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Versions: (draft-hallambaker-udf) 00 01 02 03 04 05 06

Network Working Group                                    P. Hallam-Baker
Internet-Draft                                           August 15, 2019
Intended status: Informational
Expires: February 16, 2020


        Mathematical Mesh 3.0 Part II: Uniform Data Fingerprint.
                     draft-hallambaker-mesh-udf-06

Abstract

   This document describes the 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.  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 [1] .

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
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   Internet-Drafts are draft documents valid for a maximum of six months
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   This Internet-Draft will expire on February 16, 2020.

Copyright Notice

   Copyright (c) 2019 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   described in the Simplified BSD License.

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.  UDF URIs  . . . . . . . . . . . . . . . . . . . . . . . .   7
       1.2.1.  Name Form . . . . . . . . . . . . . . . . . . . . . .   7
       1.2.2.  Locator Form  . . . . . . . . . . . . . . . . . . . .   7



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     1.3.  Secure Internet Names . . . . . . . . . . . . . . . . . .   9
   2.  Definitions . . . . . . . . . . . . . . . . . . . . . . . . .  10
     2.1.  Requirements Language . . . . . . . . . . . . . . . . . .  10
     2.2.  Defined Terms . . . . . . . . . . . . . . . . . . . . . .  10
     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 . . . . . . . . . . . . . . . . .  13
     3.4.  Truncation  . . . . . . . . . . . . . . . . . . . . . . .  14
       3.4.1.  Compression . . . . . . . . . . . . . . . . . . . . .  14
     3.5.  Presentation  . . . . . . . . . . . . . . . . . . . . . .  15
     3.6.  Alternative Presentations . . . . . . . . . . . . . . . .  15
       3.6.1.  Word Lists  . . . . . . . . . . . . . . . . . . . . .  15
       3.6.2.  Image List  . . . . . . . . . . . . . . . . . . . . .  16
   4.  Fixed Length UDFs . . . . . . . . . . . . . . . . . . . . . .  16
     4.1.  Nonce Type  . . . . . . . . . . . . . . . . . . . . . . .  16
     4.2.  OID Identified Sequence . . . . . . . . . . . . . . . . .  16
     4.3.  Encryption/Authentication Type  . . . . . . . . . . . . .  17
     4.4.  Shamir Shared Secret  . . . . . . . . . . . . . . . . . .  18
       4.4.1.  Secret Generation . . . . . . . . . . . . . . . . . .  19
       4.4.2.  Recovery  . . . . . . . . . . . . . . . . . . . . . .  19
   5.  Variable Length UDFs  . . . . . . . . . . . . . . . . . . . .  21
     5.1.  Content Digest  . . . . . . . . . . . . . . . . . . . . .  22
       5.1.1.  Content Digest Value  . . . . . . . . . . . . . . . .  22
       5.1.2.  Typed Content Digest Value  . . . . . . . . . . . . .  22
       5.1.3.  Compression . . . . . . . . . . . . . . . . . . . . .  23
       5.1.4.  Presentation  . . . . . . . . . . . . . . . . . . . .  23
       5.1.5.  Example Encoding  . . . . . . . . . . . . . . . . . .  24
       5.1.6.  Using SHA-2-512 Digest  . . . . . . . . . . . . . . .  24
       5.1.7.  Using SHA-3-512 Digest  . . . . . . . . . . . . . . .  25
       5.1.8.  Using SHA-2-512 Digest with Compression . . . . . . .  26
       5.1.9.  Using SHA-3-512 Digest with Compression . . . . . . .  27
     5.2.  Authenticator UDF . . . . . . . . . . . . . . . . . . . .  27
       5.2.1.  Content Digest Value  . . . . . . . . . . . . . . . .  28
       5.2.2.  Authentication Value  . . . . . . . . . . . . . . . .  28
     5.3.  Content Type Values . . . . . . . . . . . . . . . . . . .  30
       5.3.1.  PKIX Certificates and Keys  . . . . . . . . . . . . .  31
       5.3.2.  OpenPGP Key . . . . . . . . . . . . . . . . . . . . .  31
       5.3.3.  DNSSEC  . . . . . . . . . . . . . . . . . . . . . . .  32
   6.  UDF URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .  32
     6.1.  Name form . . . . . . . . . . . . . . . . . . . . . . . .  32
     6.2.  Locator form  . . . . . . . . . . . . . . . . . . . . . .  33
       6.2.1.  DNS Web service discovery . . . . . . . . . . . . . .  33
       6.2.2.  Content Identifier  . . . . . . . . . . . . . . . . .  33
       6.2.3.  Target URI  . . . . . . . . . . . . . . . . . . . . .  34



