On Heuristic Structure Extraction in the Diagapeyev Cipher
The Diagapeyev Cipher is an unsolved transposition cipher challenge published in 1939. To date, no official solution, decryption procedure, or verified plaintext has ever been published.
The original challenge consists solely of the following numerical ciphertext:
75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
82858 47582 81837 28462 82837 58164 75748 58162 92000
Our recent study investigates the structural properties of this cipher using heuristic optimization, including simulated annealing and hill climbing, rather than assuming a predetermined decryption method.
The paper, source code, and experimental data are available below.
The search framework combines:
- Simulated Annealing
- Hill Climbing
- Genetic Algorithms
- Trigram-based Russian language scoring
to optimize a 6×6 permutation matrix representing the transposition structure.
After approximately 682 million candidate evaluations, the search repeatedly converged on high-scoring reconstructions exhibiting structured Russian-like text fragments. While these reconstructions do not constitute a complete decryption, they display military terminology and grammatical coherence that scored significantly above random baselines under our evaluation framework.
Statistical Validation
| Metric |
Result / Value |
Significance |
| Best Log-Score |
15.84 |
Highest structural integrity |
| Monte Carlo (N = 10,000) |
p_tail ≤ 10⁻⁴ |
Extreme tail of null distribution |
| Search Evaluations |
~682 million |
Extensive permutation space exploration |
Key Findings
Statistical Extremity Our Monte Carlo null-hypothesis test (N = 10,000) shows that the observed configuration lies in the extreme upper tail of the empirical null distribution (p_tail ≤ 10⁻⁴), indicating the detected patterns are highly unlikely to occur by random chance.
Methodological Rigor The search framework leverages a trigram-based language model trained on a Russian reference corpus to evaluate local linguistic dependencies.
Emergent Patterns The observed military terminology is an interaction effect between the scoring function and search dynamics, providing a formal framework for further cryptographic analysis.
Example of the Highest-Scoring Reconstruction
ВОВ: БОЕВАЯ ЗАДАЧА УСТАНОВЛЕНА,
ПОДРАЗДЕЛЕНИЯМ НАЧАТЬ ДВИЖЕНИЕ В
СЕКТОР А.
English (approximate):
"WWII: Combat mission established. Units begin movement toward Sector A."
This translation is intended only to illustrate the linguistic structure detected by the optimization and should not be interpreted as a confirmed plaintext of the original cipher.
Paper
Title: On Heuristic Structure Extraction in Under-Specified Transposition Ciphers: A Case Study on the Diagapeyev Cipher
DOI:https://doi.org/10.5281/zenodo.21132297
GitHub:https://github.com/IchiTaku326/Diagapeyev-Cipher-Solver
I am not claiming a complete decryption. Rather, this work presents a statistically validated heuristic framework for investigating an under-specified historical transposition cipher.
Any methodological feedback, criticism, or independent verification would be greatly appreciated.