ISO/IEC 19592-2:2017
(Main)Information technology — Security techniques — Secret sharing — Part 2: Fundamental mechanisms
Information technology — Security techniques — Secret sharing — Part 2: Fundamental mechanisms
ISO/IEC 19592-2:2017 specifies cryptographic secret sharing schemes.
Technologies de l'information — Techniques de sécurité — Partage de secret — Partie 2: Mécanismes fondamentaux
General Information
Standards Content (Sample)
INTERNATIONAL ISO/IEC
STANDARD 19592-2
First edition
2017-10
Information technology — Security
techniques — Secret sharing —
Part 2:
Fundamental mechanisms
Technologies de l'information — Techniques de sécurité — Partage de
secret —
Partie 2: Mécanismes fondamentaux
Reference number
©
ISO/IEC 2017
© 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
or by any means, electronic or mechanical, including 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 ISO’s member body in the country of
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copyright@iso.org
www.iso.org
ii © ISO/IEC 2017 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 2
5 Secret sharing schemes . 3
5.1 General . 3
5.2 Shamir secret sharing scheme . 4
5.2.1 General. 4
5.2.2 Parameters . 4
5.2.3 Message sharing algorithm . 4
5.2.4 Message reconstruction algorithm . 4
5.2.5 Properties . 4
5.3 Ramp Shamir secret sharing scheme . 5
5.3.1 General. 5
5.3.2 Parameters . 5
5.3.3 Message sharing algorithm . 5
5.3.4 Message reconstruction algorithm . 6
5.3.5 Properties . 6
5.4 Additive secret sharing scheme for a general adversary structure . 6
5.4.1 General. 6
5.4.2 Parameters . 6
5.4.3 Message sharing algorithm . 7
5.4.4 Message reconstruction algorithm . 7
5.4.5 Properties . 7
5.5 Replicated additive secret sharing scheme . 7
5.5.1 General. 7
5.5.2 Parameters . 8
5.5.3 Message sharing algorithm . 8
5.5.4 Message reconstruction algorithm . 8
5.5.5 Properties . 8
5.6 Computational additive secret sharing scheme . 8
5.6.1 General. 8
5.6.2 Parameters . 9
5.6.3 Message sharing algorithm . 9
5.6.4 Message reconstruction algorithm . 9
5.6.5 Properties .10
5.6.6 Conversion protocol .10
Annex A (informative) Object identifiers .12
Annex B (informative) Numerical examples .14
Bibliography .22
© ISO/IEC 2017 – All rights reserved iii
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 document 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 and IEC 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 Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 27, IT security techniques.
A list of all parts in the ISO/IEC 19592 series can be found on the ISO website.
iv © ISO/IEC 2017 – All rights reserved
Introduction
A secret sharing scheme is a cryptographic technique used to protect the confidentiality of a message by
dividing it into a number of pieces called shares. A secret sharing scheme has two main parts: a message
sharing algorithm for dividing the message into shares and a message reconstruction algorithm for
recovering the message from all or a subset of the shares.
The fundamental functions of a secret sharing scheme are sharing and reconstructing the message.
A secret sharing scheme can also have optional features such as reconstructing the message when
some shares provided for reconstruction are erroneous. This document specifies cryptographic secret
sharing schemes which possess the two fundamental functions of message confidentiality and message
recoverability.
Secret sharing can be used to store data (for example, confidential values or cryptographic keys)
securely in distributed systems. Moreover, secret sharing is a fundamental technology for secure
multi-party computation that can be used to protect the processing of data in a distributed system. To
facilitate the effective use of the technology and to maintain interoperability, ISO/IEC 19592 (all parts)
specifies secret sharing and related technology.
NOTE Annex A lists the object identifiers assigned to the secret sharing fundamental mechanisms specified
in this document. Annex B provides numerical examples.
© ISO/IEC 2017 – All rights reserved v
INTERNATIONAL STANDARD ISO/IEC 19592-2:2017(E)
Information technology — Security techniques — Secret
sharing —
Part 2:
Fundamental mechanisms
1 Scope
This document specifies cryptographic secret sharing schemes.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 19592-1:2016, Information technology — Security techniques — Secret sharing — Part 1: General
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC 19592-1 and the
following 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
abelian group
group (3.8) (G, +) such that a + b = b + a for every a and b in G
[SOURCE: ISO/IEC 15946-1:2016, 3.1, modified]
3.2
complexity
number of unit operations required to execute a procedure
3.3
conversion protocol
protocol that converts the shares of a secret sharing scheme to the shares of another secret sharing scheme
3.4
deterministic random bit generator
DRBG
random bit generator that produces a random-appearing sequence of bits by applying a deterministic
algorithm to a suitably random initial value called a seed and, possibly, some secondary inputs upon
which the security of the random bit generator does not depend
Note 1 to entry: A DRBG takes a high-entropy, kept-secret random string as input and outputs a longer string of
bits which is computationally indistinguishable from random data to adversaries not knowing the input.
[SOURCE: ISO/IEC 18031:2011, 3.10, modified]
© ISO/IEC 2017 – All rights reserved 1
----------------------
...
Error! Reference source not found.
ISO/IEC JTC 1/SC 27 N16825
Date: 2016-12-23
ISO/IEC JTC 1/SC 27/WG 2
Secretariat: DIN
Information technology — Security techniques — Secret sharing — Part 2:
Fundamental mechanisms
Technologies de l'information ― Techniques de sécurité — Partage de secret — Partie 2: Mécanismes Fondamentaux
Error! Reference source not found.
