Information technology -- Security techniques -- Key management

ISO/IEC 11770-4:2017 defines key establishment mechanisms based on weak secrets, i.e. secrets that can be readily memorized by a human, and hence, secrets that will be chosen from a relatively small set of possibilities. It specifies cryptographic techniques specifically designed to establish one or more secret keys based on a weak secret derived from a memorized password, while preventing offline brute-force attacks associated with the weak secret. ISO/IEC 11770-4:2017 is not applicable to the following aspects of key management: - life-cycle management of weak secrets, strong secrets, and established secret keys; - mechanisms to store, archive, delete, destroy, etc. weak secrets, strong secrets, and established secret keys.

Technologies de l'information -- Techniques de sécurité -- Gestion de clés

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INTERNATIONAL ISO/IEC
STANDARD 11770-4
Second edition
2017-11
Information technology — Security
techniques — Key management —
Part 4:
Mechanisms based on weak secrets
Technologies de l'information — Techniques de sécurité — Gestion
de clés —
Partie 4: Mécanismes basés sur des secrets faibles
Reference number
ISO/IEC 11770-4:2017(E)
ISO/IEC 2017
---------------------- Page: 1 ----------------------
ISO/IEC 11770-4:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO/IEC 2017, Published in Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form

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ii © ISO/IEC 2017 – All rights reserved
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ISO/IEC 11770-4:2017(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative reference ......................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols and abbreviated terms ........................................................................................................................................................... 6

5 Requirements .......................................................................................................................................................................................................... 8

6 Password-authenticated key agreement ..................................................................................................................................10

6.1 General ........................................................................................................................................................................................................10

6.2 Balanced Key Agreement Mechanism 1 (BKAM1) ................................................................................................10

6.2.1 General...................................................................................................................................................................................10

6.2.2 Prior shared parameters ........................................................................................................................................11

6.2.3 Functions .............................................................................................................................................................................11

6.2.4 Key agreement operation ......................................................................................................................................14

6.3 Balanced Key Agreement Mechanism 2 (BKAM2) ................................................................................................15

6.3.1 General...................................................................................................................................................................................15

6.3.2 Prior shared parameters ........................................................................................................................................15

6.3.3 Functions .............................................................................................................................................................................16

6.3.4 Key agreement operation ......................................................................................................................................19

6.4 Augmented Key Agreement Mechanism 1 (AKAM1) ..........................................................................................22

6.4.1 General...................................................................................................................................................................................22

6.4.2 Prior shared parameters ........................................................................................................................................22

6.4.3 Functions .............................................................................................................................................................................23

6.4.4 Key agreement operation ......................................................................................................................................24

6.5 Augmented Key Agreement Mechanism 2 (AKAM2) ..........................................................................................25

6.5.1 General...................................................................................................................................................................................25

6.5.2 Prior shared parameters ........................................................................................................................................26

6.5.3 Functions .............................................................................................................................................................................26

6.5.4 Key agreement operation ......................................................................................................................................29

6.6 Augmented Key Agreement Mechanism 3 (AKAM3) ..........................................................................................30

6.6.1 General...................................................................................................................................................................................30

6.6.2 Prior shared parameters ........................................................................................................................................30

6.6.3 Functions .............................................................................................................................................................................31

6.6.4 Key agreement operation ......................................................................................................................................33

7 Password-authenticated key retrieval ........................................................................................................................................35

7.1 General ........................................................................................................................................................................................................35

7.2 Key Retrieval Mechanism 1 (KRM1)..................................................................................................................................35

7.2.1 General...................................................................................................................................................................................35

7.2.2 Prior shared parameters ........................................................................................................................................36

7.2.3 Functions .............................................................................................................................................................................36

7.2.4 Key retrieval operation ........................................................................................................................................... .37

Annex A (normative) Functions for data type conversion ..........................................................................................................38

Annex B (normative) Object identifiers .........................................................................................................................................................42

Annex C (informative) Guidance on choice of parameters .........................................................................................................45

Bibliography .............................................................................................................................................................................................................................47

© ISO/IEC 2017 – All rights reserved iii
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ISO/IEC 11770-4:2017(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.

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 ISO documents should be noted. This document 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 shall not be held responsible for identifying any 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 users and does not

constitute an endorsement.

For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following

URL: www.iso.org/iso/foreword.html.

This document was prepared by ISO/IEC JTC 1, Information technology, SC 27, IT Security techniques.

This second edition cancels and replaces the first edition (ISO/IEC 11770-4:2006), which has been

technically revised. It also incorporates the Technical Corrigendum ISO/IEC 11770-4:2006/Cor1:2009.

