBG .36
9.3.3 Additional entropy sources for a DRBG .36
9.3.4 Hybrid DRBG .37
9.4 Additional inputs for a DRBG .37
9.5 Internal state for a DRBG .37
9.6 Internal state transition function for a DRBG .38
9.7 Output generation function for a DRBG .39
9.8 Support functions for a DRBG .39
9.8.1 DRBG support functions overview .39
9.8.2 DRBG health test .39
9.8.3 DRBG deterministic algorithm test .40
9.8.4 DRBG software/firmware integrity test .40
9.8.5 DRBG critical functions test .40
9.8.6 DRBG software/firmware load test .40
9.8.7 DRBG manual key entry test .40
9.8.8 DRBG continuous random bit generator test .40
9.9 Additional requirements for DRBG keys .41
Annex A (normative) Combining RBGs .43
Annex B (normative) Conversion methods .44
B.1 Random number generation .44
B.1.1 Techniques for generating random numbers .44
B.1.2 The simple discard method .44
B.1.3 The complex discard method .44
B.1.4 The simple modular method .45
B.1.5 The complex modular method .45
B.2 Extracting bits in the Dual_EC_DRBG .46
B.2.1 Potential bias in an elliptic curve over a prime field F .46
p
B.2.2 Adjusting for the missing bit(s) of entropy in the x coordinates .47
B.2.3 Values for E .48
B.2.4 Observations .50
Annex C (normative) DRBGs .51
C.1 DRBG mechanism examples .51
C.2 DRBGs based on hash-functions .51
C.2.1 Introduction to DRBGs based on hash-functions .51
C.2.2 Hash_DRBG .51
C.2.3 HMAC_DRBG .59
C.3 DRBGs based on block ciphers .65
C.3.1 Introduction to DRBGs based on block ciphers .65
C.3.2 CTR_DRBG .65
C.3.3 OFB_DRBG .74
C.4 DRBGs based on number theoretic problems .76
C.4.1 Introduction to DRBGs based on number theoretic problems .76
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ISO/IEC 18031:2011(E)
C.4.2 Dual Elliptic Curve DRBG (Dual_EC_DRBG) . 76
C.4.3 Micali Schnorr DRBG (MS_DRBG) . 85
C.5 DRBG based on multivariate quadratic equations . 95
C.5.1 Introduction to a DRBG based on multivariate quadratic equations . 95
C.5.2 Multivariate Quadratic DRBG (MQ_DRBG) . 95
Annex D (normative) Application specific constants . 107
D.1 Constants for the Dual_EC_DRBG . 107
D.1.1 Introduction to Dual_EC_DRBG required constants . 107
D.1.2 Curves over prime fields. 107
D.1.3 Curves over binary fields . 110
D.2 Default moduli for the MS_DRBG (…) . 120
D.2.1 Introduction to MS_DRBG default moduli . 120
D.2.2 Default modulus n of size 1024 bits . 120
D.2.3 Default modulus n of size 2048 bits . 120
D.2.4 Default modulus n of size 3072 bits . 120
D.2.5 Default modulus n of size 7680 bits . 120
D.2.6 Default modulus n of size 15360 bits . 121
Annex E (informative) NRBG examples . 123
E.1 Canonical coin tossing example . 123
E.1.1 Overview . 123
E.1.2 Description of basic process . 123
E.1.3 Relation to standard NRBG components . 123
E.1.4 Optional variations . 124
E.1.5 Peres unbiasing procedure . 124
E.2 Hypothetical noisy diode example . 125
E.2.1 Overview . 125
E.2.2 General structure . 125
E.2.3 Details of operation . 126
E.2.4 Failsafe design consequences . 130
E.2.5 Modified example . 130
E.3 Mouse movement example . 130
Annex F (informative) Security considerations . 132
F.1 Attack model . 132
F.2 The security of hash-functions . 132
F.3 Algorithm and key size selection . 132
F.3.1 Introduction . 132
F.3.2 Equivalent algorithm strengths . 133
F.3.3 Selection of appropriate DRBGs . 134
F.4 The security of block cipher DRBGs . 135
F.5 Conditioned entropy sources and the derivation function . 135
Annex G (informative) Discussion on the estimation of entropy . 136
Annex H (informative) RBG assurance . 137
Annex I (informative) RBG boundaries . 138
Annex J (informative) Rationale for the design of statistical tests . 140
J.1 Introduction . 140
J.2 Runs test . 140
J.3 Long runs test . 140
Bibliography . 142

