Historically, substitution ciphers have been highly vulnerable to frequency analysis [3]. Today, modern computational technique specifically Metropolis-Hastings Markov Chain Monte Carlo (MCMC) algorithms can fully automate this decryption by optimizing a fitness score based on n-gram statistics. However, these statistical methods share a fundamental limitation: they require an adequate sample size. As ciphertext length decreases, its statistical profile diverges too far from standard English, ultimately rendering the attack ineffective. This study experimentally quantifies this ‘Breaking Point’ the minimum ciphertext length necessary for an MCMC attack to reliably converge on the correct plaintext. Our results reveal a clear threshold: while texts exceeding 200 characters are consistently vulnerable, messages under 150 characters (such as typical SMS texts or tweets) demonstrate significant resistance to this class of automated cryptanalysis.

Automated statistical attacks on monoalphabetic substitution ciphers face a practical hurdle: they require a minimum text length to succeed. In real-world scenarios—where message sizes are often limited by system protocols or user behavior—this boundary dictates whether automated cryptanalysis will work. Our findings highlight a clear divide. Short, constrained texts like SMS messages, API keys, and 2FA codes prove highly resistant to automated MCMC-based attacks. However, once a message reaches paragraph length (such as an email or news snippet), it becomes extremely vulnerable. Our tests demonstrated that standard hardware can rapidly decrypt these longer texts in a matter of seconds. Interestingly, the transition between ‘secure’ and ‘vulnerable’ is highly volatile. In the intermediate range of around 200 characters, our algorithm’s success was essentially a coin toss, achieving perfect decryption 60% of the time, but failing entirely in the other 40%. Ultimately, this research demonstrates that classical ciphers shouldn’t be entirely written off as historical artifacts. Against modern automated attacks, a message’s length effectively serves as its own security parameter.

[1] J. Chen and J. S. Rosenthal, “Decrypting Classical Cipher Text Using Markov Chain Monte Carlo,” Statistics and Computing, vol. 22, no. 2, pp. 397–413, 2012. [2] Practical Cryptography. (n.d.). Quadgram statistics. [Online]. Available: http://practicalcryptography.com/cryptanalysis/text-characterisation/quadgrams/ [3] C. E. Shannon, “Communication Theory of Secrecy Systems,” Bell System Technical Journal, vol. 28, no. 4, pp. 656–715, 1949. [4] A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996. [5] P. Diaconis, “The Markov Chain Monte Carlo Revolution,” Bulletin of the American Mathematical Society, vol. 46, no. 2, pp. 179–205, 2009.

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APA

Joel Mathew, Ashish L (February 2026). Breaking Point Analysis of MCMC Cryptanalysis for Substitution Ciphers. International Journal of Engineering and Techniques (IJET), 12(1). https://doi.org/{{doi}}

IEEE

Joel Mathew, Ashish L, “Breaking Point Analysis of MCMC Cryptanalysis for Substitution Ciphers,” International Journal of Engineering and Techniques (IJET), vol. 12, no. 1, February 2026, doi: {{doi}}.

© 2025 International Journal of Engineering and Techniques (IJET).

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