ISO/IEC 14888-3:2018/FDAmd 1

FINAL DRAFT
Amendment
ISO/IEC
14888-3:2018/
FDAM 1
ISO/IEC JTC 1/SC 27
IT Security techniques — Digital
Secretariat: DIN
signatures with appendix —
Voting begins on:
2026-08-20
Part 3:
Discrete logarithm based
Voting terminates on:
2026-10-15
mechanisms
AMENDMENT 1
Techniques de sécurité IT — Signatures numériques avec
appendice —
Partie 3: Mécanismes basés sur un logarithme discret
AMENDEMENT 1
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO­
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
Reference number
ISO/IEC 14888­3:2018/FDAM 1:2026(en) © ISO/IEC 2026

FINAL DRAFT
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
Amendment
ISO/IEC
14888-3:2018/
FDAM 1
ISO/IEC JTC 1/SC 27
IT Security techniques — Digital
Secretariat: DIN
signatures with appendix —
Voting begins on:
Part 3:
Discrete logarithm based
Voting terminates on:
mechanisms
AMENDMENT 1
Techniques de sécurité IT — Signatures numériques avec
appendice —
Partie 3: Mécanismes basés sur un logarithme discret
AMENDEMENT 1
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO/IEC 2026
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO­
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland Reference number
ISO/IEC 14888­3:2018/FDAM 1:2026(en) © ISO/IEC 2026

© ISO/IEC 2026 – All rights reserved
ii
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
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.
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 or www.iec.ch/members_experts/refdocs).
ISO and IEC draw attention to the possibility that the implementation of this document may involve the
use of (a) patent(s). ISO and IEC take no position concerning the evidence, validity or applicability of any
claimed patent rights in respect thereof. As of the date of publication of this document, ISO and IEC had not
received notice of (a) patent(s) which may be required to implement this document. However, implementers
are cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents and https://patents.iec.ch. ISO and IEC shall not be held
responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of 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 www.iso.org/iso/foreword.html.
In the IEC, see www.iec.ch/understanding-standards.
This document was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 27, Information security, cyber security, and privacy protection.
A list of all parts in the ISO/IEC 14888 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards
body. A complete listing of these bodies can be found at www.iso.org/members.html and
www.iec.ch/national-committees.

© ISO/IEC 2026 – All rights reserved
iii
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
IT Security techniques — Digital signatures with appendix —
Part 3:
Discrete logarithm based mechanisms
AMENDMENT 1
Introduction
After Note 4, replace the paragraph with the following text:
This document includes 15 mechanisms: two of which (DSA and Pointcheval/Vaudenay algorithm) were in
ISO/IEC 14888-3:1998, three of which (EC-DSA, EC-KCDSA, and EC-GDSA) were from ISO/IEC 15946-2:2002,
three of which (KCDSA, IBS-1 and IBS-2) were added in ISO/IEC 14888-3:2006, four of which (SDSA, EC-
RDSA, EC-SDSA and EC-FSDSA) were added in ISO/IEC 14888-3:2006/Amd 1:2010, two of which (SM2 and
Chinese IBS) were added in ISO/IEC 14888-3:2018 and one of which (EdDSA) is added in this document.
Reword Note 5 as follows:
The mechanisms of EC-DSA, EC-GDSA, EC-RDSA and EC-FSDSA can be vulnerable to a key substitution attack.
[10]
The attack is realized if an adversary can find two distinct public keys and one signature such that the
signature is valid for both public keys. There are several approaches to avoiding this attack and its possible
impact on the security of a cryptographic system. For example, the public key corresponding to the private
signing key can be added into the message to be signed. EdDSA includes this protection in its design.

Clause 2, Normative references
Add the following:
ISO/IEC 29192-5, Information technology — Security techniques — Lightweight cryptography — Part 5: Hash-
functions
Clause 3, Terms and definitions
Insert the following definition after 3.6:
3.7
complete twisted Edwards curve group
cyclic group (3.2) defined on the points of a complete twisted Edwards curve over a finite field
Note 1 to entry Let FrGF be a finite field where r is an odd prime. Let a and d be distinct non-zero elements of

22 22
F such that a is a square in F and d is a non-square in F. Then the affine curve ax yd1 xy is a complete
twisted Edwards curve defined over F. The set E of points of this curve consists of a collection of certain affine points
from FF× , namely those that satisfy the curve equation. Let “+” denote the binary operation known as “Edwards-
curve addition”, defined for all affine points of E by

© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
xy,, xy xy xy /,11dx xy yy ya xx / dxxx yy .
     
11 22 12 21 12 12 12 12 12 12
The identity element for “+” is 01, . The set E together with the binary operation “+” forms a finite

commutative group E that is the complete twisted Edwards curve group for this curve.

