Internet DRAFT - draft-hallambaker-mesh-udf
draft-hallambaker-mesh-udf
Network Working Group P. M. Hallam-Baker
Internet-Draft ThresholdSecrets.com
Intended status: Informational 28 June 2023
Expires: 30 December 2023
Mathematical Mesh 3.0 Part II: Uniform Data Fingerprint.
draft-hallambaker-mesh-udf-18
Abstract
This document describes the underlying naming and addressing schemes
used in the Mathematical Mesh. The means of generating Uniform Data
Fingerprint (UDF) values and their presentation as text sequences and
as URIs are described.
A UDF consists of a binary sequence, the initial eight bits of which
specify a type identifier code. For convenience, UDFs are typically
presented to the user in the form of a Base32 encoded string. Type
identifier codes have been selected so as to provide a useful
mnemonic indicating their purpose when presented in Base32 encoding.
Two categories of UDF are described. Data UDFs provide a compact
presentation of a fixed length binary data value in a format that is
convenient for data entry. A Data UDF may represent a cryptographic
key, a nonce value or a share of a secret. Fingerprint UDFs provide
a compact presentation of a Message Digest or Message Authentication
Code value.
A Strong Internet Name (SIN) consists of a DNS name which contains at
least one label that is a UDF fingerprint of a policy document
controlling interpretation of the name. SINs allow a direct trust
model to be applied to achieve end-to-end security in existing
Internet applications without the need for trusted third parties.
UDFs may be presented as URIs to form either names or locators for
use with the UDF location service. An Encrypted Authenticated
Resource Locator (EARL) is a UDF locator URI presenting a service
from which an encrypted resource may be obtained and a symmetric key
that may be used to decrypt the content. EARLs may be presented on
paper correspondence as a QR code to securely provide a machine-
readable version of the same content. This may be applied to
automate processes such as invoicing or to provide accessibility
services for the partially sighted.
[Note to Readers]
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Discussion of this draft takes place on the MATHMESH mailing list
(mathmesh@ietf.org), which is archived at
https://mailarchive.ietf.org/arch/search/?email_list=mathmesh.
This document is also available online at
http://mathmesh.com/Documents/draft-hallambaker-mesh-udf.html.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on 30 December 2023.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1. UDF Types . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1. Cryptographic Keys and Nonces . . . . . . . . . . . . 5
1.1.2. Fingerprint type UDFS . . . . . . . . . . . . . . . . 6
1.2. Using UDFs in URIs . . . . . . . . . . . . . . . . . . . 7
1.2.1. Name Form . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2. Locator Form . . . . . . . . . . . . . . . . . . . . 7
1.3. Secure Internet Names . . . . . . . . . . . . . . . . . . 9
2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1. Requirements Language . . . . . . . . . . . . . . . . . . 10
2.2. Defined Terms . . . . . . . . . . . . . . . . . . . . . . 10
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2.3. Related Specifications . . . . . . . . . . . . . . . . . 11
2.4. Implementation Status . . . . . . . . . . . . . . . . . . 11
3. Architecture . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1. Base32 Presentation . . . . . . . . . . . . . . . . . . . 12
3.1.1. Precision Improvement . . . . . . . . . . . . . . . . 12
3.2. Type Identifier . . . . . . . . . . . . . . . . . . . . . 12
3.3. Content Type Identifier . . . . . . . . . . . . . . . . . 14
3.4. Truncation . . . . . . . . . . . . . . . . . . . . . . . 14
3.4.1. Compressed presentation . . . . . . . . . . . . . . . 15
3.5. Presentation . . . . . . . . . . . . . . . . . . . . . . 15
3.6. Alternative Presentations . . . . . . . . . . . . . . . . 16
3.6.1. Word Lists . . . . . . . . . . . . . . . . . . . . . 16
3.6.2. Image List . . . . . . . . . . . . . . . . . . . . . 16
4. Fixed Length UDFs . . . . . . . . . . . . . . . . . . . . . . 16
4.1. Nonce Type . . . . . . . . . . . . . . . . . . . . . . . 16
4.2. OID Identified Sequence . . . . . . . . . . . . . . . . . 17
4.3. Encryption/Authentication Type . . . . . . . . . . . . . 18
4.4. Key Pair Derivation . . . . . . . . . . . . . . . . . . . 18
4.4.1. Extraction step . . . . . . . . . . . . . . . . . . . 21
4.4.2. Elliptic Curve Diffie Hellman Key Pairs type 1-4 . . 22
4.4.3. Elliptic Curve Diffie Hellman Key Pairs type 5-7 . . 23
4.4.4. RSA Key Pairs . . . . . . . . . . . . . . . . . . . . 24
4.4.5. Any Key Algorithm . . . . . . . . . . . . . . . . . . 26
4.5. Shamir Shared Secret . . . . . . . . . . . . . . . . . . 27
4.5.1. Secret Generation . . . . . . . . . . . . . . . . . . 28
4.5.2. Recovery . . . . . . . . . . . . . . . . . . . . . . 29
5. Variable Length UDFs . . . . . . . . . . . . . . . . . . . . 30
5.1. Content Digest . . . . . . . . . . . . . . . . . . . . . 31
5.1.1. Content Digest Value . . . . . . . . . . . . . . . . 31
5.1.2. Typed Content Digest Value . . . . . . . . . . . . . 31
5.1.3. Content Digest Compression . . . . . . . . . . . . . 32
5.1.4. Content Digest Presentation . . . . . . . . . . . . . 32
5.1.5. Example Encoding . . . . . . . . . . . . . . . . . . 33
5.1.6. Using SHA-2-512 Digest . . . . . . . . . . . . . . . 33
5.1.7. Using SHA-3-512 Digest . . . . . . . . . . . . . . . 34
5.1.8. Using SHA-2-512 Digest with Compression . . . . . . . 34
5.1.9. Using SHA-3-512 Digest with Compression . . . . . . . 35
5.2. Authenticator UDF . . . . . . . . . . . . . . . . . . . . 35
5.2.1. Authentication Content Digest Value . . . . . . . . . 36
5.2.2. Authentication Value . . . . . . . . . . . . . . . . 36
5.3. Content Type Values . . . . . . . . . . . . . . . . . . . 38
5.3.1. PKIX Certificates and Keys . . . . . . . . . . . . . 39
5.3.2. OpenPGP Key . . . . . . . . . . . . . . . . . . . . . 40
5.3.3. DNSSEC . . . . . . . . . . . . . . . . . . . . . . . 40
6. UDF URIs . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.1. Name form URI . . . . . . . . . . . . . . . . . . . . . . 41
6.2. Locator form URI . . . . . . . . . . . . . . . . . . . . 41
6.2.1. DNS Web service discovery . . . . . . . . . . . . . . 41
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6.2.2. Content Identifier . . . . . . . . . . . . . . . . . 42
6.2.3. Target URI . . . . . . . . . . . . . . . . . . . . . 42
6.2.4. Postprocessing . . . . . . . . . . . . . . . . . . . 42
6.2.5. Decryption and Authentication . . . . . . . . . . . . 43
6.2.6. QR Presentation . . . . . . . . . . . . . . . . . . . 43
7. Strong Internet Names . . . . . . . . . . . . . . . . . . . . 43
8. Security Considerations . . . . . . . . . . . . . . . . . . . 43
8.1. Confidentiality . . . . . . . . . . . . . . . . . . . . . 44
8.2. Availability . . . . . . . . . . . . . . . . . . . . . . 44
8.3. Integrity . . . . . . . . . . . . . . . . . . . . . . . . 44
8.4. Work Factor and Precision . . . . . . . . . . . . . . . . 44
8.5. Semantic Substitution . . . . . . . . . . . . . . . . . . 45
8.6. QR Code Scanning . . . . . . . . . . . . . . . . . . . . 46
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 46
9.1. Protocol Service Name . . . . . . . . . . . . . . . . . . 46
9.2. Well Known . . . . . . . . . . . . . . . . . . . . . . . 47
9.3. URI Registration . . . . . . . . . . . . . . . . . . . . 47
9.4. Media Types Registrations . . . . . . . . . . . . . . . . 48
9.4.1. Media Type: application/pkix-keyinfo . . . . . . . . 48
9.4.2. Media Type: application/udf . . . . . . . . . . . . . 49
9.5. Uniform Data Fingerprint Type Identifier Registry . . . . 50
9.5.1. The name of the registry . . . . . . . . . . . . . . 50
9.5.2. Required information for registrations . . . . . . . 50
9.5.3. Applicable registration policy . . . . . . . . . . . 50
9.5.4. Size, format, and syntax of registry entries . . . . 50
9.5.5. Initial assignments and reservations . . . . . . . . 51
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 51
11. Appendix A: Prime Values for Secret Sharing . . . . . . . . . 51
12. Appendix B: Shamir Shared Secret Recovery Using Lagrange
Interpolation . . . . . . . . . . . . . . . . . . . . . . . 54
13. Normative References . . . . . . . . . . . . . . . . . . . . 57
14. Informative References . . . . . . . . . . . . . . . . . . . 59
1. Introduction
A Uniform Data Fingerprint (UDF) is a generalized format for
presenting and interpreting short binary sequences representing
cryptographic keys or fingerprints of data of any specified type.
The UDF format provides a superset of the OpenPGP [RFC4880]
fingerprint encoding capability with greater encoding density and
readability.
This document describes the syntax and encoding of UDFs, the means of
constructing and comparing them and their use in other Internet
addressing schemes.
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1.1. UDF Types
Two categories of UDF are described. Data UDFs provide a compact
presentation of a fixed length binary data value in a format that is
convenient for data entry. A Data UDF may represent a cryptographic
key or nonce value or a part share of a key generated using a secret
sharing mechanism. Fingerprint UDFs provide a compact presentation
of a Message Digest or Message Authentication Code value.
Both categories of UDF are encoded as a UDF binary sequence, the
first octet of which is a Type Identifier and the remaining octets
specify the binary value according to the type identifier and data
referenced.
UDFs are typically presented to the user as a Base32 encoded sequence
in groups of four characters separated by dashes. This format
provides a useful balance between compactness and readability. The
type identifier codes have been selected so as to provide a useful
mnemonic when presented in Base32 encoding.
The following are examples of UDF values:
Nonce: NA3F-EQAS-PCNR-B7T2-YC5T-GJLA-ZNRA
Secret: EN5H-Y5QJ-W62O-7OEC-4VEK-YKSB-GU
SHA-2 Digest:MB5S-R4AJ-3FBT-7NHO-T26Z-2E6Y-WFH4
SHA-3 Digest:KCM5-7VB6-IJXJ-WKHX-NZQF-OKGZ-EWVN
Public Key: OAYC-4MAH-AYBS-WZLQ-AUAA-GIYA-AQQD-QHJM-UFOO-Q5HB-KBOS-O
WV4-UTLW-JDBH-3VHS-U7NH-OUKT-L4HU-FEPX-ZJY
Like email addresses, UDFs are not a Uniform Resource Identifier
(URI) but may be expressed in URI form by adding the scheme
identifier (UDF) for use in contexts where an identifier in URI
syntax is required. A UDF URI MAY contain a domain name component
allowing it to be used as a locator
1.1.1. Cryptographic Keys and Nonces
A Nonce (N) UDF represents a short, fixed length randomly chosen
binary value.
Nonce UDFs are used within many Mesh protocols and data formats where
it is necessary to represent a nonce value in text form.
Nonce UDF:
NA3F-EQAS-PCNR-B7T2-YC5T-GJLA-ZNRA
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An Encryption/Authentication (E) UDF has the same format as a Random
UDF but is identified as being intended to be used as a symmetric key
for encryption and/or authentication.
KeyValue:
7A 7C 76 09 B7 B4 EF B8 82 E5 48 AC 2A 41 35
Encryption/Authenticator UDF:
EN5H-Y5QJ-W62O-7OEC-4VEK-YKSB-GU
A Share (S) UDF also represents a short, fixed length binary value
but only provides one share in secret sharing scheme. Recovery of
the binary value requires a sufficient number of shares.
Share UDFs are used in the Mesh to support key and data escrow
operations without the need to rely on trusted hardware. A share UDF
can be copied by hand or printed in human or machine-readable form
(e.g. QR code).