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       6.2.4.  Postprocessing  . . . . . . . . . . . . . . . . . . .  34
       6.2.5.  Decryption and Authentication . . . . . . . . . . . .  34
       6.2.6.  QR Presentation . . . . . . . . . . . . . . . . . . .  35
   7.  Strong Internet Names . . . . . . . . . . . . . . . . . . . .  35
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  35
     8.1.  Confidentiality . . . . . . . . . . . . . . . . . . . . .  35
     8.2.  Availability  . . . . . . . . . . . . . . . . . . . . . .  35
     8.3.  Integrity . . . . . . . . . . . . . . . . . . . . . . . .  35
     8.4.  Work Factor and Precision . . . . . . . . . . . . . . . .  36
     8.5.  Semantic Substitution . . . . . . . . . . . . . . . . . .  37
     8.6.  QR Code Scanning  . . . . . . . . . . . . . . . . . . . .  37
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  38
     9.1.  Protocol Service Name . . . . . . . . . . . . . . . . . .  38
     9.2.  Well Known  . . . . . . . . . . . . . . . . . . . . . . .  39
     9.3.  URI Registration  . . . . . . . . . . . . . . . . . . . .  39
     9.4.  Media Types Registrations . . . . . . . . . . . . . . . .  39
       9.4.1.  Media Type: application/pkix-keyinfo  . . . . . . . .  39
       9.4.2.  Media Type: application/udf-encryption  . . . . . . .  40
       9.4.3.  Media Type: application/udf-secret  . . . . . . . . .  41
     9.5.  Uniform Data Fingerprint Type Identifier Registry . . . .  42
       9.5.1.  The name of the registry  . . . . . . . . . . . . . .  42
       9.5.2.  Required information for registrations  . . . . . . .  42
       9.5.3.  Applicable registration policy  . . . . . . . . . . .  43
       9.5.4.  Size, format, and syntax of registry entries  . . . .  43
       9.5.5.  Initial assignments and reservations  . . . . . . . .  43
   10. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  44
   11. Appendix A: Prime Values for Secret Sharing . . . . . . . . .  44
   12. Recovering Shamir Shared Secret . . . . . . . . . . . . . . .  45
   13. References  . . . . . . . . . . . . . . . . . . . . . . . . .  47
     13.1.  Normative References . . . . . . . . . . . . . . . . . .  47
     13.2.  Informative References . . . . . . . . . . . . . . . . .  48
     13.3.  URIs . . . . . . . . . . . . . . . . . . . . . . . . . .  49
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  50

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 five 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:

NC6B-EYP6-O3JR-54HY-IE45-FOUU-TIPQ
EAR2-UJUY-H7TF-SFLK-CWAW-TKC4-O5HQ
SAQG-A7BL-6YQ6-G5K3-HYKQ-I54D-VWHG-C
MB5S-R4AJ-3FBT-7NHO-T26Z-2E6Y-WFH4
KCM5-7VB6-IJXJ-WKHX-NZQF-OKGZ-EWVN
ACXQ-PQRC-54KV-6XXU-L3ZU-W2NZ-QVA5
OAYC-4MAH-AYBS-WZLQ-AUAA-GIYA-AQQE-E7UO-6QMY-7EGD-C63V-TROP-P2W5-HX6E-IDBE-YVJW-B4SY-GM5U-T2LF-7HQ

   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:
     NC6B-EYP6-O3JR-54HY-IE45-FOUU-TIPQ





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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:
     23 AA 26 98  3F E6 59 15  6A 15 81 69  A8 5C 77 4F