Clause 4, Symbols and abbreviated terms
Add the following symbols/abbreviated terms:
ad,
twisted Edwards curve coefficients
EdDSA Edwards curve Digital Signature Algorithm
Replace the definition of E with the following:

E
an elliptic curve defined by two elliptic curve coefficients, a and a , or a twisted Edwards curve
1 2
defined by two curve coefficients a and d
Replace the definition of E with the following:
E
a finite commutative group; for the mechanisms based on a multiplicative group, the elements of E
*
are in Z ; for the mechanisms based on an additive group of elliptic curve points, the elements of E
p
are the points on an elliptic curve E over GF(r) or the points on the twisted Edwards curve E over GF(r)
Replace the definition of #E with the following:
#E the cardinality of E; for the mechanisms based on a multiplicative group Z *, #E is p − 1; for the
p
mechanisms based on an additive group of elliptic curve points, #E is one more than the number of
points on the elliptic curve E over GF(r) [including 0 (the point at infinity)]; for the mechanisms
E
based on twisted Edwards curve points, #E is the number of points on the twisted Edwards curve
E over GF(r)
5.2.2
At the end of Note 2, add the text:
Mechanisms can also permit a larger range for K or specify some algebraic format of K .

5.3.5
Add the following text at the end of the subclause:
For EdDSA the verification mechanism is specified in 6.13.

6.1
Replace the first paragraph with the following:

© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
Clause 6 specifies twelve certificate-based mechanisms. These make use of arithmetic in the multiplicative
group Z *, the additive group of elliptic curve points, or the additive group of points on twisted Edwards
p
curves. The mechanisms using arithmetic in the multiplicative group Z *, are the Digital Signature Algorithm
p
(DSA), the Korean Certificate-based Digital Signature Algorithm (KCDSA), the Pointcheval/Vaudenay
algorithm, and the Schnorr Digital Signature Algorithm (SDSA). The mechanisms using arithmetic in the
additive group of elliptic curve points are the Elliptic Curve DSA (EC-DSA), the Elliptic Curve KCDSA (EC-
KCDSA), the Elliptic Curve German Digital Signature Algorithm (EC-GDSA), the Elliptic Curve Russian Digital
Signature Algorithm (EC-RDSA), the Elliptic Curve Schnorr Digital Signature Algorithm (EC-SDSA), the
Elliptic Curve Full Schnorr Digital Signature Algorithm (EC-FSDSA), the SM2 algorithm, and the Edwards-
curve Digital Signature Algorithm (EdDSA).

At the end of the second paragraph insert the text:
The curves Ed25519 and Ed448 for EdDSA are specified in 6.13.

6.3.2
Replace the penultimate paragraph (starting "Three choices") with the following:
The pair (α,β) for KCDSA shall be chosen in accordance with the chosen security level, as shown in Table 1 in
5.1.3.1. Typical examples are (2 048, 224) and (3 072, 256).
The hash-function h shall be one of the approved hash-functions from ISO/IEC 10118-3 and ISO/IEC 29192-5.
The security strength γ of the hash-function h shall meet or exceed the security strength associated with the
pair (α,β).
6.5.2
Replace the paragraph under the listing (starting "Four choices") with the following:
Three choices for α are permitted in SDSA, namely 1 024, 2 048, and 3 072. The values of γ and β shall be
selected in accordance with the value of α, as specified in Table 1 in 5.1.3.1, such that γ ≥ β. The hash-function
h shall be one of the approved hash-functions from ISO/IEC 10118-3, and its security strength shall meet or
exceed the security strength associated with the pair (α,β).

6.6.1
In the second paragraph, replace the last sentence "The hash-function h . 10118-3" with the following.
The hash function h shall be one of SHA-224, SHA-512/224, SHA3-224, SHA-256, SHA-512/256, SHA3-256,
SHAKE-128 (d=256 bits), SHA-384, SHA3-384, SHA-512, SHA3-512, and SHAKE-256 (d=512 bits) specified
in ISO/IEC 10118-3. The security level γ shall meet or exceed the level associated with the parameter α (see
Table 1 in 5.1.3.1).
6.12.5.7
Add the following text after 6.12.5.7:
6.13  EdDSA
6.13.1  General
EdDSA (Edwards Curve Digital Signature Algorithm) is a signature mechanism with verification key Y′ equal
to the encoding of YX  G , where G is a specified point on a twisted Edwards curve and X is a multiple of
 
© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
8. The parameter D is equal to 1. The message is prepared such that M is empty and MM= , the message
1 2
to be signed. The witness R is computed as the encoding of LK  G for randomizer K .
 
The coefficients AB,,C of the EdDSA signature formula are set as

AB,,CT ,,TS ,
 

where TT ,,TH1  RYM and H is the hash function defined in 6.13.2.
 