Key: EN5H-Y5QJ-W62O-7OEC-4VEK-YKSB-GU
Share 0: SAQJ-Q3WI-I2VY-LJJL-4AOE-NO46-6P5T-Y
Share 1: SAQQ-2YYU-C5GV-HFLI-A622-QLUR-XW2R-A
Share 2: SARI-EV27-47XS-DBNE-F5HQ-TIME-Q5XR-O
1.1.2. Fingerprint type UDFS
Fingerprint type UDFs contains a fingerprint value calculated over a
content data item and an IANA media type.
A Content Digest type UDF is a fingerprint type UDF in which the
fingerprint is formed using a cryptographic algorithm. Two digest
algorithms are currently supported, SHA-2-512 (M, for Merkle Damgard)
and SHA-3-512 (K, for Keccak).
The inclusion of the media type in the calculation of the UDF value
provides protection against semantic substitution attacks in which
content that has been found to be trustworthy when interpreted as one
content type is presented in a context in which it is interpreted as
a different content type in which it is unsafe.
SHA-2-512: MB5S-R4AJ-3FBT-7NHO-T26Z-2E6Y-WFH4
SHA-3-512: KCM5-7VB6-IJXJ-WKHX-NZQF-OKGZ-EWVN
An Authentication UDF (A) is formed in the same manner as a
fingerprint but using a Message Authentication Code algorithm and a
symmetric key.
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Authentication UDFs are used to express commitments and to provide a
means of blinding fingerprint values within a protocol by means of a
nonce.
SHA-2-512: AATU-V2VR-5MHY-54G3-OKRN-OC5J-AEZM
1.2. Using UDFs in URIs
The UDF URI scheme allows use of a UDF in contexts where a URF is
expected. The UDF URI scheme has two forms, name and locator.
1.2.1. Name Form
Name form UDF URIs identify a data resource but do not provide a
means of discovery. The URI is simply the scheme (udf) followed by
the UDF value:
udf:MB5S-R4AJ-3FBT-7NHO-T26Z-2E6Y-WFH4
1.2.2. Locator Form
Locator form UDF URIs identify a data resource and provide a hint
that MAY provide a means of discovery. If the content is not
available from the location indicated, content obtained from a
different source that matches the fingerprint MAY be used instead.
udf://example.com/MB5S-R4AJ-3FBT-7NHO-T26Z-2E6Y-WFH4
UDF locator form URIs presenting a fingerprint type UDF provide a
tight binding of the content to the locator. This allows the
resolved content to be verified and rejected if it has been modified.
UDF locator form URIs presenting an Encryptor/Authenticator type UDF
provide a mechanism for identification, discovery and decryption of
encrypted content. UDF locators of this type are known as Encrypted/
Authenticated Resource Locators (EARLs).
Regardless of the type of the embedded UDF, UDF locator form URIs are
resolved by first performing DNS Web Service Discovery to identify
the Web Service Endpoint for the mmm-udf service at the specified
domain.
Resolution is completed by presenting the Content Digest Fingerprint
of the UDF value specified in the URI to the specified Web Service
Endpoint and performing a GET method request on the result.
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For example, Alice subscribes to Example.com, a purveyor of cat and
kitten images. The company generates paper and electronic invoices
on a monthly basis.
To generate the paper invoice, Example.com first creates a new
encryption key:
EDQB-6NYS-T57S-DVKF-4FHT-BHPO-ATC4-UL
One or more electronic forms of the invoice are encrypted under the
key EDQB-6NYS-T57S-DVKF-4FHT-BHPO-ATC4-UL and placed on the
Example.com Web site so that the appropriate version is returned if
Alice scans the QR code.
The key is then converted to form an EARL for the example.com UDF
resolution service:
udf://example.com/EDQB-6NYS-T57S-DVKF-4FHT-BHPO-ATC4-UL
The EARL is then rendered as a QR code:
(Artwork only available as svg: No external link available, see
draft-hallambaker-mesh-udf-18.html for artwork.)
Figure 1: QR Code with embedded decryption and location key
A printable invoice containing the QR code is now generated and sent
to Alice.
When Alice receives the invoice, she can pay it by simply scanning
the invoice with a device that recognizes at least one of the invoice
formats supported by Example.com.
The UDF EARL locator shown above is resolved by first determining the
Web Service Endpoint for the mmm-udf service for the domain
example.com.
Discover ("example.com", "mmm-udf") =
https://example.com/.well-known/mmm-udf/
Next the fingerprint of the source UDF is obtained.
UDF (EDQB-6NYS-T57S-DVKF-4FHT-BHPO-ATC4-UL) =
MCU7-43LV-OH4V-5JPL-4GT4-5TPW-DJ33-5BDH-MQMP-UPHQ-3XLX-4GGO-U34N-FWJK
Combining the Web Service Endpoint and the fingerprint of the source
UDF provides the URI from which the content is obtained using the
normal HTTP GET method:
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https://example.com/.well-known/mmm-udf/MCU7-43LV-OH4V-5JPL-4GT4-
5TPW-DJ33-5BDH-MQMP-UPHQ-3XLX-4GGO-U34N-FWJK
Having established that Alice can read postal mail sent to a physical
address and having delivered a secret to that address, this process
might be extended to provide a means of automating the process of
enrolment in electronic delivery of future invoices.
1.3. Secure Internet Names
A SIN is an Internet Identifier that contains a UDF fingerprint of a
security policy document that may be used to verify the
interpretation of the identifier. This permits traditional forms of
Internet address such as URIs and RFC822 email addresses to be used
to express a trusted address that is independent of any trusted third
party.
This document only describes the syntax and interpretation of the
identifiers themselves. The means by which the security policy
documents bound to an address govern interpretation of the name is
discussed separately in [draft-hallambaker-mesh-trust].
For example, Example Inc holds the domain name example.com and has
deployed a private CA whose root of trust is a PKIX certificate with
the UDF fingerprint MB2GK-6DUF5-YGYYL-JNY5E-RWSHZ.
Alice is an employee of Example Inc., she uses three email addresses:
alice@example.com A regular email address (not a SIN).
alice@mm--mb2gk-6duf5-ygyyl-jny5e-rwshz.example.com A strong email
address that is backwards compatible.
alice@example.com.mm--mb2gk-6duf5-ygyyl-jny5e-rwshz A strong email
address that is backwards incompatible.
All three forms of the address are valid RFC822 addresses and may be
used in a legacy email client, stored in an address book application,
etc. But the ability of a legacy client to make use of the address
differs. Addresses of the first type may always be used. Addresses
of the second type may only be used if an appropriate MX record is
provisioned. Addresses of the third type will always fail unless the
resolver understands that it is a SIN requiring special processing.
These rules allow Bob to send email to Alice with either 'best
effort' security or mandatory security as the circumstances demand.
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2. Definitions
This section presents the related specifications and standard, the
terms that are used as terms of art within the documents and the
terms used as requirements language.
2.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
2.2. Defined Terms
Cryptographic Digest Function A hash function that has the
properties required for use as a cryptographic hash function.
These include collision resistance, first pre-image resistance and
second pre-image resistance.
Content Type An identifier indicating how a Data Value is to be
interpreted as specified in the IANA registry Media Types.
Commitment A cryptographic primitive that allows one to commit to a
chosen value while keeping it hidden to others, with the ability
to reveal the committed value later.
Data Value The binary octet stream that is the input to the digest
function used to calculate a digest value.
Data Object A Data Value and its associated Content Type
Digest Algorithm A synonym for Cryptographic Digest Function
Digest Value The output of a Cryptographic Digest Function
Data Digest Value The output of a Cryptographic Digest Function for
a given Data Value input.
Fingerprint A presentation of the digest value of a data value or
data object.
Fingerprint Presentation The representation of at least some part of
a fingerprint value in human or machine-readable form.
Fingerprint Improvement The practice of recording a higher precision
presentation of a fingerprint on successful validation.
Fingerprint Work Hardening The practice of generating a sequence of
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fingerprints until one is found that matches criteria that permit
a compressed presentation form to be used. The compressed
fingerprint thus being shorter than but presenting the same work
factor as an uncompressed one.
Hash A function which takes an input and returns a fixed-size
output. Ideally, the output of a hash function is unbiased and
not correlated to the outputs returned to similar inputs in any
predictable fashion.
Precision The number of significant bits provided by a Fingerprint
Presentation.
Work Factor A measure of the computational effort required to
perform an attack against some security property.
2.3. Related Specifications
This specification makes use of Base32 [RFC4648] encoding, SHA-2
[SHA-2] and SHA-3 [SHA-3] digest functions in the derivation of basic
fingerprints. The derivation of keyed fingerprints additionally
requires the use of the HMAC [RFC2014] and HKDF [RFC5869] functions.
Resolution of UDF URI Locators makes use of DNS Web Service Discovery
[draft-hallambaker-web-service-discovery].
2.4. Implementation Status
The implementation status of the reference code base is described in
the companion document [draft-hallambaker-mesh-developer].
3. Architecture
A Uniform Data Fingerprint (UDF) is a presentation of a UDF Binary
Data Sequence.
This document specifies seven UDF Binary Data Sequence types and one
presentation.
The first octet of a UDF Binary Data Sequence identifies the UDF type
and is referred to as the Type identifier.
UDF Binary Data Sequence types are either fixed length or variable
length. A variable length Binary Data Sequence MUST be truncated for
presentation. Fixed length Binary Data Sequences MUST not be
truncated.
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3.1. Base32 Presentation
The default UDF presentation is Base32 Presentation.
Variable length Binary Data Sequences are truncated to an integer
multiple of 20 bits that provides the desired precision before
conversion to Base32 form.
Fixed length Binary Data Sequences are converted to Base32 form
without truncation.
After conversion to Base32 form, dash '-' characters are inserted
between groups of 4 characters to aid reading. This representation
improves the accuracy of both data entry and verification.
3.1.1. Precision Improvement
Precision improvement is the practice of using a high precision UDF
(e.g. 260 bits) calculated from content data that has been validated
according to a lower precision UDF (e.g. 120 bits).
This allows a lower precision UDF to be used in a medium such as a
business card where space is constrained without compromising
subsequent uses.
Applications SHOULD make use of precision improvement wherever
possible.
3.2. Type Identifier
A Version Identifier consists of a single byte.
The byte codes have been chosen so that the first character of the
Base32 presentation of the UDF provides a mnemonic for its type. A
SHA-2 fingerprint UDF will always have M (for Merkle Damgard) as the
initial letter, a SHA-3 fingerprint UDF will always have K (for
Keccak) as the initial letter, and so on.
The following version identifiers are specified in this document:
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+=========+=========+==========================================+
| Type ID | Initial | Algorithm |
+=========+=========+==========================================+
| 0 | A | HMAC_SHA_2_512 |
+---------+---------+------------------------------------------+
| 1 | A | HMAC_SHA_3_512 |
+---------+---------+------------------------------------------+
| 32 | E | HKDF_AES_512 |
+---------+---------+------------------------------------------+
| 33 | E | HKDF_AES_512 |
+---------+---------+------------------------------------------+
| 80 | K | SHA_3_512 |
+---------+---------+------------------------------------------+
| 81 | K | SHA_3_512 (20 compressed) |
+---------+---------+------------------------------------------+
| 82 | K | SHA_3_512 (30 compressed) |
+---------+---------+------------------------------------------+
| 83 | K | SHA_3_512 (40 compressed) |
+---------+---------+------------------------------------------+
| 84 | K | SHA_3_512 (50 compressed) |
+---------+---------+------------------------------------------+
| 96 | M | SHA_2_512 |
+---------+---------+------------------------------------------+
| 97 | M | SHA_2_512 (20 compressed) |
+---------+---------+------------------------------------------+
| 98 | M | SHA_2_512 (30 compressed) |
+---------+---------+------------------------------------------+
| 99 | M | SHA_2_512 (40 compressed) |
+---------+---------+------------------------------------------+
| 100 | M | SHA_2_512 (50 compressed) |
+---------+---------+------------------------------------------+
| 104 | N | Nonce Data |
+---------+---------+------------------------------------------+
| 112 | O | OID distinguished sequence (DER encoded) |
+---------+---------+------------------------------------------+
| 144 | S | Shamir Secret Share |
+---------+---------+------------------------------------------+
| 200 | Z | Secret seed |
+---------+---------+------------------------------------------+
Table 1
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3.3. Content Type Identifier
A secure cryptographic digest algorithm provides a unique digest
value that is probabilistically unique for a particular byte sequence
but does not fix the context in which a byte sequence is interpreted.