   Encryption/Authenticator UDF:
     EAR2-UJUY-H7TF-SFLK-CWAW-TKC4-O5HQ

   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:     EAR2-UJUY-H7TF-SFLK-CWAW-TKC4-O5HQ
   Share 0: SAQG-A7BL-6YQ6-G5K3-HYKQ-I54D-VWHG-C
   Share 1: SAQZ-2TRR-KQB6-BENB-CIKI-PBK6-72SX-G
   Share 2: SARN-UIBW-WHS5-3LPG-4YKA-VEZ2-J66I-K

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: ACXQ-PQRC-54KV-6XXU-L3ZU-W2NZ-QVA5

1.2.  UDF 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://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:

   EDX6-OS5A-D4LO-IPT5-EVOR-4QFW-AZWE-4Q

   One or more electronic forms of the invoice are encrypted under the
   key EDX6-OS5A-D4LO-IPT5-EVOR-4QFW-AZWE-4Q 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/EDX6-OS5A-D4LO-IPT5-EVOR-4QFW-AZWE-4Q

   The EARL is then rendered as a QR code:

   [[This figure is not viewable in this format.  The figure is
   available at http://mathmesh.com/Documents/draft-hallambaker-mesh-
   udf.html [2].]]


   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 (EDX6-OS5A-D4LO-IPT5-EVOR-4QFW-AZWE-4Q) =
   MDWZ-WDB7-FZLG-46QL-UURR-FQ36-UQ2A-6YIX-BG4T-32A2-QHPE-5UPP-MMKA-3YR2





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   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:

   https://example.com/.well-known/mmm-udf/MDWZ-WDB7-FZLG-46QL-UURR-
   FQ36-UQ2A-6YIX-BG4T-32A2-QHPE-5UPP-MMKA-3YR2

   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.




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   These rules allow Bob to send email to Alice with either 'best
   effort' security or mandatory security as the circumstances demand.

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.





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   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
      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



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   presentation.  Fixed length Binary Data Sequences MUST not be
   truncated.

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                           |
     | 32      | E       | HKDF-AES-512                             |
     | 80      | K       | SHA-3-512                                |
     | 81      | K       | SHA-3-512 (20 bits compressed)           |
     | 82      | K       | SHA-3-512 (30 bits compressed)           |
     | 83      | K       | SHA-3-512 (40 bits compressed)           |
     | 84      | K       | SHA-3-512 (50 bits compressed)           |
     | 96      | M       | SHA-2-512                                |
     | 97      | M       | SHA-2-512 (20 bits compressed)           |
     | 98      | M       | SHA-2-512 (30 bits compressed)           |
     | 99      | M       | SHA-2-512 (40 bits compressed)           |
     | 100     | M       | SHA-2-512 (50 bits compressed)           |
     | 104     | N       | Nonce data                               |
     | 108     | O       | OID distinguished sequence (DER encoded) |
     | 144     | S       | Shamir Secret Sharing                    |
     +---------+---------+------------------------------------------+

                                  Table 1

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.






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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.

3.4.1.  Compression

   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 a 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.




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   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.

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 permits encoding of
   16 bits.  These encodings allow a 120 bit fingerprint to be encoded
   in 9 and 8 words respectively.





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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.

   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:









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      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:


     42 7E 8E F4  19 8F 90 C3  17 B7 59 C5  CF 7E AD D3
     DF C4 40 C2  4C 55 36 0F  25 83 33 B4  9E 96 5F 9E

   The equivalent DER encoding is:


     30 2E 30 07  06 03 2B 65  70 05 00 03  23 00 04 20
     42 7E 8E F4  19 8F 90 C3  17 B7 59 C5  CF 7E AD D3
     DF C4 40 C2  4C 55 36 0F  25 83 33 B4  9E 96 5F 9E

   To encode this key as a UDF OID sequence we prepend the value OID and
   convert to Base32:

OAYC-4MAH-AYBS-WZLQ-AUAA-GIYA-AQQE-E7UO-6QMY-7EGD-C63V-TROP-P2W5-HX6E-IDBE-YVJW-B4SY-GM5U-T2LF-7HQ

   The corresponding UDF content digest value is more compact and allows
   us to identify the key unambiguously but does not provide the value:

   MD7J-UW6O-EUSZ-UWKO-JQTB-JFKY-EF5S

4.3.  Encryption/Authentication Type

   An Encryption/Authentication Type UDF consists of the type identifier
   octet 0 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




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   be used.  Requirements for such processes and procedures are
   described in [RFC4086] .