Copyright notice
This ISO document is a Draft International Standard and is copyright-protected by ISO. Except as
permitted under the applicable laws of the user's country, neither this ISO draft nor any extract
from it may be reproduced, stored in a retrieval system or transmitted in any form or by any
means, electronic, photocopying, recording or otherwise, without prior written permission being
secured.
Requests for permission to reproduce should be addressed to either ISO at the address below or
ISO's 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 copyright@iso.org
Web www.iso.org
Reproduction may be subject to royalty payments or a licensing agreement.
Violators may be prosecuted.
ii Error! Reference source not found.
Error! Reference source not found.
Contents Page
Foreword iv
Introduction v
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 Symbols and abbreviated terms .2
5 Secret sharing schemes .3
5.1 General .3
5.2 Shamir secret sharing scheme .4
5.2.1 General .4
5.2.2 Parameters .4
5.2.3 Message sharing algorithm .4
5.2.4 Message reconstruction algorithm.4
5.2.5 Properties .5
5.3 Ramp Shamir secret sharing scheme .5
5.3.1 General .5
5.3.2 Parameters .5
5.3.3 Message sharing algorithm .6
5.3.4 Message reconstruction algorithm.6
5.3.5 Properties .6
5.4 Additive secret sharing scheme for a general adversary structure .7
5.4.1 General .7
5.4.2 Parameters .7
5.4.3 Message sharing algorithm .7
5.4.4 Message reconstruction algorithm.7
5.4.5 Properties .8
5.5 Replicated additive secret sharing scheme .8
5.5.1 General .8
5.5.2 Parameters .8
5.5.3 Message sharing algorithm .9
5.5.4 Message reconstruction algorithm.9
5.5.5 Properties .9
5.6 Computational additive secret sharing scheme .9
5.6.1 General .9
5.6.2 Parameters .9
5.6.3 Message sharing algorithm . 10
5.6.4 Message reconstruction algorithm. 10
5.6.5 Properties . 10
5.6.6 Conversion Protocol . 11
Annex A (normative) Object identifiers . 13
Annex B (informative) Numerical examples . 15
B.1 Shamir secret sharing scheme . 15
B.2 Ramp Shamir secret sharing scheme . 15
Error! Reference source not found. iii
Error! Reference source not found.
B.3 Additive secret sharing scheme for a general adversary structure . 16
B.4 Additive secret sharing scheme . 16
B.5 Computational additive secret sharing scheme . 16
Bibliography 22
iv Error! Reference source not found.
Error! Reference source not found.
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 document 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 and IEC 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 Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 27, IT security techniques.
A list of all parts in the ISO/IEC 19592 series can be found on the ISO website.
Error! Reference source not found. v
Error! Reference source not found.
Introduction
A secret sharing scheme is a cryptographic technique used to protect the confidentiality of a message by
dividing it into a number of pieces called shares. A secret sharing scheme has two main parts: a message
sharing algorithm for dividing the message into shares and a message reconstruction algorithm for
recovering the message from all or a subset of the shares.
The fundamental functions of a secret sharing scheme are sharing and reconstructing the message. A
secret sharing scheme can also have optional features such as reconstructing the message when some
shares provided for reconstruction are erroneous. This document specifies cryptographic secret sharing
schemes which possess the two fundamental functions of message confidentiality and message
recoverability.
Secret sharing can be used to store data (for example, confidential values or cryptographic keys)
securely in distributed systems. Moreover, secret sharing is a fundamental technology for secure multi-
party computation that can be used to protect the processing of data in a distributed system. To
facilitate the effective use of the technology and to maintain interoperability, ISO/IEC 19592 (all parts)
specifies secret sharing and related technology.
NOTE Annex A lists the object identifiers assigned to the secret sharing fundamental mechanisms specified in
this document. Annex B provides numerical examples.
vi Error! Reference source not found.
Error! Reference source not found. Error! Reference source not found.
Information technology — Security techniques — Secret
sharing — Part 2: Fundamental mechanisms
1 Scope
This document specifies cryptographic secret sharing schemes.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 19592-1:2016, Information technology — Security techniques — Secret sharing — Part 1:
General
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC 19592-1 and the
following 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
abelian group
group (3.8) (G, +) such that a + b = b + a for every a and b in G
[SOURCE: ISO/IEC 15946-1:2016, 3.1, modified]
3.2
complexity
number of unit operations required to execute a procedure
3.3
conversion protocol
protocol that converts the shares of a secret sharing scheme to the shares of another secret sharing
scheme
3.4
deterministic random bit generator
DRBG
Error! Reference source not found. 1
Error! Reference source not found.
random bit generator that produces a random-appearing sequence of bits by applying a deterministic
algorithm to a suitably random initial value called a seed and, possibly, some secondary inputs upon
which the security of the random bit generator does not depend
Note 1 to entry: A DRBG takes a high-entropy, kept-secret random string as input and outputs a longer string of
bits which is computationally indistinguishable from random data to adversaries not knowing the input.
[SOURCE: ISO/IEC 18031:2011, 3.10, modified]
3.5
field
set of elements K and a pair of operations (+, *) defined on K such that: (i) a * (b + c) = a * b + a * c for
every a, b and c in K, (ii) K together with + forms an abelian group (3.1) (with identity element 0), and
(iii) K excluding 0 together with * forms an abelian group
[SOURCE: ISO/IEC 15946-1:2016, 3.4, modified]
3.6
finite c
...
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