While such ambiguity may be tolerated in a fingerprint format
designed for a single specific field of use, it is not acceptable in
a general-purpose format.
For example, the SSH and OpenPGP applications both make use of
fingerprints as identifiers for the public keys used but using
different digest algorithms and data formats for representing the
public key data. While no such vulnerability has been demonstrated
to date, it is certainly conceivable that a crafty attacker might
construct an SSH key in such a fashion that OpenPGP interprets the
data in an insecure fashion. If the number of applications making
use of fingerprint format that permits such substitutions is
sufficiently large, the probability of a semantic substitution
vulnerability being possible becomes unacceptably large.
A simple control that defeats such attacks is to incorporate a
content type identifier within the scope of the data input to the
hash function.
3.4. Truncation
Different applications of fingerprints demand different tradeoffs
between compactness of the representation and the number of
significant bits. A larger the number of significant bits reduces
the risk of collision but at a cost to convenience.
Modern cryptographic digest functions such as SHA-2 produce output
values of at least 256 bits in length. This is considerably larger
than most uses of fingerprints require and certainly greater than can
be represented in human readable form on a business card.
Since a strong cryptographic digest function produces an output value
in which every bit in the input value affects every bit in the output
value with equal probability, it follows that truncating the digest
value to produce a finger print is at least as strong as any other
mechanism if digest algorithm used is strong.
Using truncation to reduce the precision of the digest function has
the advantage that a lower precision fingerprint of some data content
is always a prefix of a higher prefix of the same content. This
allows higher precision fingerprints to be converted to a lower
precision without the need for special tools.
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3.4.1. Compressed presentation
The Content Digest UDF types make use of work factor compression.
Additional type identifiers are used to indicate digest values with
20, 30, 40 or 50 trailing zero bits allowing a UDF fingerprint
offering the equivalent of up to 150 bits of precision to be
expressed in 20 characters instead of 30.
To use compressed UDF identifiers, it is necessary to search for
content that can be compressed. If the digest algorithm used is
secure, this means that by definition, the fastest means of search is
brute force. Thus, the reduction in fingerprint size is achieved by
transferring the work factor from the attacker to the defender. To
maintain a work factor of 2^120 with an identifier of 2^80 bits, it
is necessary for the content generator to perform a brute force
search at a cost of the order of 2^40 operations.
For example, the smallest allowable work factor for a UDF
presentation of a public key fingerprint is 92 bits. This would
normally require a presentation with 20 significant characters.
Reducing this to 16 characters requires a brute force search of
approximately 10^6 attempts. Reducing this to 12 characters would
require 10^12 attempts and to 10 characters, 10^15 attempts.
Omission of support for higher levels of compression than 2^50 is
intentional.
In addition to allowing use of shorter presentations, work factor
compression MAY be used as evidence of proof of work.
3.5. Presentation
The presentation of a fingerprint is the format in which it is
presented to either an application or the user.
Base32 encoding is used to produce the preferred text representation
of a UDF fingerprint. This encoding uses only the letters of the
Latin alphabet with numbers chosen to minimize the risk of ambiguity
between numbers and letters (2, 3, 4, 5, 6 and 7).
To enhance readability and improve data entry, characters are grouped
into groups of four. This means that each block of four characters
represents an increase in work factor of approximately one million
times.
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3.6. Alternative Presentations
Applications that support UDF MUST support use of the Base32
presentation. Applications MAY support alternative presentations.
3.6.1. Word Lists
The use of a Word List to encode fingerprint values was introduced by
Patrick Juola and Philip Zimmerman for the PGPfone application. The
PGP Word List is designed to facilitate exchange and verification of
fingerprint values in a voice application. To minimize the risk of
misinterpretation, two-word lists of 256 values each are used to
encode alternative fingerprint bytes. The compact size of the lists
used allowed the compilers to curate them so as to maximize the
phonetic distance of the words selected.
The PGP Word List is designed to achieve a balance between ease of
entry and verification. Applications where only verification is
required may be better served by a much larger word list, permitting
shorter fingerprint encodings.
For example, a word list with 16384 entries permits 14 bits of the
fingerprint to be encoded at once, 65536 entries permit encoding of
16 bits. These encodings allow a 120-bit fingerprint to be encoded
in 9 and 8 words respectively.
3.6.2. Image List
An image list is used in the same manner as a word list affording
rapid visual verification of a fingerprint value. For obvious
reasons, this approach is not suited to data entry but is preferable
for comparison purposes. An image list of 1,048,576 images would
provide a 20-bit encoding allowing 120 bit precision fingerprints to
be displayed in six images.
4. Fixed Length UDFs
Fixed length UDFs are used to represent cryptographic keys, nonces
and secret shares and have a fixed length determined by their
function that cannot be truncated without loss of information.
All fixed length Binary Data Sequence values are an integer multiple
of eight bits.
4.1. Nonce Type
A Nonce Type UDF consists of the type identifier octet 104 followed
by the Binary Data Sequence value.
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The Binary Data Sequence value is an integer number of octets that
SHOULD have been generated in accordance with processes and
procedures that ensure that it is sufficiently unpredictable for the
purposes of the protocol in which the value is to be used.
Requirements for such processes and procedures are described in
[RFC4086].
Nonce Type UDFs are intended for use in contexts where it is
necessary for a randomly chosen value to be unpredictable but not
secret. For example, the challenge in a challenge/response
mechanism.
4.2. OID Identified Sequence
An OID Identified Sequence Type UDF consists of the type identifier
octet 108 followed by the Binary Data Sequence value.
The Binary Data Sequence value is an octet sequence that contains the
DER encoding of the following ASN.1 data:
OIDInfo ::= SEQUENCE {
algorithm AlgorithmIdentifier,
data BIT STRING }
AlgorithmIdentifier ::= SEQUENCE {
algorithm OBJECT IDENTIFIER,
parameters ANY DEFINED BY algorithm OPTIONAL }
OID Identified Sequences are intended to allow arbitrary data
sequences to be encoded in the UDF format without exhausting the
limited type identifier space.
In particular, OID Identified Sequences MAY be used to specify public
and private key values.
Given the following Ed25519 public key:
38 1D 2C A1 5C E8 74 E1 50 5D 27 5A BC A4 D7 64
8C 27 DD 4F 2A 7D A7 75 15 35 F0 F4 29 1F 7C A7
The equivalent DER encoding is:
30 2E 30 07 06 03 2B 65 70 05 00 03 23 00 04 20
38 1D 2C A1 5C E8 74 E1 50 5D 27 5A BC A4 D7 64
8C 27 DD 4F 2A 7D A7 75 15 35 F0 F4 29 1F 7C A7
To encode this key as a UDF OID sequence we prepend the value OID and
convert to Base32:
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OID: OAYC-4MAH-AYBS-WZLQ-AUAA-GIYA-AQQD-QHJM-UFOO-Q5HB-KBOS-O
WV4-UTLW-JDBH-3VHS-U7NH-OUKT-L4HU-FEPX-ZJY
The corresponding UDF content digest value is more compact and allows
us to identify the key unambiguously but does not provide the value:
MALR-MJJ7-FZZB-RJWW-I6V7-KRFR-L2PW
4.3. Encryption/Authentication Type
Encryption and Authenticator Type UDFs consists of the type
identifier specifying the algorithm to be used on the key data
followed by the Binary Data Sequence value.
The Binary Data Sequence value is an integer number of octets that
SHOULD have been generated in accordance with processes and
procedures that ensure that it is sufficiently unpredictable and
unguessable for the purposes of the protocol in which the value is to
be used. Requirements for such processes and procedures are
described in [RFC4086].
Encryption and Authenticator Type UDFs are intended to be used as a
means of specifying secret cryptographic keying material. For
example, the input to a Key Derivation Function used to encrypt a
document. Accordingly, the identifier UDF corresponding to an
Encryption or Authenticator type UDF is a UDF fingerprint of the UDF
in Base32 presentation with content type 'application/udf'.
4.4. Key Pair Derivation
The key pair derivation type is used to specify a public key pair
value by means of a sufficiently random input to a deterministic key
generation function.
A key pair derivation Type UDF consists of the type identifier octet
200 followed by the Binary Data Sequence value.
The first two octets of the Binary Data Sequence value comprise the
Key Specifier which specifies the algorithm and key uses for which
the private key is to be derived.
* Bits 6-7 of the first octet specify the key use.
* Bits 0-5 of the first byte and bits 0-7 of the second specify the
key type in network byte order.
In the unlikely event that this code space is ever exhausted,
allocation of a new UDF type code will be required.
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The following key uses are specified:
+======+================+================+
| Code | Algorithm | Description |
+======+================+================+
| 0 | Any | Any |
+------+----------------+----------------+
| 1 | Encryption | Encryption |
+------+----------------+----------------+
| 2 | Signature | Signature |
+------+----------------+----------------+
| 3 | Authentication | Authentication |
+------+----------------+----------------+
Table 2
Two types of key type are defined: Explicit and Generic.
Explicit key types specify a public key cryptographic algorithm and
all the parameters required to generate a key pair. Generic key
types are used to specify a type of key but not the algorithm which
MUST be specified when the key is generated.
Derivation of key pairs for the following algorithms is specified in
this document:
+=========+=======================+==============================+
| Code | Algorithm | Description |
+=========+=======================+==============================+
| 0 | Any | Seed MAY be used to generate |
| | | keypairs for any algorithm |
+---------+-----------------------+------------------------------+
| 1 | X25519 | X25519 keypair as described |
| | | in RFC7748 |
+---------+-----------------------+------------------------------+
| 2 | X448 | X448 keypair as described in |
| | | RFC7748 |
+---------+-----------------------+------------------------------+
| 3 | Ed25519 | Ed25519 keypair as described |
| | | in RFC8032 |
+---------+-----------------------+------------------------------+
| 4 | Ed448 | Ed448 keypair as described |
| | | in RFC8032 |
+---------+-----------------------+------------------------------+
| 5 | P256 | NIST curve P-256 |
+---------+-----------------------+------------------------------+
| 6 | P384 | NIST curve P-384 |
+---------+-----------------------+------------------------------+
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| 7 | P521 | NIST curve P-521 |
+---------+-----------------------+------------------------------+
| 8 | RSA2048 | 2048 bit RSA keypair |
+---------+-----------------------+------------------------------+
| 9 | RSA3072 | 3072 bit RSA keypair |
+---------+-----------------------+------------------------------+
| 10 | RSA4096 | 4096 bit RSA keypair |
+---------+-----------------------+------------------------------+
| 11-255 | ReservedIetf | Reserved for IETF |
| | | recommended algorithms |
+---------+-----------------------+------------------------------+
| 256 | MeshProfileDevice | Mesh device profile |
+---------+-----------------------+------------------------------+
| 257 | MeshActivationDevice | Mesh device activation |
+---------+-----------------------+------------------------------+
| 258 | MeshProfileAccount | Mesh account account |
+---------+-----------------------+------------------------------+
| 259 | MeshActivationAccount | Mesh account activation |
+---------+-----------------------+------------------------------+
| 260 | MeshProfileService | Mesh service profile |
+---------+-----------------------+------------------------------+
| 261 | MeshActivationService | Mesh host activation |
+---------+-----------------------+------------------------------+
| 262-511 | ReservedMesh | Reserved for future Mesh use |
+---------+-----------------------+------------------------------+
Table 3
The key parameter derivation function takes as inputs, the UDF seed
value seed, the parameter identifier param and an optional string
specifying a key name keyname.
KeyParam (seed, param, keyname)
The value param is an octet sequence determined by the actual key
type generated. The first two octets of parm are always equal to the
key identifier for the key algorithm and key usage being generated.
If the key derivation algorithm requires multiple inputs, additional
octets are specified for each of the different inputs required.
The HKDF function [RFC5869] is used to derive key pairs for all the
algorithms specified in this document. Derivation functions for
additional key algorithms MAY use a different function for this
purpose provided that it meets the applicable security requirements.
The HKDF function is specified as a two-step extract-expand process
with an optional non-secret value input at both steps.
