[Article] Naibbe cipher paper

[Torsten]

Dear Michael,

Thank you for your response. While I appreciate your engagement, I don't find that your response successfully addresses the fundamental issues raised in my review.

Specifically:

1. Scope of the paper and intended claims

I appreciate your clarification that the Naibbe cipher is intended as a "proof of concept" rather than a definitive historical solution.

However, you state that the paper's goal is to demonstrate that a substitution cipher "can live deep inside the VMS's statistical envelope." This formulation is fundamentally circular when the cipher is explicitly constructed to match VMS statistics. A proof of concept must demonstrate something that was previously uncertain or unknown. Here, the outcome is predetermined by design. This reasoning structure conflates construction with discovery. A genuine proof of concept would demonstrate that when one applies general cryptographic principles (not fitted to the VMS), VMS-like statistics emerge unexpectedly. Instead, the Naibbe cipher demonstrates only that one can deliberately engineer a system to produce predetermined outputs.


2. Fitted vs. Emergent Properties

Your defense hinges on distinguishing "explicitly targeted" properties from "emergent" ones. This distinction deserves careful scrutiny.

You list several features as emergent: Character entropy, Conditional character entropy, Glyph and glyph-pair frequencies, Token and type length distributions, Skewed pairs

Character entropy, this is not truly emergent when:

• Glyph-to-letter mappings are selected from VMS vocabulary
  
• Table structures follow VMS word grammar (Zattera 2022)
  

Quasi-Zipfian distribution: You state this "naturally arises" from the unigram-bigram structure. However:

• The unigram-bigram ratio (47.2%-52.8%) was explicitly tuned to match VMS
  
• The table ratio (5:2:2:2:1:1) was fitted to VMS frequency distribution
  
• The claim that quasi-Zipfian distributions are "emergent" from letter-by-letter homophonic substitution requires demonstration with unfitted parameters
  

Token and type length distributions: These follow directly from:

• The Zattera slot grammar (taken from VMS)
  
• The unigram/bigram split (fitted to VMS)
  
• The affix inventory lengths (derived from VMS)
  

A truly emergent property would be one that appears despite not being directly targeted. For example, if the cipher unexpectedly reproduced VMS long-range correlations without being designed to do so, that would constitute genuine emergence.


3. Randomness, Determinism, and Mechanism Design

You state there is "no logical contradiction" between using cards for pseudorandomness and proposing non-random scribal biases to explain long-range correlations. I disagree. This reveals a fundamental ambiguity about the cipher's purpose.

If cryptographic security is the goal, then:

• Randomness is essential (it prevents pattern-based attacks)
  
• Scribal "biases" and "bursts" are security vulnerabilities
  
• Non-random deviations should be prevented, not encouraged
  

If VMS replication is the goal, then:

• The specific randomization mechanism is irrelevant
  
• Any table-selection method achieving the target ratios suffices
  
• Cards are not "historically convenient" but rather unnecessarily complex
  

You cannot have it both ways. Either this is a serious historical cipher proposal (in which case the security properties matter), or it is a statistical replication exercise (in which case the cards are theater).

I previously suggested that deterministic table cycling (α, β₁, β₂, β₃, repeat) would achieve better results without requiring any physical apparatus. You do not address this point. If the goal is historical plausibility, why choose the more complex option?

The most parsimonious explanation: cards were chosen because they provide a veneer of historical authenticity to what is fundamentally a modern statistical modeling exercise.


6.  Long-range correlations

You acknowledge the cipher's failure to reproduce long-range correlations and frames this as a "limitation" that could potentially be addressed with "non-random deviations." This significantly understates the problem.

Long-range correlations represent a significant feature of the VMS script. The Naibbe cipher faces two fundamental problems in accounting for them:

First, the structural impossibility: N-gram substitution encryption operates locally on plaintext, processing one letter or letter-pair at a time. The cipher's random table selection and random plaintext respacing explicitly destroy any sequential dependencies present in the source text. No plausible mechanism exists for long-range correlations to emerge as an epiphenomenon from these local, randomized operations.

