ISO/IEC 14888-3:2018/Amd 1:2026

• Status: Published
• Publication Date: 10-Nov-2026
• ICS: 35.030 - IT Security
• 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: 6060 - International Standard published
• Start Date: 11-Nov-2026
• Completion Date: 11-Nov-2026

• Amends: ISO/IEC 14888-3:2018 - IT Security techniques — Digital signatures with appendix — Part 3: Discrete logarithm based mechanisms
• Effective Date: 04-May-2024

ISO/IEC 14888-3:2018/Amd 1 is an ISO/IEC amendment to IT Security techniques - Digital signatures with appendix - Part 3: Discrete logarithm based mechanisms. It updates that part with Edwards Curve Digital Signature Algorithm (EdDSA), new twisted Edwards curve terminology, object identifiers, encoding and decoding rules, and worked examples. The document is aimed at people who implement, verify, specify, or compare digital-signature mechanisms based on discrete logarithms.

What does ISO/IEC 14888-3:2018/Amd 1 specify?

ISO/IEC 14888-3:2018/Amd 1 revises the third part of the ISO/IEC 14888 series so that it covers EdDSA alongside the other certificate-based mechanisms already in the part. The amendment touches the introduction, clauses 2 to 6, and Annexes A, B, F, G, and H.

In practice, the document is a technical update for systems that use discrete logarithm based signatures with an appendix. It keeps the structure of the parent part, while adding EdDSA definitions, procedures, identifiers, and examples.

Annex	What it covers
Annex A	Object identifiers assigned to the signature mechanisms and algorithm parameter structures
Annex B	Point encoding and decoding for EdDSA
Annex F	Worked examples, including Ed25519 and Ed448
Annex G	Comparison of certificate-based mechanisms using elliptic curve
Annex H	Claimed features for the mechanisms

What are the key requirements of ISO/IEC 14888-3:2018/Amd 1?

ISO/IEC 14888-3:2018/Amd 1 adds EdDSA as a full mechanism in Clause 6.13 and updates the surrounding rules so that it fits the rest of the part. The most important practical points are the curve model, the key and point encoding rules, the signing steps, and the verification check.

Clause 6 now includes EdDSA among the certificate-based mechanisms

Clause 6.1 says the part specifies twelve certificate-based mechanisms. They use arithmetic in the multiplicative group Z*_p, the additive group of elliptic curve points, or the additive group of points on twisted Edwards curves. For a reader, this tells you which mathematical setting each mechanism expects, and therefore which kind of library support you need.

The same clause names Ed25519 and Ed448 as the EdDSA curves specified in Clause 6.13. That matters because EdDSA is not treated as a generic Edwards-curve method here - it is tied to the specific procedures and parameters in the new subclause.

EdDSA has its own signing and verification model

Clause 6.13.1 defines EdDSA as a signature mechanism with verification key Y′ equal to the encoding of Y = [X]G, where G is a specified point on a twisted Edwards curve and X is a multiple of 8. The message preparation step sets up the message in a specific way, and the witness R is derived from a randomizer K. In practice, implementers need to follow these exact preparation and encoding rules, not just use any Edwards-curve signature code.

Clause 6.13.3 defines how the signature key and verification key are generated. The signature key starts from a secret random or pseudo-random bitstring X′, which is hashed and processed to derive the secret integer X. For Ed25519 and Ed448, this derivation is different, and the bit-level masking rules are specific. That matters because the key pair is not formed by a simple random scalar alone.

EdDSA uses curve-specific parameters and hash functions

Clause 6.13.2 states that Ed25519 and Ed448 use the complete twisted Edwards curve group defined by a and d modulo p. It also assigns the hash functions H′ and H used by each curve, and for Ed448 it introduces dom4(0,context) as the domain-separation string.

For implementers, this means the curve parameters, hash function choice, and context handling are part of the mechanism. They are not optional formatting details.

Signature generation uses a derived randomizer, witness, and scalar

Clause 6.13.4 gives the signature process in stages: derive the randomizer K from the secret key material and message, compute L = [K]G, encode it as the witness R, compute the assignment T from the hash of R, Y′, and the message, and then compute S. The signature is the pair (R, S′), and the appendix is formed by concatenating that pair with an optional text field.

This is important because a verifier must expect the appendix format exactly as defined here, including the optional text field and the encoding of S′ in octets.

Verification checks decoding first, then the group equation

Clause 6.13.5 requires the verifier to retrieve R and S from the appendix, decode the verification key Y, decode R to a point, and decode S to an integer in range. If decoding fails or any condition is violated, the signature is rejected. The final check is a group equation involving [S]G, L, and [T]Y.

In practice, this means signature verification starts with strict input validation. The amendment also notes that a simpler equivalent check is sufficient, although not required.

The amendment also tightens hash-function and attack-related guidance

Clause 6.3.2 for KCDSA, Clause 6.5.2 for SDSA, and Clause 6.6.1 for EC-DSA restrict the approved hash-functions and tie them to security-strength rules. The added note in the introduction says some elliptic-curve variants may be vulnerable to a key substitution attack, and that EdDSA includes protection by design. For readers, this is a reminder to match the hash function and security level to the mechanism, and to consider how the public key is bound into the signed data.