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4.4.1. Extraction step
The HKDF extraction step calculates a PRK value from a salt and IKM:
HKDF-Extract(salt, IKM) -> PRK
The IKM value is the binary presentation of the complete Binary Data
Sequence as originally specified. The salt value is null.
The output from the extraction step forms the input to the expand
step:
HKDF-Expand(PRK, info, L) -> OKM
The info parameter of the HKDF function is the concatenation of alg,
param and the UTF8 binary representation of keyname.
info = alg + param + keyname.UTF8()
An X25519 key may be derived as follows:
Fingerprint =
ZAAA-CDJ5-DHPA-DUUW-WIPQ-UXNC-DSAR-U7A
IKM =
00 01 0D 3D 19 DE 01 D2 96 B2 1F 0A 5D A2 1C 81
1A 7C
salt =
00 01
PRK =
DA 2E 80 6F 2D B1 54 56 7E 27 B4 91 49 0A 35 3A
5D 99 92 AA A2 2F 2D 2A 50 4B 13 5B 87 DF 63 67
62 92 67 9C B3 B8 10 47 31 52 A2 42 FA 04 84 39
7A 64 15 84 C0 6B 51 F7 19 4A 20 35 BA 2E D1 59
OKM =
E7 22 39 E1 AB 77 AC 9C B4 6A A0 12 27 68 9E 28
14 60 2F A8 76 08 38 5E D5 E6 5D E7 0C C8 42 E8
Key =
E7 22 39 E1 AB 77 AC 9C B4 6A A0 12 27 68 9E 28
14 60 2F A8 76 08 38 5E D5 E6 5D E7 0C C8 42 E8
Derivation of an X448 key:
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Fingerprint =
ZAAA-FFQA-3LE5-SAHG-E6K6-HOTN-TVLB-K4A
Key =
AE 6A 6D 0B CC 48 C3 31 E7 55 0F 52 F9 96 83 C5
15 7C 8A 74 80 36 B7 E9 17 24 D7 DD A1 56 76 3C
15 00 68 B7 23 F5 DB 32 48 1B 72 C0 2E B0 22 45
A3 B8 80 67 B3 88 06 9F
Derivation of an Ed25519 key:
Fingerprint =
ZAAA-GZ5N-PSNF-7LMS-QJZN-3O2X-GJXV-X6I
Key =
3A 36 00 56 2E EC 2F 24 A7 8C 22 F3 A9 A2 EF 1B
6E AF 07 D4 99 28 53 A5 5B 0A CC EE 4C 3B 7D 30
Derivation of an Ed448 key:
Fingerprint =
ZAAA-ILZB-KTQV-YWUK-FO7E-MQVV-EWPR-UPA
Key =
DF 5A 89 B8 1D 56 92 41 32 D1 B2 C9 4F 74 69 E3
C9 E5 5F 23 33 A1 CE 22 54 08 EE 53 46 0F 9B 13
9D 54 95 2B F9 D9 77 2A FA 07 3C 9D 89 CC C5 0E
7E 86 7E 84 7C 58 5D 89
4.4.2. Elliptic Curve Diffie Hellman Key Pairs type 1-4
The generation of key pairs for X25519, X448, Ed25519 and Ed448 is
specified in [RFC7748] and [RFC8032]. In each case, the public and
private key parameters are generated from a string of random octets
whose transformation to the secret scalar function is described in
the document.
Thus, info is the null string and the value L is specified as
follows:
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+===========+=====+
| Algorithm | L |
+===========+=====+
| X25519 | 256 |
+-----------+-----+
| X448 | 448 |
+-----------+-----+
| Ed25519 | 256 |
+-----------+-----+
| Ed448 | 448 |
+-----------+-----+
Table 4
4.4.3. Elliptic Curve Diffie Hellman Key Pairs type 5-7
The generation of key pairs for the curves P-256, P-384 and P-521
described in [RFC5903] is not mandated by the specification. FIPS
186-4 specifies two approaches. A modified form of the mechanism Key
Pair Generation Using Extra Random Bits specified in B.4.1 is used as
follows:
The number of random bits L is given by the following table:
+===========+=====+
| Algorithm | L |
+===========+=====+
| P-256 | 320 |
+-----------+-----+
| P-384 | 448 |
+-----------+-----+
| P-521 | 592 |
+-----------+-----+
Table 5
Note that this rounds up the number of random bits required to the
nearest integer multiple of 8.
The OKM value is interpreted as an integer in Network Byte Order,
that is the first byte contains the most significant bits, to yield
the parameter c.
The parameter c is reduced modulo the value of the prime field n to
yield the secret scalar value d:
d = (c mod (n?1)) + 1.
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A P-256 key may be derived as follows:
Fingerprint =
ZAAA-LLBO-4A4E-LFMH-EJ73-XVFG-7PZ5-V7Y
IKM =
00 05 AC 2E E0 38 45 95 87 22 7F BB D4 A6 FB F3
DA FF
salt =
00 05
PRK =
0F 48 0F 0C 93 30 AE EE 41 FD 8F A2 1C C2 C6 CA
3A E1 4B 54 E7 83 C0 25 85 F0 CD 2A 65 3F 18 A7
9F 2A 5A ED 6A E3 64 6A 05 7D 1A 1A B8 68 B3 F3
4F A9 10 9A 05 E1 A4 9A 2C CC 40 43 36 8A 24 C0
OKM =
E2 00 EC 22 63 17 D5 E5 52 F9 CD B6 45 23 A9 8B
EF 32 26 E0 24 A0 E7 2B 7F CB C2 0B CB FA 0F 5C
59 D1 7C 4A D8 12 2E 4C
Key = 823521039787465146191678159095729811571036184098859836027994
10986678676075099
Derivation of a P-384 key:
Fingerprint =
ZAAA-NPLI-G7Z3-WFD2-GBJ6-OONN-ELTO-MHA
Key = 369049211431889063087900251703207474490953076630513949620729
23012683284321458397574918591433311657724460124046828583
Derivation of a P-521 key:
Fingerprint =
ZAAA-PQCC-YFVT-LRWP-7MUZ-GJV3-HLX2-JPQ
Key = 634654264002940134552342747000178673315150389242882127875899
96717989335708073735991026483008684752699986204269344550
4370476919922072068801363203357706689700
4.4.4. RSA Key Pairs
Generation of RSA key pairs requires two parameters, p, q which are
prime.
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The value of the param input used to calculate info is the value of
the key identifier value with one of the following tag values
concatenated to the end.
+===========+=======+========================+
| Parameter | Tag | UTF8 equivalent string |
+===========+=======+========================+
| p | [112] | p |
+-----------+-------+------------------------+
| q | [113] | q |
+-----------+-------+------------------------+
Table 6
The value of L is the same for generating the OKM values from which q
are derived and is determined by the algorithm identifier:
+===========+======+
| Algorithm | L |
+===========+======+
| RSA-2048 | 1024 |
+-----------+------+
| RSA-3072 | 1536 |
+-----------+------+
| RSA-4096 | 2048 |
+-----------+------+
Table 7
The RSA parameter p is the smallest prime integer that is greater
than the OKM value corresponding to the info value "p" interpreted as
an integer in Network Byte Order.
The RSA parameter q is the smallest prime integer that is greater
than the OKM value corresponding to the info value "q" interpreted as
an integer in Network Byte Order.
Note that this algorithm does not mandate a particular method of
primality testing nor does it impose any additional testing on the
values p or q. If an application requires the use of primes with
conditions it will be necessary to attempt multiple key derivations
with different Binary Data Sequence values until parameters with the
desired properties are found.
An RSA-2048 may be derived as follows:
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Fingerprint =
ZAAA-RJ5I-OSMI-X2KH-MBHX-KUPB-OC54-NQI
IKM =
00 08 A7 A8 74 98 8B E9 47 60 4F 75 51 E1 70 BB
C6 C1
salt =
00 08
[Generation of the PRK as before]
Info(p) =
70
OKM(p) =
92 D4 DA FA C4 22 DB 17 B0 04 93 C6 F1 D2 7A AF
34 6F 69 98 54 1A F5 F3 E3 ED DA 98 F5 64 EE 6A
Info(q) =
71
OKM(q) =
01 50 07 9F B3 53 70 5A 7E 95 63 BD 19 8D 52 59
2F EE 38 E7 8F D4 46 D9 4C 55 E6 DD 39 CA DB 36
Key P = 664137588122357253348380132353218815863396125741622195396345
89986848279686793
Key Q = 593713231506709718978311683387355253795918273379156509909895
725618914057069
4.4.5. Any Key Algorithm
The Any key algorithm allows a single UDF value to be used to derive
key pairs for multiple algorithms. The IKM value is the same for
each key pair derived. The salt value is changed according to the
algorithm for which the key is to be derived.
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Fingerprint =
ZAAA-A6WP-XMGW-FUOF-2T5L-AHNL-FBPY-RSY
To generate an RSA-2048 key
salt =
00 08
Key P = 184377705562733023433840697873299239654937691662139401284561
64676903354830137
Key Q = 741016989403010251265552685128898155357242513700210607224783
50575007811846521
To generate an X25519 key
salt =
00 08
Key =
System.Byte[]
4.5. Shamir Shared Secret
The UDF format MAY be used to encode shares generated by a secret
sharing mechanism. The only secret sharing mechanism currently
supported is the Shamir Secret Sharing mechanism [Shamir79]. Each
secret share represents a point represents a point _on (x, f(x))_, a
polynomial in a modular field _p_. The secret being shared is an
integer multiple of 32 bits represented by the polynomial value
_f(0)_.
A Shamir Shared Secret Type UDF consists of the type identifier octet
144 followed by the Binary Data Sequence value describing the share
value.
The first octet of the Binary Data Sequence value specifies the
threshold value and the x value of the particular share:
* Bits 4-7 of the first byte specify the threshold value.
* Bits 0-3 of the first byte specify the x value minus 1.
The remaining octets specify the value _f(x)_ in network byte (big-
endian) order with leading padding if necessary so that the share has
the same number of bytes as the secret.
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The algorithm requires that the value _p_ be a prime larger than the
integer representing the largest secret being shared. For
compactness of representation we chose _p_ to be the smallest prime
that is greater than 2_^n_ where _n_ is an integer multiple of 32.
This approach leaves a small probability that a set of chosen
polynomial parameters cause one or more share values be larger than
2_^n_. Since it is the value of the secret rather than the polynomial
parameters that is of important, such parameters MUST NOT be used.
4.5.1. Secret Generation
To share a secret of _L_ bits with a threshold of _n_ we use a _f(x)_
a polynomial of degree _n_ in the modular field _p_:
f(x) = a_0 + a_1.x + a_2.x^2 + ... a_n.x^n
where:
L Is the length of the secret in bits, an integer multiple of 32.
n Is the threshold, the number of shares required to reconstitute
the secret.
a_0 Is the integer representation of the secret to be shared.
a_1 ... a_n Are randomly chosen integers less than p
p Is the smallest prime that is greater than 2^L.
For L=128, p = 2^128+51.
The values of the key shares are the values _f_(1), _f_(2),..._f_(n).
The most straightforward approach to generation of Shamir secrets is
to generate the set of polynomial coefficients, a_0, a_1, ... a_n and
use these to generate the share values _f_(1), _f_(2),..._f_(n).
Note that if this approach is adopted, there is a small probability
that one or more of the values _f_(1), _f_(2),..._f_(n) exceeds the
range of values supported by the encoding. Should this occur, at
least one of the polynomial coefficients MUST be replaced.
An alternative means of generating the set of secrets is to select up
to _n-1_ secret share values and use secret recovery to determine at
least one additional share. If _n_ shares are selected, the shared
secret becomes an output of rather than an input to the process.
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4.5.2. Recovery
To recover the value of the shared secret, it is necessary to obtain
sufficient shares to meet the threshold and recover the value _f(0)_
= a_0.
Applications MAY employ any approach that returns the correct result.
The use of Lagrange basis polynomials is described in Appendix C.
Alice decides to encrypt an important document and split the
encryption key so that there are five key shares, three of which will
be required to recover the key.
Alice's master secret is
3E AF 8C 7C 4A 85 F7 EC 7E FC F0 B2 DF 9C F5 F0
This has the UDF representation:
H2XY-Y7CK-QX36-Y7X4-6CZN-7HHV-6A
The master secret is converted to an integer applying network byte
order conventions. Since the master secret is 128 bits, it is
guaranteed to be smaller than the modulus. The resulting value
becomes the polynomial value a0.