   Encryption/Authentication 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/Authentication type UDF is a UDF fingerprint of the
   Encryption/Authentication Type UDF in Base32 presentation with
   content type 'application/udf-encryption'.

4.4.  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:

   o  Bits 4-7 of the first byte specify the threshold value.

   o  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.

   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.








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4.4.1.  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.

   a0 Is the integer representation of the secret to be shared.

   a1 ... an  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.

4.4.2.  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.





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   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
     97 BE C3 8C  EC 32 E3 A8  14 BE 38 AC  49 B3 58 D0

   This has the UDF representation:

   ECL3-5Q4M-5QZO-HKAU-XY4K-YSNT-LDIA

   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 = 201703930001559361817193071124445092048
   a1 = 150940799172659682039015718883035617571
   a2 = 86155479518555634547489350117128484052

   The master secret is the value f(0) = a0.  The key shares are the
   values f(1), f(2)...f(5):

   f(1) = 98517841771836214940323532692840982164
   f(2) = 167642712579224337158432694495493840384
   f(3) = 68796175502785265008145949100635455201
   f(4) = 142260597463457461952837903940034038122
   f(5) = 47753611540302464529133951581921377640

   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 4A 1D D8  9D 72 E5 BC  D3 C8 0C 4F  A6 96 F3 26
     94
   f(2) =
     31 7E 1E CF  DF FB B5 F1  FB 6F 25 E1  68 DC 85 5E
     00
   f(3) =
     32 33 C1 A9  54 86 A3 83  1F 0A 0A ED  F3 1A 69 FE
     E1
   f(4) =
     33 6B 06 64  FB 13 AE 70  3E 98 BB 75  45 50 A1 09
     6A
   f(5) =
     34 23 ED 02  D3 A2 D6 B9  5A 1B 37 77  5F 7F 2A 7D
     68

   The UDF presentation of the key shares is thus:

   f(1) = SAYE-UHOY-TVZO-LPGT-ZAGE-7JUW-6MTJ-I
   f(2) = SAYX-4HWP-3753-L4P3-N4S6-C2G4-QVPA-A
   f(3) = SAZD-HQNJ-KSDK-HAY7-BIFO-34Y2-NH7O-C
   f(4) = SAZW-WBTE-7MJ2-44B6-TC5X-KRKQ-UEEW-U
   f(5) = SA2C-H3IC-2ORN-NOK2-DM3X-OX37-FJ6W-Q

   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:

   1.  Applying the digest algorithm to determine the Content Digest
       Value

   2.  Applying the digest algorithm to determine the Typed Content
       Digest Value

   3.  Determining the compression level from bytes 0-3 of the Typed
       Content Digest Value.

   4.  Determining the Type Identifier octet from the Digest algorithm
       identifier and compression level.

   5.  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.  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 leading zero bits  Compression factor = 0

   29 or fewer leading zero bits  Compression factor = 20

   39 or fewer leading zero bits  Compression factor = 30

   49 or fewer leading zero bits  Compression factor = 40

   50 or more leading 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.  Presentation

   The type identifier is determined by the algorithm and compression
   factor as follows:











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              +---------+---------+-----------+-------------+
              | Type ID | Initial | Algorithm | Compression |
              +---------+---------+-----------+-------------+
              | 80      | K       | SHA-3-512 | 0           |
              | 81      | K       | SHA-3-512 | 20          |
              | 82      | K       | SHA-3-512 | 30          |
              | 83      | K       | SHA-3-512 | 40          |
              | 84      | K       | SHA-3-512 | 50          |
              | 96      | M       | SHA-2-512 | 0           |
              | 97      | M       | SHA-2-512 | 20          |
              | 98      | M       | SHA-2-512 | 30          |
              | 99      | M       | SHA-2-512 | 40          |
              | 100     | M       | SHA-2-512 | 50          |
              +---------+---------+-----------+-------------+

                                  Table 2

   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.