Second, the detectable primary table dominance: Even without long-range correlations, the Naibbe cipher creates its own problematic statistical signature. The cipher maps Latin letter frequencies to VMS token frequencies through six tables weighted 5:2:2:2:1:1. This weighting means the primary table (α) is used 38.5% of the time, while the five secondary tables are each used far less frequently (15.4%, 15.4%, 15.4%, 7.7%, 7.7%). This creates strong, detectable correlations between plaintext letters and specific ciphertext tokens—precisely what a robust cipher should prevent: In an longer ciphertext, the most frequent tokens would always represent letters encrypted by the primary table, preserving their rank-order frequency from the plaintext.

The mathematical basis: Latin 'e' appears in ~12-13% of letters. When encrypted via the primary table α (38.5% of the time), this produces α's 'e' token at a frequency of ~4.8% of all tokens. The next most frequent Latin letter 't' (~9%) produces α's 't' token at only ~3.5% frequency. Secondary table 'e' tokens each appear at ~1.9% frequency. Therefore, α's 'e' token is very likely to be the single most frequent token type in typical ciphertexts.

The cryptographic implication: This violates a fundamental principle of homophonic substitution ciphers: homophones should distribute frequencies evenly to obscure plaintext letter frequencies. The Naibbe cipher's weighted tables achieve the opposite—they concentrate frequency, making the most common tokens strong indicators of plaintext identity.

You propose speculative mechanisms (non-random biases, quire-level effects) that might induce long-range correlations, but these remain untested and potentially contradictory to the cipher's design. More critically, addressing the correlation deficit would not resolve the primary table dominance problem—indeed, these two issues may be fundamentally in tension with each other.


7. Position-Dependent Effects

You state that "nothing in Naibbe's design prevents positional behavior being layered on" but acknowledges it would be "inelegant." This significantly understates the challenge.

The Core Problem is that the Naibbe cipher operates at the word level:

• Input: plaintext letters → Output: complete Voynichese words
  
• No awareness of line position during encryption
  
• Word lengths determined by plaintext identity and table selection
  

VMS position effects include:

• Paragraph-initial words from specific vocabulary subset
  
• Line-first words are slightly longer on average
  
• Line-second words are slightly shorter
  
• Gallows distribution varies by line position
  
• Line-final <m> appears ~62% of time (with variation by section)
  
• Different patterns in Currier A vs. B
  

To retrofit position awareness would require:

• During encryption: Scribe must know future line breaks before determining word selection
  
• Line-break awareness: Scribe must track token count and estimate when line break will occur
  
• Position-conditional word selection: Different word types for different positions
  
• Interaction with respacing: Random respacing must somehow be overridden or constrained by position requirements
  

This is not "layering on" a feature—it's redesigning the entire cipher architecture to be position-aware from the ground up.

The Naibbe cipher's architecture is specifically incompatible with position effects because it makes word-level decisions independently of positional context.


8. Historical Plausibility: The Complexity Gap Remains

You acknowledge Naibbe is at "the high end of plausible complexity" but argues this is acceptable given:

• Survival bias in cipher record
  
• VMS represents substantial investment
  
• Multiple scribes could distribute effort
  
• Elaborate cipher needed to resist century of decryption attempts
  

I find each of these arguments unpersuasive.

Survival Bias:
You argument is that our 15th-century cipher corpus is small and biased. However:

• We have hundreds of diplomatic ciphers from this period
  
• We have treatises describing cipher systems
  
• We have cipher nomenclators from multiple European courts
  
• The progression from simple substitution → homophonic substitution → nomenclators is well-documented
  

The gap between attested systems (2-4 homophones per letter) and Naibbe (18 options per letter + apparatus) is not explained by sampling bias—it's an order-of-magnitude difference in complexity.

You are arguing that the VMS's substantial investment justifies exploring complex ciphers. This reverses the causal logic.