Since a threshold of three shares is required, we will need a second
order polynomial. The co-efficients of the polynomial a1, a2 are
random numbers smaller than the modulus:
a0 = 83323637073608890605557692967272904176
a1 = 255162942599465260402270874517662057695
a2 = 19137550451637655947705938030584278875
The master secret is the value f(0) = a0. The key shares are the
values f(1), f(2)...f(5):
f(1) = 17341763203773343492159898083751029239
f(2) = 329917357158151571737548586693165923559
f(3) = 203318173928184951599936500212952615
f(4) = 49046747013918573524437769800196750928
f(5) = 136165276757184273992687479161349106991
The first byte of each share specifies the recovery information
(quorum, x value), the remaining bytes specify the share value in
network byte order:
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f(1) =
30 0D 0B E6 F0 4E 0E CA 3A F1 2A 6F 3A 9B CE E9
F7
f(2) =
31 F8 33 C5 90 41 23 D3 AA F7 E5 E0 0B BB 6D 3C
E7
f(3) =
32 00 27 28 5C 23 C5 14 3C 93 2F 43 26 3E 77 EE
27
f(4) =
33 24 E6 0F 53 F5 F2 8B EF C3 06 98 8A 24 EE FE
50
f(5) =
34 66 70 7A 77 B7 AC 3A C4 87 6B E0 37 6E D2 6D
2F
The UDF presentation of the key shares is thus:
f(1) = SAYA-2C7G-6BHA-5SR2-6EVG-6OU3-Z3U7-O
f(2) = SAY7-QM6F-SBAS-HU5K-67S6-AC53-NU6O-O
f(3) = SAZA-AJZI-LQR4-KFB4-SMXU-GJR6-O7XC-O
f(4) = SAZS-JZQP-KP27-FC7P-YMDJ-RCRE-537F-A
f(5) = SA2G-M4D2-O632-YOWE-Q5V6-AN3O-2JWS-6
To recover the value f(0) from any three shares, we need to fit a
polynomial curve to the three points and use it to calculate the
value at x=0 using the Lagrange polynomial basis.
5. Variable Length UDFs
Variable length UDFs are used to represent fingerprint values
calculated over a content type identifier and the cryptographic
digest of a content data item. The fingerprint value MAY be
specified at any integer multiple of 20 bits that provides a work
factor sufficient for the intended purpose.
Two types of fingerprint are specified:
Digest fingerprints Are computed with the same cryptographic digest
algorithm used to calculate the digest of the content data.
Message Authentication Code fingerprints Are computed using a
Message Authentication Code.
For a given algorithm (and key, if requires), if two UDF fingerprints
are of the same content data and content type, either the fingerprint
values will be the same or the initial characters of one will be
exactly equal to the other.
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5.1. Content Digest
A Content Digest Type UDF consists of the type identifier octet
followed by the Binary Data Sequence value.
The type identifier specifies the digest algorithm used and the
compression level. Two digest algorithms are currently specified
with four compression levels for each making a total of eight
possible type identifiers.
The Content Digest UDF for given content data is generated by the
steps of:
0. Applying the digest algorithm to determine the Content Digest
Value
1. Applying the digest algorithm to determine the Typed Content
Digest Value
2. Determining the compression level from bytes 0-3 of the Typed
Content Digest Value.
3. Determining the Type Identifier octet from the Digest algorithm
identifier and compression level.
4. Truncating bytes 4-63 of the Typed Content Digest Value to
determine the Binary Data Sequence value.
5.1.1. Content Digest Value
The Content Digest Value (CDV) is determined by applying the digest
algorithm to the content data:
CDV = H(<Data>)
Where
H(x) is the cryptographic digest function
<Data> is the binary data.
5.1.2. Typed Content Digest Value
The Typed Content Digest Value (TCDV) is determined by applying the
digest algorithm to the content type identifier and the CDV:
TCDV = H (<Content-ID> + ?:? + CDV)
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Where
A + B represents concatenation of the binary sequences A and B.
<Content-ID> is the IANA Content Type of the data in UTF8 encoding
The two-step approach to calculating the Type Content Digest Value
allows an application to attempt to match a set of content data
against multiple types without the need to recalculate the value of
the content data digest.
5.1.3. Content Digest Compression
The compression factor is determined according to the number of
trailing zero bits in the first 8 bytes of the Typed Content Digest
Value as follows:
19 or fewer trailing zero bits Compression factor = 0
29 or fewer trailing zero bits Compression factor = 20
39 or fewer trailing zero bits Compression factor = 30
49 or fewer trailing zero bits Compression factor = 40
50 or more trailing zero bits Compression factor = 50
The least significant bits of each octet are regarded to be
'trailing'.
Applications MUST use compression when creating and comparing UDFs.
Applications MAY support content generation techniques that search
for UDF values that use a compressed representation. Presentation of
a content digest value indicating use of compression MAY be used as
an indicator of 'proof of work'.
5.1.4. Content Digest Presentation
The type identifier is determined by the algorithm and compression
factor as specified above.
The Binary Data Sequence value is taken from the Typed Content Digest
Value starting at the 9^th octet and as many additional bytes as are
required to meet the presentation precision.
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5.1.5. Example Encoding
In the following examples, <Content-ID> is the UTF8 encoding of the
string "text/plain" and <Data> is the UTF8 encoding of the string
"UDF Data Value"
Data =
55 44 46 20 44 61 74 61 20 56 61 6C 75 65
ContentType =
74 65 78 74 2F 70 6C 61 69 6E
5.1.6. Using SHA-2-512 Digest
H(<Data>) =
48 DA 47 CC AB FE A4 5C 76 61 D3 21 BA 34 3E 58
10 87 2A 03 B4 02 9D AB 84 7C CE D2 22 B6 9C AB
02 38 D4 E9 1E 2F 6B 36 A0 9E ED 11 09 8A EA AC
99 D9 E0 BD EA 47 93 15 BD 7A E9 E1 2E AD C4 15
<Content-ID> + ':' + H(<Data>) =
74 65 78 74 2F 70 6C 61 69 6E 3A 48 DA 47 CC AB
FE A4 5C 76 61 D3 21 BA 34 3E 58 10 87 2A 03 B4
02 9D AB 84 7C CE D2 22 B6 9C AB 02 38 D4 E9 1E
2F 6B 36 A0 9E ED 11 09 8A EA AC 99 D9 E0 BD EA
47 93 15 BD 7A E9 E1 2E AD C4 15
H(<Content-ID> + ':' + H(<Data>)) =
C6 AF B7 C0 FE BE 04 E5 AE 94 E3 7B AA 5F 1A 40
5B A3 CE CC 97 4D 55 C0 9E 61 E4 B0 EF 9C AE F9
EB 83 BB 9D 5F 0F 39 F6 5F AA 06 DC 67 2A 67 71
4F FF 8F 83 C4 55 38 36 38 AE 42 7A 82 9C 85 BB
The prefixed Binary Data Sequence is thus
60 C6 AF B7 C0 FE BE 04 E5 AE 94 E3 7B AA 5F 1A
40 5B A3 CE CC 97 4D 55 C0 9E 61 E4 B0 EF 9C AE
F9 EB 83 BB 9D 5F 0F 39 F6 5F AA 06 DC 67 2A 67
71 4F FF 8F 83 C4 55 38 36 38 AE 42 7A 82 9C 85
The 125 bit fingerprint value is MDDK-7N6A-727A-JZNO-STRX-XKS7-DJAF
This fingerprint MAY be specified with higher or lower precision as
appropriate.
100 bit precision MDDK-7N6A-727A-JZNO-STRX
120 bit precision MDDK-7N6A-727A-JZNO-STRX-XKS7
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200 bit precision MDDK-7N6A-727A-JZNO-STRX-XKS7-DJAF-XI6O-ZSLU-2VOA
260 bit precision MDDK-7N6A-727A-JZNO-STRX-XKS7-DJAF-XI6O-ZSLU-2VOA-
TZQ6-JMHP-TSXP
5.1.7. Using SHA-3-512 Digest
H(<Data>) =
6D 2E CF E6 93 5A 0C FC F2 A9 1A 49 E0 0C D8 07
A1 4E 70 AB 72 94 6E CC BB 47 48 F1 8E 41 49 95
07 1D F3 6E 0D 0C 8B 60 39 C1 8E B4 0F 6E C8 08
65 B4 C4 45 9B A2 7E 97 74 7B BE 68 BC A8 C2 17
<Content-ID> + ':' + H(<Data>) =
74 65 78 74 2F 70 6C 61 69 6E 3A 6D 2E CF E6 93
5A 0C FC F2 A9 1A 49 E0 0C D8 07 A1 4E 70 AB 72
94 6E CC BB 47 48 F1 8E 41 49 95 07 1D F3 6E 0D
0C 8B 60 39 C1 8E B4 0F 6E C8 08 65 B4 C4 45 9B
A2 7E 97 74 7B BE 68 BC A8 C2 17
H(<Content-ID> + ':' + H(<Data>)) =
8A 86 8A 06 1C 54 6E 7E 3F 75 5F 39 88 F9 FD 2F
8E C8 45 93 1B 80 A8 2F 29 16 7B A3 BE 21 1F 8A
75 61 88 A1 D5 7F 07 D5 9D 68 A4 2D 17 F4 4D 23
F9 E4 0B B2 1A 8D B9 F5 8D FC EC BD 01 F4 37 7C
The prefixed Binary Data Sequence is thus
50 8A 86 8A 06 1C 54 6E 7E 3F 75 5F 39 88 F9 FD
2F 8E C8 45 93 1B 80 A8 2F 29 16 7B A3 BE 21 1F
8A 75 61 88 A1 D5 7F 07 D5 9D 68 A4 2D 17 F4 4D
23 F9 E4 0B B2 1A 8D B9 F5 8D FC EC BD 01 F4 37
The 125 bit fingerprint value is KCFI-NCQG-DRKG-47R7-OVPT-TCHZ-7UXY
5.1.8. Using SHA-2-512 Digest with Compression
The content data "UDF Compressed Document 4187123" produces a UDF
Content Digest SHA-2-512 binary value with 20 trailing zeros and is
therefore presented using compressed presentation:
Data = "
55 44 46 20 43 6F 6D 70 72 65 73 73 65 64 20 44
6F 63 75 6D 65 6E 74 20 34 31 38 37 31 32 33"
The UTF8 Content Digest is given as:
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H(<Data>) =
36 21 FA 2A C5 D8 62 5C 2D 0B 45 FB 65 93 FC 69
C1 ED F7 00 AE 6F E3 3D 38 13 FE AB 76 AA 74 13
6D 5A 2B 20 DE D6 A5 CF 6C 04 E6 56 3F F3 C0 C7
C4 1D 3F 43 DD DC F1 A5 67 A7 E0 67 9A B0 C6 B7
<Content-ID> + ':' + H(<Data>) =
74 65 78 74 2F 70 6C 61 69 6E 3A 36 21 FA 2A C5
D8 62 5C 2D 0B 45 FB 65 93 FC 69 C1 ED F7 00 AE
6F E3 3D 38 13 FE AB 76 AA 74 13 6D 5A 2B 20 DE
D6 A5 CF 6C 04 E6 56 3F F3 C0 C7 C4 1D 3F 43 DD
DC F1 A5 67 A7 E0 67 9A B0 C6 B7
H(<Content-ID> + ':' + H(<Data>)) =
8E 14 D9 19 4E D6 02 12 C3 30 A7 BB 5F C7 17 6D
AE 9A 56 7C A8 2A 23 1F 96 75 ED 53 10 EC E8 F2
60 14 24 D0 C8 BC 55 3D C0 70 F7 5E 86 38 1A 0B
CB 55 9C B2 87 81 27 FF 3C EC E2 F0 90 A0 00 00
The prefixed Binary Data Sequence is thus
61 8E 14 D9 19 4E D6 02 12 C3 30 A7 BB 5F C7 17
6D AE 9A 56 7C A8 2A 23 1F 96 75 ED 53 10 EC E8
F2 60 14 24 D0 C8 BC 55 3D C0 70 F7 5E 86 38 1A
0B CB 55 9C B2 87 81 27 FF 3C EC E2 F0 90 A0 00
The 125 bit fingerprint value is MGHB-JWIZ-J3LA-EEWD-GCT3-WX6H-C5W2
5.1.9. Using SHA-3-512 Digest with Compression
The content data "UDF Compressed Document 774665" produces a UDF
Content Digest SHA-3-512 binary value with 20 trailing zeros and is
therefore presented using compressed presentation:
Data =
55 44 46 20 43 6F 6D 70 72 65 73 73 65 64 20 44
6F 63 75 6D 65 6E 74 20 37 37 34 36 36 35
The UTF8 SHA-3-512 Content Digest is KEJI-Y225-BDUG-XX22-MXKE-5ITF-
YVYM
5.2. Authenticator UDF
An authenticator Type UDF consists of the type identifier octet
followed by the Binary Data Sequence value.