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

















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   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

   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

   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













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   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

   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

   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:

   1.  Applying the digest algorithm to determine the Content Digest
       Value

   2.  Applying the MAC algorithm to determine the Authentication value

   3.  Determining the Type Identifier octet from the Digest algorithm
       identifier and compression level.

   4.  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.  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 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

   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.

   As described in the security considerations section, the use of
   fingerprints to identify a bare public key and the use of




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   fingerprints to identify a public key and associated security policy
   information are very different.

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:

      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.







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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.

   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

   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.






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   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

   The locator form of an unkeyed UDF URI is resolved by the following
   steps:

   o  Use DNS Web service discovery to determine the Web Service
      Endpoint.

   o  Determine the content identifier from the source URI.

   o  Append the content identifier to the Web Service Endpoint as a
      suffix to form the target URI.

   o  Retrieve content from the Web Service Endpoint by means of a GET
      method.

   o  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.

   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.




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   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
      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:

   o  DARE Envelope format as specified in [draft-hallambaker-mesh-dare]

   o  Cryptographic Message Syntax (CMS) Symmetric Key Package as
      specified in [RFC6031]






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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] .

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.








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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.

   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



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   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.

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.





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9.  IANA Considerations

   Registrations are requested in the following registries:

   o  Service Name and Transport Protocol Port Number

   o  well-known URI registry

   o  Uniform Resource Identifier (URI) Schemes

   o  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
      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








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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]

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]



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   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 &amp; 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

9.4.2.  Media Type: application/udf-encryption

   Type name:  application

   Subtype name:  udf-encryption

   Required parameters:  None

   Optional parameters:  None

   Encoding considerations:  None

   Security considerations:  Described in [This]

   Interoperability considerations:  None

   Published specification:  [This]



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   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 &amp; 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

9.4.3.  Media Type: application/udf-secret

   Type name:  application

   Subtype name:  udf- secret

   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



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   Additional information:  Deprecated alias names for this type: None

      Magic number(s): None

      File extension(s): None

      Macintosh file type code(s): None

   Person &amp; 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

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




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   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,

9.5.5.  Initial assignments and reservations

   The following entries should be added to the registry as initial
   assignments:

   Code  Description                      Reference
   ---  -------------------               ---------
   00   HMAC and SHA-2-512                [This document]
   32   HKDF-AES-512                      [This document]
   80   SHA-3-512                         [This document]
   81   SHA-3-512 with 20 trailing zeros  [This document]
   82   SHA-3-512 with 30 trailing zeros  [This document]
   82   SHA-3-512 with 40 trailing zeros  [This document]
   83   SHA-3-512 with 50 trailing zeros  [This document]
   96   SHA-2-512                         [This document]
   97   SHA-2-512 with 20 trailing zeros  [This document]
   98   SHA-2-512 with 30 trailing zeros  [This document]
   99   SHA-2-512 with 40 trailing zeros  [This document]
   100  SHA-2-512 with 50 trailing zeros  [This document]
   104  Random nonce                      [This document]
   144  Shamir Secret Share               [This document]







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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 (2^32)^n that is larger than the
   secret to be encoded and determining the next largest number that is
   prime.

                 +----------------+----------------------+
                 | Number of bits | Offset = Primen - 2n |
                 +----------------+----------------------+
                 | 32             | 15                   |
                 | 64             | 13                   |
                 | 96             | 61                   |
                 | 128            | 51                   |
                 | 160            | 7                    |
                 | 192            | 133                  |
                 | 224            | 735                  |
                 | 256            | 297                  |
                 | 288            | 127                  |
                 | 320            | 27                   |
                 | 352            | 55                   |
                 | 384            | 231                  |
                 | 416            | 235                  |
                 | 448            | 211                  |
                 | 480            | 165                  |
                 | 512            | 75                   |
                 +----------------+----------------------+

                                  Table 3

   For example, the prime to be used to share a 128 bit value is 2^128 +
   51.







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12.  Recovering Shamir Shared Secret

   The value of a Shamir Shared secret may be recovered using Lagrange
   basis polynomials.