What terms does ISO/IEC 14888-3:2018/Amd 1 define?

• EdDSA (Edwards Curve Digital Signature Algorithm) - A signature mechanism whose verification key is the encoding of a point derived from a secret scalar and a base point on a twisted Edwards curve.
• complete twisted Edwards curve group - A cyclic group formed by the points of a complete twisted Edwards curve over a finite field.
• E - The finite commutative group used by the mechanisms; for some mechanisms it is Z*_p, and for elliptic-curve mechanisms it is the point set of the curve.
• #E - The cardinality of E, meaning the size of the group used by the mechanism.
• a, d - The twisted Edwards curve coefficients.
• G - The specified base point used to form public keys and signatures in EdDSA.

Who uses ISO/IEC 14888-3:2018/Amd 1?

ISO/IEC 14888-3:2018/Amd 1 is used by engineers who design and implement digital-signature functions, by security architects who choose between DSA, EC-based schemes, SM2, and EdDSA, and by product teams that need object identifiers and parameter structures for interoperable systems. It also supports test labs and reviewers that check key generation, point encoding, signature creation, and verification behavior against the specified procedures.

What changed in ISO/IEC 14888-3:2018/Amd 1 from the previous edition?

This amendment adds EdDSA and its two named curve profiles, Ed25519 and Ed448, to the part. It also:

• adds ISO/IEC 29192-5 to the normative references
• introduces the definition of complete twisted Edwards curve group
• adds symbols and terms for EdDSA and twisted Edwards curve coefficients
• updates hash-function requirements in Clause 6.3.2, 6.5.2, and 6.6.1
• adds the new Clause 6.13 for EdDSA
• replaces Annex A with updated OIDs and parameter structures
• adds Annex B text for EdDSA point encoding and decoding
• adds Annex F examples for Ed25519 and Ed448
• updates the comparison table in Annex G
• updates the claimed-features table in Annex H

Which standards are used with ISO/IEC 14888-3:2018/Amd 1?

ISO/IEC 14888-3:2018/Amd 1 adds ISO/IEC 29192-5 as a normative reference for lightweight cryptography hash-functions. The amendment also relies on ISO/IEC 10118-3 for approved hash-functions used in KCDSA, SDSA, EC-DSA, and related mechanisms. In practice, these references tell the implementer which hash functions are acceptable for the signature mechanisms in this part.

What does the ISO/IEC 14888-3:2018/Amd 1 document contain?

The document contains a revised technical introduction, updated definitions and symbols, a new EdDSA clause, and revised annex material. Annex A gives ASN.1 module text for algorithm identifiers and parameter types, which is useful for protocol and certificate encoding.

Annex B adds the point-encoding and point-decoding procedures for EdDSA, including separate decoding paths for Ed25519 and Ed448. Annex F provides worked examples for key generation, signing, and verification for both Ed25519 and Ed448, so readers can compare an implementation against a concrete trace. Annex G and Annex H provide comparison and feature-summary tables that help with mechanism selection and system documentation.

International
Standard
ISO/IEC 14888-3
Fourth edition
IT Security techniques — Digital
2018-11
signatures with appendix —
AMENDMENT 1
Part 3:
2026-11
Discrete logarithm based
mechanisms
AMENDMENT 1
Techniques de sécurité IT — Signatures numériques avec
appendice —
Partie 3: Mécanismes basés sur un logarithme discret
AMENDEMENT 1
Reference number
ISO/IEC 14888-3:2018/Amd. 1:2026(en) © ISO/IEC 2026

ISO/IEC 14888-3:2018/Amd. 1:2026(en)
© ISO/IEC 2026
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© ISO/IEC 2026 – All rights reserved
ii
ISO/IEC 14888-3:2018/Amd. 1:2026(en)
Foreword
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Commission) form the specialized system for worldwide standardization. National bodies that are
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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).
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use of (a) patent(s). ISO and IEC take no position concerning the evidence, validity or applicability of any
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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
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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/Amd. 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
[10]
attack. 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/Amd. 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 are
p
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 mech-
p
anisms 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 based on
E
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/Amd. 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,
SHAKE128 (d=256 bits), SHA-384, SHA3-384, SHA-512, SHA3-512, and SHAKE256 (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/Amd. 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/Amd. 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 octets as 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/Amd. 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 verification key Y′ , assignment TT ,T from 6.13.5.4 and decoded integer S

corresponding to the second part of the signature S ' from 6.13.5.2.
The verifier checks the group equation cS  Gc  Lc  TY .
         2
If this equality holds, then the signature is verified else the signature shall be rejected.
NOTE It is sufficient, but not required, to instead check SG LT Y .
   2
Annex A
Replace the entirety of Annex A with the following:

© ISO/IEC 2026 – All rights reserved
ISO/IEC 14888-3:2018/Amd. 1:2026(en)
This annex lists the object identifiers assigned to the digital signature mechanisms specified in this
document, and defines algorithm parameter structures.

DigitalSignatureWithAppendixDL {
iso(1) sta
...