This edition includes the following significant changes with respect to the previous edition:

— revision of the Balanced Key Agreement Mechanism 1 (BKAM1) to address the attacks reported in

Reference [6];

— addition of a new Balanced Key Agreement Mechanism 2 (BKAM2) based on the J-PAKE scheme of

Reference [5];

— addition of a new Augmented Key Agreement Mechanism 3 (AKAM3) based on the AugPAKE scheme

of Reference [23].
A list of all parts in the ISO/IEC 11770 series can be found on the ISO website.
iv © ISO/IEC 2017 – All rights reserved
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ISO/IEC 11770-4:2017(E)
Introduction

The mechanisms specified in this document are designed to achieve one of the following three goals.

a) Balanced password-authenticated key agreement: Establish one or more shared secret keys

between two entities that share a common weak secret. In a balanced password-authenticated key

agreement mechanism, the shared secret keys are the result of a data exchange between the two

entities; the shared secret keys are established if, and only if, the two entities have used the same

weak secret; and neither of the two entities can predetermine the values of the shared secret keys.

b) Augmented password-authenticated key agreement: Establish one or more shared secret keys

between two entities A and B, where A has a weak secret and B has verification data derived from

a one-way function of A’s weak secret. In an augmented password-authenticated key agreement

mechanism, the shared secret keys are the result of a data exchange between the two entities; the

shared secret keys are established if, and only if, the two entities have used the weak secret and the

corresponding verification data; and neither of the two entities can predetermine the values of the

shared secret keys.

NOTE 1 This type of key agreement mechanism is unable to protect A’s weak secret being discovered by

B, but only increases the cost for an adversary to get A's weak secret from B. A typical application scenario

would involve use between a client (A) and a server (B).

c) Password-authenticated key retrieval: Establish one or more secret keys for an entity, A,

associated with another entity, B, where A has a weak secret and B has a strong secret associated

with A's weak secret. In an authenticated key retrieval mechanism, the secret keys, retrievable by

A (not necessarily derivable by B), are the result of a data exchange between the two entities, and

the secret keys are established if, and only if, the two entities have used the weak secret and the

associated strong secret. However, although B’s strong secret is associated with A's weak secret,

the strong secret does not (in itself) contain sufficient information to permit either the weak secret

or the secret keys established in the mechanism to be determined.

NOTE 2 This type of key retrieval mechanism is used in those applications where A does not have secure

storage for a strong secret, and requires B’s assistance to retrieve the strong secret. Such a mechanism is

appropriate for use between a client (A) and a server (B).

The International Organization for Standardization (ISO) and International Electrotechnical

Commission (IEC) draw attention to the fact that it is claimed that compliance with this document may

involve the use of patents.

ISO and IEC take no position concerning the evidence, validity and scope of these patent rights. The

holders of these patent rights have assured ISO and IEC that they are willing to negotiate licences under

reasonable and non-discriminatory terms and conditions with applicants throughout the world. In this

respect, the statements of the holders of these patent rights are registered with ISO and IEC. Information

may be obtained from:
National Institute of Advanced Industrial Science and Technology
1–1–1 Umezono
Tsukuba, Ibaraki
305–8560 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 all such patent rights.

ISO (www.iso.org/patents) and IEC (http://patents.iec.ch) maintain online databases of patents

relevant to their documents. Users are encouraged to consult the databases for the most up to date

information concerning patents.
© ISO/IEC 2017 – All rights reserved v
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INTERNATIONAL STANDARD ISO/IEC 11770-4:2017(E)
Information technology — Security techniques — Key
management —
Part 4:
Mechanisms based on weak secrets
1 Scope

This document defines key establishment mechanisms based on weak secrets, i.e. secrets that can be

readily memorized by a human, and hence, secrets that will be chosen from a relatively small set of

possibilities. It specifies cryptographic techniques specifically designed to establish one or more secret

keys based on a weak secret derived from a memorized password, while preventing offline brute-force

attacks associated with the weak secret. This document is not applicable to the following aspects of key

management:

— life-cycle management of weak secrets, strong secrets, and established secret keys;

— mechanisms to store, archive, delete, destroy, etc. weak secrets, strong secrets, and established

secret keys.
2 Normative reference
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
augmented password-authenticated key agreement

password-authenticated key agreement where entity A uses a password-based weak secret and entity B

uses verification data derived from a one-way function of A's weak secret to negotiate and authenticate

one or more shared secret keys
3.2
balanced password-authenticated key agreement

password-authenticated key agreement where two entities A and B use a shared common password-

based weak secret to negotiate and authenticate one or more shared secret keys
3.3
brute-force attack

attack on a cryptosystem that employs an exhaustive search of a set of keys, passwords or other data

© ISO/IEC 2017 – All rights reserved 1
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ISO/IEC 11770-4:2017(E)
3.4
collision-resistant hash-function

hash-function satisfying the following property: it is computationally infeasible to find any two distinct

inputs which map to the same output

Note 1 to entry: Computational feasibility depends on the specific security requirements and environment. Refer

to ISO/IEC 10118-1:2016, Annex C.
[SOURCE: ISO/IEC 10118-1:2016, 3.1]
3.5
dictionary attack