The type identifier specifies the digest and Message Authentication
Code algorithm. Two algorithm suites are currently specified. Use
of compression is not supported.
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The Authenticator UDF for given content data and key is generated by
the steps of:
0. Applying the digest algorithm to determine the Content Digest
Value
1. Applying the MAC algorithm to determine the Authentication value
2. Determining the Type Identifier octet from the Digest algorithm
identifier and compression level.
3. Truncating the Authentication value to determine the Binary Data
Sequence value.
The key used to calculate and Authenticator type UDF is always a
UNICODE string. If use of a binary value as a key is required, the
value MUST be converted to a string format first. For example, by
conversion to an Encryption/Authentication type UDF.
5.2.1. Authentication Content Digest Value
The Content Digest Value (CDV) is determined in the exact same
fashion as for a Content Digest UDF by applying the digest algorithm
to the content data:
CDV = H(<Data>))
Where
H(x) is the cryptographic digest function
<Data> is the binary data.
5.2.2. Authentication Value
The Authentication Value (AV) is determined by applying the digest
algorithm to the content type identifier and the CDV:
AV = MAC (<OKM>, (<Content-ID> + ?:? + CDV))
Where
<OKM> is the authentication key as specified below
MAC( <Key>, <data>) is the result of applying the Message
Authentication Code algorithm to with Key <Key> and data <data>
The value <OKM> is calculated as follows:
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IKM = UTF8 (Key)
PRK = MAC (UTF8 ("KeyedUDFMaster"), IKM)
OKM = HKDF-Expand(PRK, UTF8 ("KeyedUDFExpand"), HashLen)
Where the function UTF8(string) converts a string to the binary UTF8
representation, HKDF-Expand is as defined in [RFC5869] and the
function MAC(k,m) is the HMAC function formed from the specified hash
H(m) as specified in [RFC2014].
Keyed UDFs are typically used in circumstances where user interaction
requires a cryptographic commitment type functionality
In the following example, <Content-ID> is the UTF8 encoding of the
string "text/plain" and <Data> is the UTF8 encoding of the string
"Konrad is the traitor". The randomly chosen key is NDD7-6CMX-H2FW-
ISAL-K4VB-DQ3E-PEDM.
Data =
4B 6F 6E 72 61 64 20 69 73 20 74 68 65 20 74 72
61 69 74 6F 72
ContentType =
74 65 78 74 2F 70 6C 61 69 6E
Key =
4E 44 44 37 2D 36 43 4D 58 2D 48 32 46 57 2D 49
53 41 4C 2D 4B 34 56 42 2D 44 51 33 45 2D 50 45
44 4D
Processing is performed in the same manner as an unkeyed fingerprint
except that compression is never used:
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H(<Data>) =
93 FC DA F9 FA FD 1E 26 50 26 C3 C1 28 43 40 73
D8 BC 3D 62 87 73 2B 73 B8 EC 93 B6 DE 80 FF DA
70 0A D1 CE E8 F4 36 68 EF 4E 71 63 41 53 91 5C
CE 8C 5C CE C7 9A 46 94 6A 35 79 F9 33 70 85 01
<Content-ID> + ':' + H(<Data>) =
74 65 78 74 2F 70 6C 61 69 6E 3A 93 FC DA F9 FA
FD 1E 26 50 26 C3 C1 28 43 40 73 D8 BC 3D 62 87
73 2B 73 B8 EC 93 B6 DE 80 FF DA 70 0A D1 CE E8
F4 36 68 EF 4E 71 63 41 53 91 5C CE 8C 5C CE C7
9A 46 94 6A 35 79 F9 33 70 85 01
PRK(Key) =
77 D3 0A 08 39 BD 9D C0 97 44 DA 33 15 0A 42 5E
CD 17 80 03 B3 CF CC 89 7A C7 84 12 B4 51 5B 25
DC 26 F5 E1 1B 20 F3 89 2E 9A 1A 7B 0E 73 23 39
0E C3 4C EF 2D 40 DA 05 B4 70 C6 1C 82 C1 49 33
HKDF(Key) =
BF A9 B4 58 9C 1D 68 D7 9A B7 11 F6 C8 98 59 14
20 D7 82 67 C5 84 22 E5 A0 F9 93 52 B1 C3 87 EB
05 06 CB C4 E4 D6 E6 EE 1F F0 D4 7A 97 68 5E CE
28 1C CA AF D8 B5 D1 24 4A 71 EC E3 AC B5 D2 04
MAC(<key>, <Content-ID> + ':' + H(<Data>)) =
4C C3 7F D3 F9 9E 52 CF 07 90 74 53 84 65 95 BC
1A 2B A5 D1 68 9D 05 6D 06 C5 CA BF 17 CB E0 49
95 39 57 08 79 C4 E5 49 D3 3A 59 A3 32 05 45 A6
30 26 25 AE 8A F4 47 C6 1F B5 33 7F AD 69 A6 30
The prefixed Binary Data Sequence is thus
00 4C C3 7F D3 F9 9E 52 CF 07 90 74 53 84 65 95
BC 1A 2B A5 D1 68 9D 05 6D 06 C5 CA BF 17 CB E0
49 95 39 57 08 79 C4 E5 49 D3 3A 59 A3 32 05 45
A6 30 26 25 AE 8A F4 47 C6 1F B5 33 7F AD 69 A6
The 125 bit fingerprint value is ABGM-G76T-7GPF-FTYH-SB2F-HBDF-SW6B
5.3. Content Type Values
While a UDF fingerprint MAY be used to identify any form of static
data, the use of a UDF fingerprint to identify a public key signature
key provides a level of indirection and thus the ability to identify
dynamic data. The content types used to identify public keys are
thus of particular interest.
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As described in the security considerations section, the use of
fingerprints to identify a bare public key and the use of
fingerprints to identify a public key and associated security policy
information are quite different.
application/pkix-cert A PKIX Certificate
application/pkix-crl A PKIX CRL
application/pkix-keyinfo Content type identifier for PKIX KeyInfo
data type
application/pgp-keys Content type identifier for OpenPGP Key
application/dns A DNS resource record in binary format
application/udf-encryption UDF Fingerprint list
application/udf-lock UDF Fingerprint list
5.3.1. PKIX Certificates and Keys
UDF fingerprints MAY be used to identify PKIX certificates, CRLs and
public keys in the ASN.1 encoding used in PKIX certificates.
Since PKIX certificates and CLRs contain security policy information,
UDF fingerprints used to identify certificates or CRLs SHOULD be
presented with a minimum of 200 bits of precision. PKIX applications
MUST not accept UDF fingerprints specified with less than 200 bits of
precision for purposes of identifying trust anchors.
PKIX certificates, keys and related content data are identified by
the following content types:
application/pkix-cert A PKIX Certificate
application/pkix-crl A PKIX CRL
application/pkix-keyinfo The SubjectPublicKeyInfo structure defined
in the PKIX certificate specification encoded using DER encoding
rules.
The SubjectPublicKeyInfo structure is defined in [RFC5280] as
follows:
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SubjectPublicKeyInfo ::= SEQUENCE {
algorithm AlgorithmIdentifier,
subjectPublicKey BIT STRING }
This schema results in an identical DER encoding to the OIDInfo
sequence specified in section XXX. The distinction between these
productions is that the OIDInfo schema is intended to be used to
encode arbitrary data while the application/pkix-keyinfo content type
is only intended to be used to describe public keys.
5.3.2. OpenPGP Key
OpenPGPv5 keys and key set content data are identified by the
following content type:
application/pgp-keys An OpenPGP key set.
5.3.3. DNSSEC
DNSSEC record data consists of DNS records which are identified by
the following content type:
application/dns A DNS resource record in binary format
6. UDF URIs
The UDF URI scheme describes a means of constructing URIs from a UDF
value.
Two forms or UDF URI are specified, Name and Locator. In both cases
the URI MUST specify the scheme type "UDF", and a UDF fingerprint and
MAY specify a query identifier and/or a fragment identifier.
By definition a Locator form URI contains an authority field which
MUST be a DNS domain name. The use of IP address forms for this
purpose is not permitted.
Name Form URIs allow static content data to be identified without
specifying the means by which the content data may be retrieved.
Locator form URIs allow static content data or dynamic network
resources to be identified and the means of retrieval.
The syntax of a UDF URI is a subset of the generic URI syntax
specified in [RFC3986]. The use of userinfo and port numbers is not
supported and the path part of the uri is a UDF in base32
presentation.
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URI = "UDF:" udf [ "?" query ] [ "" fragment ]
udf = name-form / locator-form
name-form = udf-value
locator-form = "//" authority "/" udf-value
authority = host
host = reg-name
6.1. Name form URI
Name form UDF URIs provide a means of presenting a UDF value in a
context in which a URI form of a name is required without providing a
means of resolution.
Adding the UDF scheme prefix to a UDF fingerprint does not change the
semantics of the fingerprint itself. The semantics of the name
result from the context in which it is used.
For example, a UDF value of any type MAY be used to give a unique
targetNamespace value in an XML Schema [XMLSchema]
6.2. Locator form URI
The locator form of an unkeyed UDF URI is resolved by the following
steps:
* Use DNS Web service discovery to determine the Web Service
Endpoint.
* Determine the content identifier from the source URI.
* Append the content identifier to the Web Service Endpoint as a
suffix to form the target URI.
* Retrieve content from the Web Service Endpoint by means of a GET
method.
* Perform post processing as specified by the UDF type.
6.2.1. DNS Web service discovery
DNS Web Discovery is performed as specified in
[draft-hallambaker-web-service-discovery] for the service mmm-udf and
domain name specified in the URI. For a full description of the
discovery mechanism, consult the referenced specification.
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The use of DNS Web Discovery permits service providers to make full
use of the load balancing and service description capabilities
afforded by use of DNS SRV and TXT records in accordance with the
approach described in [RFC6763].
If no SRV or TXT records are specified, DNS Web Discovery specifies
that the Web Service Endpoint be the Well Known Service [RFC5785]
with the prefix /.well-known/srv/mmm-udf.
6.2.2. Content Identifier
For all UDF types other than Secret Share, the Content Identifier
value is the UDF SHA-2-512 Content Digest of the canonical form of
the UDF specified in the source URI presented at twice the precision
to a maximum of 440 bits.
If the UDF is of type Secret Share, the shared secret MUST be
recovered before the content identifier can be resolved. The shared
secret is then expressed as a UDF of type Encryption/Authentication
and the Content Identifier determined as for an Encryption/
Authentication type UDF.
6.2.3. Target URI
The target URI is formed by appending a slash separator '/' and the
Content Identifier value to the Web Service Endpoint.
Since the path portion of a URI is case sensitive, the UDF value MUST
be specified in upper case and MUST include separator marks.
6.2.4. Postprocessing
After retrieving the content data, the resolver MUST perform post
processing as indicated by the content type:
Nonce No additional post processing is required.
Content Digest The resolver MUST verify that the content returned
matches the UDF fingerprint value.
Authenticator The resolver MUST verify that the content returned
matches the UDF fingerprint value.
Encryption/Authentication The content data returned is decrypted and
authenticated using the key specified in the UDF value as the
initial keying material (see below).
Secret Share (set) The content data returned is decrypted and
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authenticated using the shared secret as the initial keying
material (see below).
6.2.5. Decryption and Authentication
The steps performed to decode cryptographically enhanced content data
depends on the content type specified in the returned content. Two
formats are currently supported:
* DARE Envelope format as specified in [draft-hallambaker-mesh-dare]
* Cryptographic Message Syntax (CMS) Symmetric Key Package as
specified in [RFC6031]
6.2.6. QR Presentation
Encoding of a UDF URI as a QR code requires only the characters in
alphanumeric encoding, thus achieving compactness with minimal
overhead.