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ISO/IEC 18031:2011(E)
Foreword
ISO (the International Organization for Standardization) and IEC (the International 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 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 established a joint technical 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 circulated to national bodies for voting. Publication as
an International Standard 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 18031 was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 27, IT Security techniques.
This second edition cancels and replaces the first edition (ISO/IEC 18031:2005), which has been technically
revised. It also incorporates the Technical Corrigendum ISO/IEC 18031:2005/Cor.1:2009.

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ISO/IEC 18031:2011(E)
Introduction
This International Standard sets out specific requirements that when met will result in the development of a
random bit generator that may be applicable to cryptographic applications.
Numerous cryptographic applications require the use of random bits. These cryptographic applications include
the following:
 random keys and initialisation values (IVs) for encryption;
 random keys for keyed MAC algorithms;
 random private keys for digital signature algorithms;
 random values to be used in entity authentication mechanisms;
 random values to be used in key establishment protocols;
 random PIN and password generation;
 nonces.
The purpose of this International Standard is to establish a conceptual model, terminology, and requirements
related to the building blocks and properties of systems used for random bit generation in or for cryptographic
applications.
It is possible to categorize random bit generators into two types. This International Standard identifies the two
types as non-deterministic and deterministic random bit generators.
A non-deterministic random bit generator can be defined as a random bit generating mechanism that uses a
source of entropy to generate a random bit stream.
A deterministic random bit generator can be defined as a bit generating mechanism that uses deterministic
mechanisms, such as cryptographic algorithms, to generate a random bit stream. In this type of bit stream
generation, there is a specific input (normally called a seed) and perhaps some optional input, which,
depending on its application, may or may not be publicly available. The seed is processed by a function which
provides an output.
NOTE This International Standard also recognizes and discusses the existence of Hybrid Random Bit Generators.
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INTERNATIONAL STANDARD ISO/IEC 18031:2011(E)

Information technology — Security techniques — Random bit
generation
1 Scope
This International Standard specifies a conceptual model for a random bit generator for cryptographic
purposes, together with the elements of this model.
This International Standard
 specifies the characteristics of the main elements required for a non-deterministic random bit generator,
 specifies the characteristics of the main elements required for a deterministic random bit generator,
 establishes the security requirements for both the non-deterministic and the deterministic random bit
generator.
Where there is a requirement to produce sequences of random numbers from random bit strings, Annex B
gives guidelines on how this can be performed.
Techniques for statistical testing of random bit generators for the purposes of independent verification or
validation, and detailed designs for such generators, are outside the scope of this International Standard.
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 edition of the referenced
document (including any amendments) applies.
ISO/IEC 9797-2, Information technology — Security techniques — Message Authentication Codes (MACs) —
Part 2: Mechanisms using a dedicated hash-function
ISO/IEC 10116, Information technology — Security techniques — Modes of operation for an n-bit block cipher
ISO/IEC 10118-3, Information technology — Security techniques — Hash-functions — Part 3: Dedicated
hash-functions
ISO/IEC 18032, Information technology — Security techniques — Prime number generation
ISO/IEC 18033-3, Information technology — Security techniques — Encryption algorithms — Part 3: Block
ciphers
ISO/IEC 19790, Information technology — Security techniques — Security requirements for cryptographic
modules
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ISO/IEC 18031:2011(E)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
algorithm
clearly specified mathematical process for the computation of a set of rules that, if followed, will give a
prescribed result
3.2
backward secrecy
assurance that previous values cannot be determined from knowledge of the current value or subsequent
values
3.3
biased source
source of bit strings (or numbers) from a sa
...