An Encoding-Decoding algorithm based on Padovan numbers

Alaa Al-Kateeb; Jenan Shtayat

arxiv: 1907.02007 · v1 · pith:UETHGOTJnew · submitted 2019-07-03 · 💻 cs.IT · math.IT· math.NT

An Encoding-Decoding algorithm based on Padovan numbers

Jenan Shtayat , Alaa Al-Kateeb This is my paper

Pith reviewed 2026-05-25 09:38 UTC · model grok-4.3

classification 💻 cs.IT math.ITmath.NT

keywords Padovan numbersQ-matricesencoding algorithmdecoding algorithmblocked message matricescryptographykey variation

0 comments

The pith

A coding and decoding algorithm can be constructed from Padovan Q-matrices applied to blocked message matrices with a distinct key for each block.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a new encoding and decoding method that divides messages into blocks and applies Padovan Q-matrices to encrypt each block. Each message matrix receives its own key derived from the matrices, which the authors state increases security. A sympathetic reader would care because the approach replaces a single fixed key with per-block variation in a linear recurrence setting.

Core claim

The authors present an encoding-decoding algorithm using Padovan Q-matrices on blocked message matrices, where the encryption of each message matrix employs a different key to increase the security of the method.

What carries the argument

Padovan Q-matrices, which generate distinct keys applied to each blocked message matrix for encoding and subsequent decoding.

If this is right

Each message block receives its own encryption key derived from the Padovan sequence.
The encoding process operates on blocked message matrices rather than the full message at once.
Security is claimed to increase specifically because the key changes with every block.
The algorithm supplies both an encoding step and a corresponding decoding step.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be tested for computational cost against standard matrix-based ciphers that also use recurrence sequences.
If the Q-matrix construction is invertible, the scheme might extend to error-correcting variants by combining with parity checks.
Varying keys per block raises questions about key distribution overhead that the paper does not quantify.

Load-bearing premise

Constructing keys from Padovan Q-matrices and assigning a distinct key to each message block actually produces a secure and correct encoding scheme.

What would settle it

An explicit computation showing that the proposed decoding step fails to recover the original message matrix or that a fixed-key attack succeeds despite the per-block key changes.

read the original abstract

In this paper, we propose a new of coding/decoding algorithm using Padovan Q-matrices. This method is based on blocked message matrices. an advantage of this method is that the encryption of each message matrix will use a different key and that will increase the security of the method.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is an abstract-only claim of a Padovan Q-matrix coding scheme with no construction, proof, or evidence at all.

read the letter

The paper asserts a new encoding-decoding method that applies Padovan Q-matrices to blocked message matrices and claims extra security from using a different key per block. That is the entire content; the provided text stops at the abstract and supplies no matrix definitions, encoding rule, decoding procedure, example, or security argument. Similar matrix techniques already exist for Fibonacci and Lucas sequences, so the extension is not obviously new even if it were fleshed out. The work does nothing well because it contains no actual work. The soft spots are load-bearing. The central claim requires that the Padovan matrices yield a correct, invertible mapping and that per-block keys meaningfully raise security, yet none of this is derived or even sketched. Without equations or a worked case the assumption that the scheme functions remains unsupported. The abstract itself is poorly phrased and offers no literature comparison, so it is impossible to judge whether the idea is absent from prior recurrence-sequence coding papers. This manuscript is for no one. A reader interested in concrete coding constructions or recurrence-based crypto will find nothing usable. It shows no clear thinking or engagement with the literature. I would not bring it to a reading group, would not cite it, and would not send it to peer review; the editor should desk-reject it outright.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a new coding/decoding algorithm using Padovan Q-matrices applied to blocked message matrices, asserting that the use of a distinct key for each message matrix increases security.

Significance. A correctly specified, invertible, and analyzed construction based on Padovan Q-matrices could potentially contribute to matrix-based cryptographic coding methods. The current manuscript supplies no such construction, example, proof of correctness, or security argument, so no significance can be assigned.

major comments (2)

Abstract: the claim that an encoding-decoding algorithm 'exists' and confers a security benefit is unsupported; the text contains no definition of the Padovan Q-matrices, no encoding rule, no decoding procedure, and no invertibility argument.
Abstract: the stated advantage that 'the encryption of each message matrix will use a different key' is asserted without any mechanism for key generation from the Q-matrices or any analysis showing that per-block key variation improves resistance to attacks.

minor comments (1)

Abstract: grammatical and capitalization errors ('a new of coding/decoding', 'an advantage' at start of sentence).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments. The observations correctly identify that the submitted manuscript is a concise proposal lacking explicit constructions and analysis. We respond to each major comment and commit to revisions that address the gaps.

read point-by-point responses

Referee: Abstract: the claim that an encoding-decoding algorithm 'exists' and confers a security benefit is unsupported; the text contains no definition of the Padovan Q-matrices, no encoding rule, no decoding procedure, and no invertibility argument.

Authors: We agree the current text supplies only a high-level statement. The revised manuscript will add the definition of the Padovan Q-matrices, the explicit encoding and decoding rules applied to blocked message matrices, and an invertibility argument derived from the recurrence properties and determinant of the Q-matrices. revision: yes
Referee: Abstract: the stated advantage that 'the encryption of each message matrix will use a different key' is asserted without any mechanism for key generation from the Q-matrices or any analysis showing that per-block key variation improves resistance to attacks.

Authors: The manuscript notes the per-block key variation as an intended advantage but provides no supporting mechanism or analysis. The revision will describe how distinct keys are obtained from successive Padovan numbers or matrix powers and will include a brief discussion of the resulting resistance to known-plaintext or chosen-plaintext attacks on individual blocks. revision: yes

Circularity Check

0 steps flagged

No derivation chain or equations present; circularity cannot be diagnosed.

full rationale

The manuscript asserts the existence of an encoding/decoding scheme based on Padovan Q-matrices applied to blocked message matrices, with the security advantage of per-block distinct keys. No matrix definitions, encoding rules, decoding procedures, worked examples, or mathematical derivations appear in the provided text. Absent any explicit construction or chain of steps, there are no load-bearing claims that reduce by construction to fitted inputs, self-citations, or ansatzes. The paper therefore contains no circularity of the enumerated kinds; the central claim is simply an unsupported high-level proposal rather than a derivation that could be circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.0 · 5562 in / 1037 out tokens · 36719 ms · 2026-05-25T09:38:01.201437+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We propose a new coding/decoding algorithm using Padovan Q-matrices... dividing the message matrix into block matrices each of size 3×3... Qn = [[Pn-1, Pn+1, Pn], [Pn, Pn+2, Pn+1], [Pn+1, Pn+3, Pn+2]]
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

n = 4 if m=1 else m²; alphabet mod 28; di=det(Bi); C=[di, bi_k]

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.