   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-1l_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-1l_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))



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           /// 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).
           /// 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
           ///



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           /// The value to find the inverse of
           /// The modulus.
           ///
           static BigInteger ModInverse(
                       BigInteger k,
                       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.  References

13.1.  Normative References

   [draft-hallambaker-mesh-architecture]
              Hallam-Baker, P., "Mathematical Mesh 3.0 Part I:
              Architecture Guide", draft-hallambaker-mesh-
              architecture-10 (work in progress), August 2019.

   [draft-hallambaker-mesh-dare]
              Hallam-Baker, P., "Mathematical Mesh 3.0 Part III : Data
              At Rest Encryption (DARE)", draft-hallambaker-mesh-dare-04
              (work in progress), August 2019.

   [draft-hallambaker-mesh-security]
              Hallam-Baker, P., "Mathematical Mesh Part VII: Security
              Considerations", draft-hallambaker-mesh-security-01 (work
              in progress), July 2019.



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   [draft-hallambaker-web-service-discovery]
              Hallam-Baker, P., "DNS Web Service Discovery", draft-
              hallambaker-web-service-discovery-02 (work in progress),
              April 2019.

   [RFC2014]  Weinrib, A. and J. Postel, "IRTF Research Group Guidelines
              and Procedures", BCP 8, RFC 2014, DOI 10.17487/RFC2014,
              October 1996.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997.

   [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.

   [RFC4648]  Josefsson, S., "The Base16, Base32, and Base64 Data
              Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006.

   [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.

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010.

   [RFC6031]  Turner, S. and R. Housley, "Cryptographic Message Syntax
              (CMS) Symmetric Key Package Content Type", RFC 6031,
              DOI 10.17487/RFC6031, December 2010.

   [SHA-2]    NIST, "Secure Hash Standard", August 2015.

   [SHA-3]    Dworkin, M., "SHA-3 Standard: Permutation-Based Hash and
              Extendable-Output Functions", August 2015.

13.2.  Informative References

   [draft-hallambaker-mesh-developer]
              Hallam-Baker, P., "Mathematical Mesh: Reference
              Implementation", draft-hallambaker-mesh-developer-08 (work
              in progress), April 2019.







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   [draft-hallambaker-mesh-trust]
              Hallam-Baker, P., "Mathematical Mesh Part VI: The Trust
              Mesh", draft-hallambaker-mesh-trust-02 (work in progress),
              July 2019.

   [RFC4086]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", BCP 106, RFC 4086,
              DOI 10.17487/RFC4086, June 2005.

   [RFC4880]  Callas, J., Donnerhacke, L., Finney, H., Shaw, D., and R.
              Thayer, "OpenPGP Message Format", RFC 4880,
              DOI 10.17487/RFC4880, November 2007.

   [RFC5785]  Nottingham, M. and E. Hammer-Lahav, "Defining Well-Known
              Uniform Resource Identifiers (URIs)", RFC 5785,
              DOI 10.17487/RFC5785, April 2010.

   [RFC5890]  Klensin, J., "Internationalized Domain Names for
              Applications (IDNA): Definitions and Document Framework",
              RFC 5890, DOI 10.17487/RFC5890, August 2010.

   [RFC6355]  Narten, T. and J. Johnson, "Definition of the UUID-Based
              DHCPv6 Unique Identifier (DUID-UUID)", RFC 6355,
              DOI 10.17487/RFC6355, August 2011.

   [RFC6763]  Cheshire, S. and M. Krochmal, "DNS-Based Service
              Discovery", RFC 6763, DOI 10.17487/RFC6763, February 2013.

   [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.

   [Shamir79]
              "[Reference Not Found!]".

   [XMLSchema]
              Gao, S., Sperberg-McQueen, C., Thompson, H., Mendelsohn,
              N., Beech, D., and M. Maloney, "W3C XML Schema Definition
              Language (XSD) 1.1 Part 1: Structures", April 2012.

13.3.  URIs

   [1] http://mathmesh.com/Documents/draft-hallambaker-mesh-udf.html

   [2] http://mathmesh.com/Documents/draft-hallambaker-mesh-udf.html






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Author's Address

   Phillip Hallam-Baker

   Email: phill@hallambaker.com














































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