Syfer Sangraal : Holy Grail of Cryptography in the Arc of the Combinant

From	OCTADE <news0@octade.net>
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Subject	Syfer Sangraal : Holy Grail of Cryptography in the Arc of the Combinant
Date	2026-08-30 04:17 +0000
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Syfer Sangraal : Holy Grail of Cryptography in the Arc of the Combinant

    DOI : 10.5281/zenodo.22158384
    <https://doi.org/10.5281/zenodo.22158384>


== SUMMARY ==

Embark on the quest for the Syfer Sangraal system, or the holy grail of
cryptography hidden in the arc of the combinant. One system to roll
them all is the holy grail of cryptography. One algorithm to perform
every kind of cryptographic function is the new wine within the Syfer
Sangraal system.


== CONTENTS ==

1. About OCTADE
2. Fields of Research
3. Scope of Research
4. Syfer Sangraal : Holy Grail of Cryptography in the Arc of the
Combinant
5. Candidates for Syfer Sangraal Vintage
6. Simplementation : Avoiding Complexity Confusion and Mental
Intractability
7. Breakdown : Boot the Binary Bureaucrats of Byzantium
8. Project Links and Resources


[1] About OCTADE

Octade is the umbrella term for the research of Byrl Raze Buckbriar
(Raze). This research encompasses a variety of interests, especially
cryptology and cryptography as an art form, a mode of truth expression
and exploration rather than merely as software tooling. This
exploration births the quest for the Syfer Sangraal, or the Holy Grail
of Cryptography in the Arc of the Combinant.


[2] Fields of Research

  A. cryptology
  B. textual criticism
  C. theology
  D. poetry
  E. computer science
  F. history
  G. antiquities
  H. philology


[3] Scope of Research

  A. identifying essential patterns in text
  B. Holy Grail of Cryptography in the Arc of the Combinant
  C. iconoclasm and myth busting
  D. simplification of complexity
  E. expressing the arcane via the mundane
  F. translation accuracy
  G. multi-layered idioms and parables


[4] Syfer Sangraal : Holy Grail of Cryptography in the Arc of the
Combinant.

  The Combinant is the class of functions that are able to emulate
  algebraic commutativity and combinatrics without necessarily having
  actual numerical commutativity. Non-commutative operations can be
  extended in ways to emulate commutative or modular arithmetic
  possessing hard invertibility or secure trapdoor functions. The Arc
  of the Combinant is the whole range of such commutative emulation.

  The Holy Grail of Cryptography is a single, simple algorithm that
  performs all necessary functions of computational cryptography with
  provable security sans assumptions in the model, while avoiding
  mental intractability as much as possible. The necessary functions
  include secure hashing, digital signatures, verification, key
  exchanges, ciphers, random generation, authentication, access
  control, secret sharing, confidentiality, proofs, vector commitments,
  and other aspects of common usage in cryptography.

  The desirable properties of the universal Syfer Sangraal would
  presage the pending obsolescence and replacement of most or even all
  cryptosystems and their primitives. The Syfer Sangraal would replace
  all cryptographic primitives and systems with one singular algorithm
  and cryptosystem for the ages ahead. Syfer Sangraal would be based
  upon one mathematical function that can perform all the tasks of the
  obsoleted artifacts in perpetuity. This idealized system is desirable
  as the unrelenting burgeoning of cryptosystems and their complexity
  creates a paradox. It becomes infeasible to even know if
  cryptosystems are secure.

  As complexity grows the difficulty of cryptanalysis grows more than
  linearly requiring ever growing numbers of personnel, money, time,
  and resources to analyze and (hopefully) secure the growing
  collection of cryptosystems and their complex layers of
  implementation. Syfer sages have rightly predicted the breaking of
  cryptosystems and the insurmountable difficulty of provable security
  in a storm of growing complexity. Syfer Sangraal would pacify this
  weather pattern.

  If one single algorithm were to be employed to replace all
  cryptosystems, that would be the 'end of cryptography'. In that event
  no further cryptology research would be needed for securing and
  maintaining the fund of existing cryptosystems. And the mountainous
  volumes of work maintaining current cryptographic infrastructure
  would be eliminated to free up resources for other discoveries and
  inventions.

  In sum, discovery of the Syfer Sangraal would render computational
  cryptology a very boring field of endeavor and much safer and more
  secure than its current state. The Syfer Sangraal would render modern
  cryptography and cyber-security models superfluous.

  
[5] Candidates for Syfer Sangraal Vintage

  So far OCTADE research leads to several candidate algorithm classes
  as the grapes for the wine within the Syfer Sangraal.

    a. rhizome functions
    b. holoalphabetic (perfect pangram) functions
    c. ouroboros functions
    d. shingle functions
    e. mushroom functions
    f. spore functions
    g. sharx functions

  These functions are aptly named to approximate their structure and
  operation to avoid mental intractability common with maths and number
  theory. The functions can 'emulate' algebraic properties in
  interesting and useful ways. Some of these functions provide
  commutative emulation on the arc of the combinant. Neither the novel
  functions nor commutative emulation are described herein.

  The functions are the topics of research papers and simple programs
  of demonstration code being slowly cobbled together. Much research and
  testing indicates that one or more of these function classes will
  potentially satisfy the required properties of a Syfer Sangraal
  system that uses commutative emulation for multiple kinds of
  cryptographic primitives.

  
[6] Simplementation : Avoiding Complexity Confusion and Mental
Intractability

  At the core of a Syfer Sangraal system is the idea that the system
  must be mentally simple and tractable and easy to teach and grasp and
  implement in computer systems. This is termed, 'simplementation'. In
  developing a Syfer Sangraal the researcher, inventor, and teacher
  should take pains to avoid mucking up the works with strange acronyms
  and endlessly-mutating numerical prefixes and abbreviations. Names
  for things should be descriptive rather than creating an impenetrable
  jargon only comprehended by caffeinated, seasoned experts. In our
  modern society the average human brain is already greatly over-taxed
  by the requirement to make far more decisions and distinctions in a
  day than in prior generations. The sheer volume of daily mental input
  is vastly larger than previous generations and contrary to the human
  cognitive constitution.

  Syfer Sangraal Simplementation is an idea for rolling back from that
  precipice of stress and analysis paralysis to render cryptology
  simpler and easier rather than more complex or harder. Rather than
  remedy uncountable bugs and mistakes in cryptosystems and software,
  clear the field of all the dross and noise that makes the mistakes
  and pitfalls possible. This is akin to replacing the cryptographic
  football game with billiards or miniature golf.

  
[7] Breakdown : Boot the Binary Bureaucrats of Byzantium

  The discovery of the Syfer Sangraal system would allow many security
  research bodies, conferences, educational institutions, standards
  bodies, and implementers to clear their tables and their calendars.
  The Syfer Sangraal system would make possible the elimination of
  entire classes of software bugs and security failures.

  Cryptographic complexity and mental intractability benefit binary
  Byzantine bureaucrats and hostile actors. Simplicity benefits their
  victims. A Syfer Sangraal system puts power in the hands that need
  and deserve it the most. There is much more to be said yet the more
  must wait until another time.


[8] Project Links and Resources

Website   : <https://octade.net>
Fediverse : @8@star.octade.net | <https://star.octade.net/@8>
ORCiD     : <https://orcid.org/0009-0009-5144-3278>
Academia  : <https://independent.academia.edu/RazeBuckbriar>
Archive   : <https://archive.org/details/@buckbriar>
Zenodo    :
  <https://zenodo.org/search?q=metadata.identifiers:%27octade%27>
Git       : <https://codeberg.org/OCTADE>

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