7. Strong Internet Names
A Strong Internet Name is an Internet address that is bound to a
policy governing interpretation of that address by means of a Content
Digest type UDF of the policy expressed as a UDF prefixed DNS label
within the address itself.
The Reserved LDH labels as defined in [RFC5890] that begin with the
prefix mm-- are reserved for use as Strong Internet Names. The
characters following the prefix are a Content Digest type UDF in
Base32 presentation.
Since DNS labels are limited to 63 characters, the presentation of
the SIN itself is limited to 59 characters and thus 240 bits of
precision.
8. Security Considerations
This section describes security considerations arising from the use
of UDF in general applications.
Additional security considerations for use of UDFs in Mesh services
and applications are described in the Mesh Security Considerations
guide [draft-hallambaker-mesh-security].
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8.1. Confidentiality
Encrypted locator is a bearer token
8.2. Availability
Corruption of a part of a shared secret may prevent recovery
8.3. Integrity
Shared secret parts do not contain context information to specify
which secret they relate to.
8.4. Work Factor and Precision
A given UDF data object has a single fingerprint value that may be
presented at different precisions. The shortest legitimate precision
with which a UDF fingerprint may be presented has 96 significant bits
A UDF fingerprint presents the same work factor as any other
cryptographic digest function. The difficulty of finding a second
data item that matches a given fingerprint is 2^n and the difficulty
or finding two data items that have the same fingerprint is 2^(n/2).
Where n is the precision of the fingerprint.
For the algorithms specified in this document, n = 512 and thus the
work factor for finding collisions is 2^256, a value that is
generally considered to be computationally infeasible.
Since the use of 512 bit fingerprints is impractical in the type of
applications where fingerprints are generally used, truncation is a
practical necessity. The longer a fingerprint is, the less likely it
is that a user will check every character. It is therefore important
to consider carefully whether the security of an application depends
on second pre-image resistance or collision resistance.
In most fingerprint applications, such as the use of fingerprints to
identify public keys, the fact that a malicious party might generate
two keys that have the same fingerprint value is a minor concern.
Combined with a flawed protocol architecture, such a vulnerability
may permit an attacker to construct a document such that the
signature will be accepted as valid by some parties but not by
others.
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For example, Alice generates keypairs until two are generated that
have the same 100 bit UDF presentation (typically 2^48 attempts).
She registers one keypair with a merchant and the other with her
bank. This allows Alice to create a payment instrument that will be
accepted as valid by one and rejected by the other.
The ability to generate of two PKIX certificates with the same
fingerprint and different certificate attributes raises very
different and more serious security concerns. For example, an
attacker might generate two certificates with the same key and
different use constraints. This might allow an attacker to present a
highly constrained certificate that does not present a security risk
to an application for purposes of gaining approval and an
unconstrained certificate to request a malicious action.
In general, any use of fingerprints to identify data that has
security policy semantics requires the risk of collision attacks to
be considered. For this reason, the use of short, 'user friendly'
fingerprint presentations (Less than 200 bits) SHOULD only be used
for public key values.
8.5. Semantic Substitution
Many applications record the fact that a data item is trusted, rather
fewer record the circumstances in which the data item is trusted.
This results in a semantic substitution vulnerability which an
attacker may exploit by presenting the trusted data item in the wrong
context.
The UDF format provides protection against high level semantic
substitution attacks by incorporating the content type into the input
to the outermost fingerprint digest function. The work factor for
generating a UDF fingerprint that is valid in both contexts is thus
the same as the work factor for finding a second preimage in the
digest function (2^512 for the specified digest algorithms).
It is thus infeasible to generate a data item such that some
applications will interpret it as a PKIX key and others will accept
as an OpenPGP key. While attempting to parse a PKIX key as an
OpenPGP key is virtually certain to fail to return the correct key
parameters it cannot be assumed that the attempt is guaranteed to
fail with an error message.
The UDF format does not provide protection against semantic
substitution attacks that do not affect the content type.
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8.6. QR Code Scanning
The act of scanning a QR code SHOULD be considered equivalent to
clicking on an unlabeled hypertext link. Since QR codes are scanned
in many different contexts, the mere act of scanning a QR code MUST
NOT be interpreted as constituting an affirmative acceptance of terms
or conditions or as creating an electronic signature.
If such semantics are required in the context of an application,
these MUST be established by secondary user actions made subsequent
to the scanning of the QR code.
There is a risk that use of QR codes to automate processes such as
payment will lead to abusive practices such as presentation of
fraudulent invoices for goods not ordered or delivered. It is
therefore important to ensure that such requests are subject to
adequate accountability controls.
9. IANA Considerations
Registrations are requested in the following registries:
* Service Name and Transport Protocol Port Number
* well-known URI registry
* Uniform Resource Identifier (URI) Schemes
* Media Types
In addition, the creation of the following registry is requested:
Uniform Data Fingerprint Type Identifier Registry.
9.1. Protocol Service Name
The following registration is requested in the Service Name and
Transport Protocol Port Number Registry in accordance with [RFC6355]
Service Name (REQUIRED) mmm-udf
Transport Protocol(s) (REQUIRED) TCP
Assignee (REQUIRED) Phillip Hallam-Baker, phill@hallambaker.com
Contact (REQUIRED) Phillip Hallam-Baker, phill@hallambaker.com
Description (REQUIRED) mmm-udf is a Web Service protocol that
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resolves Mathematical Mesh Uniform Data Fingerprints (UDF) to
resources. The mmm-udf service name is used in service discovery
to identify a Web Service endpoint to perform resolution of a UDF
presented in URI locator form.
Reference (REQUIRED) [This document]
Port Number (OPTIONAL) None
Service Code (REQUIRED for DCCP only) None
Known Unauthorized Uses (OPTIONAL) None
Assignment Notes (OPTIONAL) None
9.2. Well Known
The following registration is requested in the well-known URI
registry in accordance with [RFC5785]
URI suffix srv/mmm-udf
Change controller Phillip Hallam-Baker, phill@hallambaker.com
Specification document(s): [This document]
Related information
[draft-hallambaker-web-service-discovery]
9.3. URI Registration
The following registration is requested in the Uniform Resource
Identifier (URI) Schemes registry in accordance with [RFC7595]
Scheme name: UDF
Status: Provisional
Applications/protocols that use this scheme name: Mathematical Mesh
Service protocols (mmm)
Contact: Phillip Hallam-Baker mailto:phill@hallambaker.com
Change controller: Phillip Hallam-Baker
References: [This document]
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9.4. Media Types Registrations
9.4.1. Media Type: application/pkix-keyinfo
Type name: application
Subtype name: pkix-keyinfo
Required parameters: None
Optional parameters: None
Encoding considerations: Binary
Security considerations: Described in [This]
Interoperability considerations: None
Published specification: [This]
Applications that use this media type: Uniform Data Fingerprint
Fragment identifier considerations: None
Additional information: Deprecated alias names for this type: None
Magic number(s): None
File extension(s): None
Macintosh file type code(s): None
Person & email address to contact for further information: Phillip
Hallam-Baker @hallambaker.com>
Intended usage: Content type identifier to be used in constructing
UDF Content Digests and Authenticators and related cryptographic
purposes.
Restrictions on usage: None
Author: Phillip Hallam-Baker
Change controller: Phillip Hallam-Baker
Provisional registration? (standards tree only): Yes
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9.4.2. Media Type: application/udf
Type name: application
Subtype name: udf
Required parameters: None
Optional parameters: None
Encoding considerations: None
Security considerations: Described in [This]
Interoperability considerations: None
Published specification: [This]
Applications that use this media type: Uniform Data Fingerprint
Fragment identifier considerations: None
Additional information: Deprecated alias names for this type: None
Magic number(s): None
File extension(s): None
Macintosh file type code(s): None
Person & email address to contact for further information: Phillip
Hallam-Baker @hallambaker.com>
Intended usage: Content type identifier to be used in constructing
UDF Content Digests and Authenticators and related cryptographic
purposes.
Restrictions on usage: None
Author: Phillip Hallam-Baker
Change controller: Phillip Hallam-Baker
Provisional registration? (standards tree only): Yes
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9.5. Uniform Data Fingerprint Type Identifier Registry
This document describes a new extensible data format employing fixed
length version identifiers for UDF types.
9.5.1. The name of the registry
Uniform Data Fingerprint Type Identifier Registry
9.5.2. Required information for registrations
Registrants must specify the Type identifier code(s) requested,
description and RFC number for the corresponding standards action
document.
The standards document must specify the means of generating and
interpreting the UDF Data Sequence Value and the purpose(s) for which
it is proposed.
Since the initial letter of the Base32 presentation provides a
mnemonic function in UDFs, the standards document must explain why
the proposed Type Identifier and associated initial letter are
appropriate. In cases where a new initial letter is to be created,
there must be an explanation of why this is appropriate. If an
existing initial letter is to be created, there must be an
explanation of why this is appropriate and/or acceptable.
9.5.3. Applicable registration policy
Due to the intended field of use (human data entry), the code space
is severely constrained. Accordingly, it is intended that code point
registrations be as infrequent as possible.
Registration of new digest algorithms is strongly discouraged and
should not occur unless, (1) there is a known security vulnerability
in one of the two schemes specified in the original assignment and
(2) the proposed algorithm has been subjected to rigorous peer
review, preferably in the form of an open, international competition
and (3) the proposed algorithm has been adopted as a preferred
algorithm for use in IETF protocols.
Accordingly, the applicable registration policy is Standards Action.
9.5.4. Size, format, and syntax of registry entries
Each registry entry consists of a single byte code,
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9.5.5. Initial assignments and reservations
The following entries should be added to the registry as initial
assignments:
Code Description Reference
---- ---------------------------------------- ---------
0 HMAC_SHA_2_512 [This document]
1 HMAC_SHA_3_512 [This document]
32 HKDF_AES_512 [This document]
33 HKDF_AES_512 [This document]
80 SHA_3_512 [This document]
81 SHA_3_512 (20 compressed) [This document]
82 SHA_3_512 (30 compressed) [This document]
83 SHA_3_512 (40 compressed) [This document]
84 SHA_3_512 (50 compressed) [This document]
96 SHA_2_512 [This document]
97 SHA_2_512 (20 compressed) [This document]
98 SHA_2_512 (30 compressed) [This document]
99 SHA_2_512 (40 compressed) [This document]
100 SHA_2_512 (50 compressed) [This document]
104 Nonce Data [This document]
112 OID distinguished sequence (DER encoded) [This document]
144 Shamir Secret Share [This document]
200 Secret seed [This document]
10. Acknowledgements
A list of people who have contributed to the design of the Mesh is
presented in [draft-hallambaker-mesh-architecture].
Thanks are due to Viktor Dukhovni, Damian Weber and an anonymous
member of the cryptography@metzdowd.com list for assisting in the
compilation of the table of prime values.
11. Appendix A: Prime Values for Secret Sharing
The following are the prime values to be used for sharing secrets of
up to 512 bits.
If it is necessary to share larger secrets, the corresponding prime
may be found by choosing a value (2^8)^n that is larger than the
secret to be encoded and determining the next largest number that is
prime.