(on a password-based system) attack on a cryptosystem that employs a search of a given list of

passwords

Note 1 to entry: A dictionary attack on a password-based system can use a stored list of specific password values

or a stored list of words from a natural language dictionary.
3.6
domain parameter

data item which is common to and known by or accessible to all entities within the domain

Note 1 to entry: The set of domain parameters may contain data items such as hash-function identifier, length of

the hash-token, length of the recoverable part of the message, finite field parameters, elliptic curve parameters,

or other parameters specifying the security policy in the domain.
[SOURCE: ISO/IEC 9796-3:2006, 3.2]
3.7
elliptic curve
cubic curve E without a singular point

Note 1 to entry: The set of points E together with an appropriately defined operation for a field that includes all

coefficients of the equation describing E is called the definition field of E. In ISO/IEC 15946-1, only finite fields

F are dealt with as the definition field. When it is necessary to describe the definition field F of E explicitly, the

curve is denoted as E/F.

Note 2 to entry: The form of a cubic curve equation used to define an elliptic curve varies depending on the field. The

general form of an appropriate cubic equation for all possible finite fields is defined in ISO/IEC 15946-1:2016, 6.1.

[SOURCE: ISO/IEC 15946-1:2016, 3.3, modified]
3.8
explicit key authentication

assurance for entity B that entity A is the only other entity that is in

possession of the correct key

Note 1 to entry: Implicit key authentication from entity A to entity B and key confirmation from entity A to entity

B together imply explicit key authentication from entity A to entity B.
[SOURCE: ISO/IEC 11770-3:2015, 3.12, modified]
3.9
hash-function

function which maps strings of bits of variable (but usually upper bounded) length to fixed-length

strings of bits, satisfying the following two properties:

— for a given output, it is computationally infeasible to find an input which maps to this output;

— for a given input, it is computationally infeasible to find a second input which maps to the same output.

Note 1 to entry: Computational feasibility depends on the specific security requirements and environment. Refer

to ISO/IEC 10118-1:2016, Annex C.
2 © ISO/IEC 2017 – All rights reserved
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ISO/IEC 11770-4:2017(E)
[SOURCE: ISO/IEC 10118-1:2016, 3.4]
3.10
hashed password
result of applying a hash-function to a password
3.11
implicit key authentication

assurance for entity B that entity A is the only other entity that can possibly

be in possession of the correct key
[SOURCE: ISO/IEC 11770-3:2015, 3.16, modified]
3.12
key

sequence of symbols that controls the operation of a cryptographic transformation (e.g. encryption,

decryption, cryptographic check function computation, signature calculation, or signature verification)

[SOURCE: ISO/IEC 11770-3:2015, 3.17]
3.13
key agreement

process of establishing a shared secret key between entities in such a way that neither of them can

predetermine the value of that key

Note 1 to entry: By predetermine, it is meant that neither entity A nor entity B can, in a computationally efficient

way, choose a smaller key space and force the computed key in the protocol to fall into that key space.

[SOURCE: ISO/IEC 11770-3:2015, 3.18]
3.14
key confirmation

assurance for entity B that entity A is in possession of the correct key

[SOURCE: ISO/IEC 11770-3:2015, 3.20, modified]
3.15
key control
ability to choose the key or the parameters used in the key computation
[SOURCE: ISO/IEC 11770-3:2015, 3.21]
3.16
key derivation function

function which takes as input a number of parameters, at least one of which shall be secret, and which

gives as output keys appropriate for the intended algorithm(s) and applications
3.17
key establishment
process of making available a shared secret key to one or more entities

Note 1 to entry: Key establishment includes key agreement, key transport and key retrieval.

3.18
key management

administration and use of generation, registration, certification, deregistration, distribution,

installation, storage, archiving, revocation, derivation and destruction of keying material in accordance

with a security policy
[SOURCE: ISO/IEC 11770-1:2010, 2.28]
© ISO/IEC 2017 – All rights reserved 3
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ISO/IEC 11770-4:2017(E)
3.19
key retrieval

process of establishing a key for one or more entities known as the retrieving entities with the

involvement of one or more other entities who are not necessarily able to access the key after the

process, and which normally requires authentication of the retrieving entity/entities by the other

entity/entities
3.20
key token

key establishment message sent from one entity to another entity during the execution of a key

establishment mechanism
3.21
key token check function

function that utilizes a key token and other publicly known parameters as input and outputs a Boolean

value during the execution of a key establishment mechanism
3.22
key token factor

value that is kept secret and that is used, possibly in conjunction with a weak secret, to create a key token