The "Resistance to Decryption" Argument

You claim that failed decryption attempts suggest the cipher must be elaborate. This is backwards reasoning:

• Failed decryption could indicate the text is not enciphered
  
• Steganography, glossolalia, or constructed languages might resist decryption without requiring complex cryptographic design
  

Collective Effort and Timeline

You suggest multiple scribes could have shared encryption duties. However:

• Training burden: Each scribe needs to learn the complex system
  
• Consistency requirement: All scribes must follow identical table-selection ratios
  
• Error propagation: Any mistake affects plaintext recoverability
  
• Coordination complexity: How do scribes maintain consistent table usage?
  

The paleographic evidence for multiple hands might actually argue against cipher complexity, as it increases the training and coordination burden.

The Stepwise Evolution Speculation

You acknowledge the evolutionary sketch (p. 29-30) is speculative but defends it as "at least interesting" that modeling preferred unigram-bigram structure. This defense is insufficient:
The fact that modern optimization within VMS-constrained parameter space yields unigram-bigram structure tells us nothing about historical development. This is, again, finding that VMS-fitted parameters produce VMS-like results.


9. The Proof-of-Concept Claim Revisited

You state: "From the standpoint of the paper's core question—'are substitution ciphers in principle capable of producing VMS-like text under 15th-century constraints?'—it is appropriate, in my view, to push into ambitious territory."

I agree this is a legitimate question. However, the paper does not successfully answer it because:

What Was Actually Demonstrated?

• A cipher explicitly fitted to VMS can produce some VMS properties (those it was fitted to)
  
• Materials existed in the 15th century (not disputed)
  
• The process is executable (not disputed)
  

What Was Not Demonstrated

• That such a cipher would arise from cryptographic first principles
  
• That such a cipher is historically plausible given the complexity gap
  
• That the cipher can produce properties it was not fitted to (it fails on long-range correlations and position effects)
  
• That the emergent properties are truly independent of the fitted ones
  

The Epistemological Problem: A valid proof of concept would demonstrate that plausible historical constraints lead to VMS-like output as an unintended consequence. Instead, the Naibbe cipher demonstrates that modern reverse-engineering can produce predetermined results.

The core disagreement can be summarized:

Your position: "I have demonstrated that it is possible in principle for a substitution cipher to produce VMS-like statistics using 15th-century materials."
My position: "You have demonstrated that by deliberately fitting parameters to VMS, you can build a system that reproduces some (but not all) VMS properties. This does not constitute evidence for the ciphertext hypothesis because the success was predetermined by design."

Prior to Naibbe: It was already known that:

• Homophonic substitution existed in the 15th century
  
• Verbose ciphers are theoretically possible
  
• Deliberate system design can produce complex outputs
  

After Naibbe: We now additionally know that:

• A cipher explicitly reverse-engineered from VMS can match some VMS properties
  
• Such a cipher fails on other properties (long-range correlations, position effects)
  
• The required complexity significantly exceeds historical attestation
  

The question is: does this increase or decrease our confidence that the VMS is enciphered text?

I argue it provides evidence against the ciphertext hypothesis because:

• The fitted parameters make success unsurprising (no predictive power)
  
• The failures on unfitted properties suggest structural mismatch
  
• The complexity gap raises serious plausibility concerns
  
• Alternative explanations (constructed language, glossolalia, text generated by self-citation) remain equally viable and more parsimonious
  

The Naibbe cipher is an impressive technical achievement demonstrating considerable ingenuity and effort. However, it does not successfully answer the question it poses because the methodology conflates engineering demonstration with scientific evidence. A true proof of concept would require that VMS-like properties emerge from historically plausible cryptographic principles applied without specific fitting to VMS statistics.

I maintain that the most honest characterization of this work is: "A demonstration that one can deliberately engineer a complex system to match predetermined statistical targets, which tells us more about the flexibility of cipher design than about the VMS itself."

The path forward requires either:

• Demonstrating that the fitted components are the unique or strongly preferred solution from historical-cryptographic principles (not modern optimization)
  
• Providing independent validation that the cipher works on VMS data not used during parameter selection
  
• Developing concrete mechanisms for the missing properties (correlations, position effects) rather than speculating they could be added later
  

Without these elements, the Naibbe cipher remains an interesting intellectual exercise but does not constitute meaningful evidence for or against the ciphertext hypothesis.

Best regards,
Torsten