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+=======+======+============+
| Bytes | Bits | Prime |
+=======+======+============+
| 1 | 8 | 2^8+1 |
+-------+------+------------+
| 2 | 16 | 2^16+1 |
+-------+------+------------+
| 3 | 24 | 2^24+43 |
+-------+------+------------+
| 4 | 32 | 2^32+15 |
+-------+------+------------+
| 5 | 40 | 2^40+15 |
+-------+------+------------+
| 6 | 48 | 2^48+21 |
+-------+------+------------+
| 7 | 56 | 2^56+81 |
+-------+------+------------+
| 8 | 64 | 2^64+13 |
+-------+------+------------+
| 9 | 72 | 2^72+15 |
+-------+------+------------+
| 10 | 80 | 2^80+13 |
+-------+------+------------+
| 11 | 88 | 2^88+7 |
+-------+------+------------+
| 12 | 96 | 2^96+61 |
+-------+------+------------+
| 13 | 104 | 2^104+111 |
+-------+------+------------+
| 14 | 112 | 2^112+25 |
+-------+------+------------+
| 15 | 120 | 2^120+451 |
+-------+------+------------+
| 16 | 128 | 2^128+51 |
+-------+------+------------+
| 17 | 136 | 2^136+85 |
+-------+------+------------+
| 18 | 144 | 2^144+175 |
+-------+------+------------+
| 19 | 152 | 2^152+253 |
+-------+------+------------+
| 20 | 160 | 2^160+7 |
+-------+------+------------+
| 21 | 168 | 2^168+87 |
+-------+------+------------+
| 22 | 176 | 2^176+427 |
+-------+------+------------+
| 23 | 184 | 2^184+27 |
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+-------+------+------------+
| 24 | 192 | 2^192+133 |
+-------+------+------------+
| 25 | 200 | 2^200+235 |
+-------+------+------------+
| 26 | 208 | 2^208+375 |
+-------+------+------------+
| 27 | 216 | 2^216+423 |
+-------+------+------------+
| 28 | 224 | 2^224+735 |
+-------+------+------------+
| 29 | 232 | 2^232+357 |
+-------+------+------------+
| 30 | 240 | 2^240+115 |
+-------+------+------------+
| 31 | 248 | 2^248+81 |
+-------+------+------------+
| 32 | 256 | 2^256+297 |
+-------+------+------------+
| 33 | 264 | 2^264+175 |
+-------+------+------------+
| 34 | 272 | 2^272+57 |
+-------+------+------------+
| 35 | 280 | 2^280+45 |
+-------+------+------------+
| 36 | 288 | 2^288+127 |
+-------+------+------------+
| 37 | 296 | 2^296+61 |
+-------+------+------------+
| 38 | 304 | 2^304+37 |
+-------+------+------------+
| 39 | 312 | 2^312+91 |
+-------+------+------------+
| 40 | 320 | 2^320+27 |
+-------+------+------------+
| 41 | 328 | 2^328+15 |
+-------+------+------------+
| 42 | 336 | 2^336+241 |
+-------+------+------------+
| 43 | 344 | 2^344+231 |
+-------+------+------------+
| 44 | 352 | 2^352+55 |
+-------+------+------------+
| 45 | 360 | 2^360+105 |
+-------+------+------------+
| 46 | 368 | 2^368+127 |
+-------+------+------------+
| 47 | 376 | 2^376+115 |
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+-------+------+------------+
| 48 | 384 | 2^384+231 |
+-------+------+------------+
| 49 | 392 | 2^392+207 |
+-------+------+------------+
| 50 | 400 | 2^400+181 |
+-------+------+------------+
| 51 | 408 | 2^408+37 |
+-------+------+------------+
| 52 | 416 | 2^416+235 |
+-------+------+------------+
| 53 | 424 | 2^424+163 |
+-------+------+------------+
| 54 | 432 | 2^432+1093 |
+-------+------+------------+
| 55 | 440 | 2^440+187 |
+-------+------+------------+
| 56 | 448 | 2^448+211 |
+-------+------+------------+
| 57 | 456 | 2^456+21 |
+-------+------+------------+
| 58 | 464 | 2^464+841 |
+-------+------+------------+
| 59 | 472 | 2^472+445 |
+-------+------+------------+
| 60 | 480 | 2^480+165 |
+-------+------+------------+
| 61 | 488 | 2^488+777 |
+-------+------+------------+
| 62 | 496 | 2^496+583 |
+-------+------+------------+
| 63 | 504 | 2^504+133 |
+-------+------+------------+
| 64 | 512 | 2^512+75 |
+-------+------+------------+
Table 8
For example, the prime to be used to share a 128 bit value is 2^128 +
51.
12. Appendix B: Shamir Shared Secret Recovery Using Lagrange
Interpolation
The value of a Shamir Shared secret may be recovered using Lagrange
basis polynomials.
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To share a secret with a threshold of _n_ shares and L bits we
constructed _f(x)_ a polynomial of degree _n_ in the modular field
_p_ where _p_ is the smallest prime greater than 2^L:
f(x) = a_0 + a_1.x + a_2.x^2 + ... a_n.x^n
The shared secret is the binary representation of the value a_0
Given _n_ shares (_x_0_, _y_0_), (_x_1_, _y_1_), ... (_x_(n-1)_,
_y_(n-1)_), The corresponding the Lagrange basis polynomials _l_0_,
_l_1_, .. _l_(n-1)_ are given by:
lm = ((x - x(m_0)) / (x(m) - x(m_0))) . ((x - x(m_1)) / (x(m) -
x(m_1))) . ... . ((x - x(m_(n-2))) / (x(m) - x(m_(n-2))))
Where the values m_0, m_1, ... m_(n-2), are the integers 0, 1, ..
_n_-1, excluding the value _m_.
These can be used to compute _f(x)_ as follows:
f(x) = y_0l_0 + y_1l_1 + ... y_(n-1)l_(n-1)
Since it is only the value of _f(0)_ that we are interested in, we
compute the Lagrange basis for the value _x_ = 0:
lz_m = ((x(m_1)) / (x(m) - x(m_1))) . ((x(m_2)) / (x(m) - x(m_2)))
Hence,
a_0 = f(0) = y_0lz_0 + y_1lz_1 + ... y_(n-1)l_(n-1)
The following C# code recovers the values.
using System;
using System.Collections.Generic;
using System.Numerics;
namespace Examples {
class Examples {
///
/// Combine a set of points (x, f(x))
/// on a polynomial of degree in a
/// discrete field modulo prime to
/// recover the value f(0) using Lagrange basis polynomials.
///
/// The values f(x).
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/// The values for x.
/// The modulus.
/// The polynomial degree.
/// The value f(0).
static BigInteger CombineNK(
BigInteger[] fx,
int[] x,
BigInteger p,
int n) {
if (fx.Length < n) {
throw new Exception("Insufficient shares");
}
BigInteger accumulator = 0;
for (var formula = 0; formula < n; formula++) {
var value = fx[formula];
BigInteger numerator = 1, denominator = 1;
for (var count = 0; count < n; count++) {
if (formula == count) {
continue; // If not the same value
}
var start = x[formula];
var next = x[count];
numerator = (numerator * -next) % p;
denominator = (denominator * (start - next)) % p;
}
var InvDenominator = ModInverse(denominator, p);
accumulator = Modulus((accumulator +
(fx[formula] * numerator * InvDenominator)), p);
}
return accumulator;
}
///
/// Compute the modular multiplicative inverse of the value
/// modulo
///
/// The value to find the inverse of
/// The modulus.
///
static BigInteger ModInverse(
BigInteger k,
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BigInteger p) {
var m2 = p - 2;
if (k < 0) {
k = k + p;
}
return BigInteger.ModPow(k, m2, p);
}
///
/// Calculate the modulus of a number with correct handling
/// for negative numbers.
///
/// Value
/// The modulus.
/// x mod p
public static BigInteger Modulus(
BigInteger x,
BigInteger p) {
var Result = x % p;
return Result.Sign >= 0 ? Result : Result + p;
}
}
}
13. Normative References
[draft-hallambaker-mesh-architecture]
Hallam-Baker, P., "Mathematical Mesh 3.0 Part I:
Architecture Guide", Work in Progress, Internet-Draft,
draft-hallambaker-mesh-architecture-21, 23 October 2022,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
mesh-architecture-21>.
[draft-hallambaker-mesh-dare]
Hallam-Baker, P., "Mathematical Mesh 3.0 Part III : Data
At Rest Encryption (DARE)", Work in Progress, Internet-
Draft, draft-hallambaker-mesh-dare-16, 23 October 2022,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
mesh-dare-16>.
[draft-hallambaker-mesh-security]
Hallam-Baker, P., "Mathematical Mesh 3.0 Part IX Security
Considerations", Work in Progress, Internet-Draft, draft-
hallambaker-mesh-security-09, 20 April 2022,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
mesh-security-09>.
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[draft-hallambaker-web-service-discovery]
Hallam-Baker, P., "DNS Web Service Discovery", Work in
Progress, Internet-Draft, draft-hallambaker-web-service-
discovery-08, 23 October 2022,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
web-service-discovery-08>.
[RFC2014] Weinrib, A. and J. Postel, "IRTF Research Group Guidelines
and Procedures", BCP 8, RFC 2014, DOI 10.17487/RFC2014,
October 1996, <https://www.rfc-editor.org/rfc/rfc2014>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/rfc/rfc2119>.
[RFC3986] Berners-Lee, T., Fielding, R., and L. Masinter, "Uniform
Resource Identifier (URI): Generic Syntax", STD 66,
RFC 3986, DOI 10.17487/RFC3986, January 2005,
<https://www.rfc-editor.org/rfc/rfc3986>.
[RFC4648] Josefsson, S., "The Base16, Base32, and Base64 Data
Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006,
<https://www.rfc-editor.org/rfc/rfc4648>.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
<https://www.rfc-editor.org/rfc/rfc5280>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
<https://www.rfc-editor.org/rfc/rfc5869>.
[RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a
Prime (ECP Groups) for IKE and IKEv2", RFC 5903,
DOI 10.17487/RFC5903, June 2010,
<https://www.rfc-editor.org/rfc/rfc5903>.
[RFC6031] Turner, S. and R. Housley, "Cryptographic Message Syntax
(CMS) Symmetric Key Package Content Type", RFC 6031,
DOI 10.17487/RFC6031, December 2010,
<https://www.rfc-editor.org/rfc/rfc6031>.
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[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/rfc/rfc7748>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/rfc/rfc8032>.
[SHA-2] NIST, "Secure Hash Standard", August 2015.
[SHA-3] Dworkin, M. J., "SHA-3 Standard: Permutation-Based Hash
and Extendable-Output Functions", August 2015.
14. Informative References
[draft-hallambaker-mesh-developer]
Hallam-Baker, P., "Mathematical Mesh: Reference
Implementation", Work in Progress, Internet-Draft, draft-
hallambaker-mesh-developer-10, 27 July 2020,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
mesh-developer-10>.
[draft-hallambaker-mesh-trust]
Hallam-Baker, P., "Mathematical Mesh 3.0 Part X: The Trust
Mesh", Work in Progress, Internet-Draft, draft-
hallambaker-mesh-trust-09, 5 August 2021,
<https://datatracker.ietf.org/doc/html/draft-hallambaker-
mesh-trust-09>.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005,
<https://www.rfc-editor.org/rfc/rfc4086>.
[RFC4880] Callas, J., Donnerhacke, L., Finney, H., Shaw, D., and R.
Thayer, "OpenPGP Message Format", RFC 4880,
DOI 10.17487/RFC4880, November 2007,
<https://www.rfc-editor.org/rfc/rfc4880>.
[RFC5785] Nottingham, M. and E. Hammer-Lahav, "Defining Well-Known
Uniform Resource Identifiers (URIs)", RFC 5785,
DOI 10.17487/RFC5785, April 2010,
<https://www.rfc-editor.org/rfc/rfc5785>.
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[RFC5890] Klensin, J., "Internationalized Domain Names for
Applications (IDNA): Definitions and Document Framework",
RFC 5890, DOI 10.17487/RFC5890, August 2010,
<https://www.rfc-editor.org/rfc/rfc5890>.
[RFC6355] Narten, T. and J. Johnson, "Definition of the UUID-Based
DHCPv6 Unique Identifier (DUID-UUID)", RFC 6355,
DOI 10.17487/RFC6355, August 2011,
<https://www.rfc-editor.org/rfc/rfc6355>.
[RFC6763] Cheshire, S. and M. Krochmal, "DNS-Based Service
Discovery", RFC 6763, DOI 10.17487/RFC6763, February 2013,
<https://www.rfc-editor.org/rfc/rfc6763>.
[RFC7595] Thaler, D., Hansen, T., and T. Hardie, "Guidelines and
Registration Procedures for URI Schemes", BCP 35,
RFC 7595, DOI 10.17487/RFC7595, June 2015,
<https://www.rfc-editor.org/rfc/rfc7595>.
[Shamir79] Shamir, A., "How to share a secret.", 1979.
[XMLSchema]
Gao, S., Sperberg-McQueen, C. M., Thompson, H. S.,
Mendelsohn, N., Beech, D., and M. Maloney, "W3C XML Schema
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Hallam-Baker Expires 30 December 2023 [Page 60]