3.23
key token generation function

function that utilizes a key token factor and other parameters as input and outputs a key token during

the execution of a key establishment mechanism
3.24
message authentication code algorithm

algorithm for computing a function which maps strings of bits and a secret key to fixed-length strings

of bits, satisfying the following two properties:
— for any key and any input string, the function can be computed efficiently;

— for any fixed key, and given no prior knowledge of the key, it is computationally infeasible to

compute the function value on any new input string, even given knowledge of a set of input strings

and corresponding function values, where the value of the ith input string may have been chosen

after observing the value of the first i-1 function values (for integers i > 1)
[SOURCE: ISO/IEC 9797-1:2011, 3.10, modified]
3.25
mutual key authentication

assurance for two entities that only the other entity is in possession of the correct key

3.26
one-way function

function with the property that it is easy to compute the output for a given input but it is computationally

infeasible to find an input which maps to a given output
[SOURCE: ISO/IEC 11770-3:2015, 3.30]
3.27
password

secret word, phrase, number, or character sequence used for entity authentication, which is a memorized

weak secret
4 © ISO/IEC 2017 – All rights reserved
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ISO/IEC 11770-4:2017(E)
3.28
password-authenticated key agreement

process of establishing one or more shared secret keys between two entities using prior shared

password-based information (which means that either both of them have the same shared password

or one has the password and the other has password verification data) and neither of them can

predetermine the values of the shared secret keys
3.29
password-authenticated key retrieval

key retrieval process where one entity A has a weak secret derived from a password and the other

entity B has a strong secret associated with A’s weak secret; these two entities, using their own secrets,

negotiate a secret key which is retrievable by A, but not (necessarily) derivable by B

3.30
password-entangled key token
key token which is derived from both a weak secret and a key token factor
3.31
password verification data
data that is used to verify an entity’s knowledge of a specific password
3.32
random element derivation function

function that utilizes a password and other parameters as input and outputs a random element

3.33
salt

random variable incorporated as secondary input to a one-way or encryption function that is used to

derive password verification data
3.34
secret
value known only to authorized entities
3.35
secret key
key used with symmetric cryptographic techniques by a specified set of entities
[SOURCE: ISO/IEC 11770-3:2015, 3.36]
3.36
secret value derivation function

function that utilizes a key token factor, a key token, and other parameters as input and outputs a secret

value which is used to compute one or more secret keys
3.37
strong secret

secret with a sufficient degree of entropy that conducting an exhaustive search for the secret is

infeasible, even given knowledge that would enable a correct guess for the secret to be distinguished

from an incorrect guess

Note 1 to entry: This may, for example, be achieved by randomly choosing the secret from a sufficiently large set

of possible values under uniform distribution.
3.38
weak secret
secret that can be conveniently memorized by a human being

Note 1 to entry: Typically, this means that the entropy of the secret is limited, so that an exhaustive search for the

secret (or, a dictionary attack) may be feasible, given knowledge that would enable a correct guess for the secret

to be distinguished from an incorrect guess.
© ISO/IEC 2017 – All rights reserved 5
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ISO/IEC 11770-4:2017(E)
4 Symbols and abbreviated terms
A, B distinguishing identities of entities represented as octet strings
a , a elliptic curve coefficients
1 2

BS2I a function that converts a bit string into an integer (described in Annex A)

b, b bits (i.e. either 0 or 1)

C, C , C functions for generating a key token based on a password and a key token factor

DL EC
c an integer satisfying 1 ≤ c ≤ q – 1
D, D , D functions for generating a key token based on only a key token factor
DL EC

E an elliptic curve defined by two elliptic curve coefficients, a and a . For the purpose

1 2

of this document, an elliptic curve is not only the set of points on the curve, but

[13]
also a group operation defined on these points as specified in ISO/IEC 15946-1 .

FE2I a function that converts a field element into an integer (described in Annex A)

FE2OS a function that converts a field element into an octet string (described in Annex A)

F(q) the finite field with q elements
G,G ,G points of order r on E over F(q)
a b

GE2OS a function that converts a group element into an octet string; when the group el-

ement is a point on E, this function converts the x-coordinate of the point into an

octet string and ignores the y-coordinate (described in Annex A)
g, g , g , g elements of multiplicative order r in F(q)
1 a b
g an element of multiplicative order q - 1 in F(q)
q-1

H a collision-resistant hash-function taking an octet string as input and giving a bit

string as output, e.g. based on one of the dedicated hash-functions specified in
[11]
ISO/IEC 10118-3

h(x, L ) a collision-resistant hash-function taking an octet string x and an integer L as

K K

input and giving a bit string of length L (in bits) as output, e.g. based on one of the

[11]
dedicated hash-functions specified in ISO/IEC 10118-3
I2FE a functio
...

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