Thus, the signature formula becomes KT XS0modq .
NOTE The mechanism is taken from Reference [47]. The notation here has been changed from Reference [47] to
conform with the notation used in the ISO/IEC 14888 series.
6.13.2  Parameters
Table 2 lists the parameters for Ed25519 and Ed448 which use the complete twisted Edwards curve group
defined by a and d modulo p.
Table 2 — Parameters for Ed25519 and Ed448
Ed25519 Ed448
p 255 448 224
21− 9 22−−1
b 256 456
c 8 4
t 32 57
H′(x) SHA-512(x) SHAKE256(x,114)
H(x) SHA-512(x) SHAKE256(dom4(0,context) || x, 114)
d −121665 / 121666 −39081
a −1 1
For Ed448, dom4(0,context) is the octet string "SigEd448" || octet(0) ||octet(OLEN(context)) || context, where
context is an octet string of at most 255 octets and OLEN(context) denotes its length in octets. "SigEd448" is
in ASCII (8 octets).
The base point G of order q2 27742317777372353535851937790883648493 on Ed25519 has
coordinates xy, where x is

and y is
The base point G of order q =
2 −138180668098951153520073867485154268803366924748821786609894547503885
on Ed448 has coordinates xy, , where x is

and y is
© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
6.13.3   Generation of signature key and verification key
The signature key of a signing entity is a secretly generated random or pseudo-random bitstring X ' of
length b .
′
The integer X , so that YX  G , is derived from X through hashing and processing.
 
 
For Ed25519 take HX SHA-512 X , storing the digest in a 64-octet large buffer. Set the lowest three
 
bits of the first octet to 0. Set the highest bit of the t-th octet to 0. Set the second highest bit of the t-th octet to
1. Interpret the first t octets as a little-endian integer, forming a secret integer X .
For Ed448 take HX SHAKE256 X,114 , storing the digest in a 114-octet large buffer. Set the lowest
 
two bits of the first octet to 0. Set all eight bits of the t-th octet to 0. Set the highest bit of the (t-1)-st octet to
1. Interpret the first t octetsas a little-endian integer, forming a secret integer X .
′
EdDSA specifies the verification key Y as the encoding of the point YX  G . The y -coordinate in the
 
range 0yp is encoded as a little-endian string of t octets. The most significant bit of the final octet is
always zero. To form the encoding of the point XG , copy the least significant bit of the x -coordinate to
 
the most significant bit of the final octet. The result is the verification key.
6.13.4  Signature process
6.13.4.1  Producing the randomizer and decoding the secret integer
′
The signing entity computes the pseudo-random integer K using the private signing key X and the message
M using the following two steps. The first step also recovers the secret integer X used in the signature
equation.

— Compute hH X of 2t octets. Construct the secret integer X from the first half of H as in

6.13.3. Let s denote the second half of the hash digest, ht ,.,ht21  .
   
— Compute HsM of 2t octets and interpret the digest as a little-endian integer K .

6.13.4.2  Producing the pre-signature
Compute the point LK  G .
 
NOTE A more efficient way to compute the same result is to first reduce K modulo q , the order of point G .
6.13.4.3  Preparing message for signing
The message is prepared such that M is the message to be signed, i.e. MM= , and M is empty.
2 2 1
6.13.4.4  Computing the witness
Let R be the encoding of L as t octets, following the same steps as in encoding Y : The y -coordinate in the
range 0yp is encoded as a little-endian string of t octets. The most significant bit of the final octet is
always zero. To form the encoding of the point KG , copy the least significant bit of the x -coordinate to
 
 
the most significant bit of the final octet. The result is the witness R .
6.13.4.5  Computing the assignment
The signing entity computes the 2t octet string HRYM and computes T as the reduction modulo q

of the negative of the resulting little-endian integer, i.e. TH RY M mod q.

© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/FDAM 1:2026(en)
Let T 1 .
6.13.4.6  Computing the second part of the signature
Compute SKTX mod q .

The signature is RS,' where S ' is the little-endian encoding of S in t octets.

For Ed25519, the three most significant bits of the final octet are always zero; for Ed448, the 10 most
significant bits of the final two octets are always zero.
6.13.4.7  Constructing the appendix

The appendix will be the concatenation of RS, and an optional text field, text.

6.13.4.8  Constructing the signed message
A signed message is the concatenation of the message, M , and the appendix, i.e. M ||((R,S′),text).
6.13.5   Verification process
6.13.5.1  General
The verifying entity acquires the necessary data items required for the verification process.
6.13.5.2   Retrieving the witness and the verification key
′
The verifier retrieves the witness R and the second part of the signature S from the appendix. The verifier
′
decodes the verification key Y to a point Y on the twisted Edwards curve, decodes R to a point L on the
twisted Edwards curve, and decodes S′ to an integer 0Sq ; if any of the conditions are violated or one of
the decodings fail, the signature shall be rejected.
6.13.5.3   Preparing message for verification
The verifier retrieves M from the signed message and divides the message into two parts M and M such
1 2
that MM= and M is empty.
2 1
6.13.5.4  Retrieving the assignment
The input to the assignment function is computed as in 6.13.4.5 by TT ,,TH1  RY' Mqmod ,
 
again interpreting the hash digest as a little-endian integer of 2t octets and reducing it modulo q .
6.13.5.5  Verifying the signature
The inputs to this stage are system parameters a, d defining the curve and base point G, Edwards curve
point Y decoded from the verificat
...