## Efficient Cryptanalysis of Homophonic Substitution Ciphers

Citations: | 1 - 0 self |

### BibTeX

@MISC{Dhavare_efficientcryptanalysis,

author = {Amrapali Dhavare and Richard M. Low and Mark Stamp},

title = {Efficient Cryptanalysis of Homophonic Substitution Ciphers},

year = {}

}

### OpenURL

### Abstract

Substitution ciphers are among the earliest methods of encryption. Examples of classic substitution ciphers include the well-known simple substitution and the less well-known homophonic substitution. Simple substitution ciphers are indeed simple— both in terms of their use and their cryptanalysis. Homophonic substitutions are also easy to use, but far more challenging to break. Even with modern computing technology, homophonic substitutions can present a significant cryptanalytic challenge. This paper focuses on the design and implementation of an efficient algorithm to break homophonic substitution ciphers. We employ a nested hill climb approach that generalizes the fastest known attack on simple substitution ciphers. We test our algorithm on a wide variety of homophonic substitutions and provide success rates as a function of both the ciphertext alphabet size and ciphertext length. Finally, we apply our technique to the “Zodiac 340 ” cipher, which is an unsolved message created by the infamous Zodiac killer.

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Citation Context ... simple substitution cipher, hill climb, heuristic search, Zodiac 340 cipher 1 Introduction Substitution ciphers are among the oldest encryption methods—they are simple, intuitive, and widely studied =-=[21]-=-. Many variants of the substitution cipher have been developed, including monoalphabetic systems, which employ a fixed substitution, and polyalphabetic systems, where the substitution varies. Example ... |

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Citation Context ...on homophonic substitution ciphers. We also provide extensive test results. The attack proposed here can be viewed as a generalization of the fastest known algorithm for breaking simple substitutions =-=[7]-=-. However, a direct generalization of the algorithm in [7] is not sufficient to solve a homophonic substitution. Therefore, we combine our generalized simple substitution algorithm with an additional ... |

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Citation Context ...permutation can be obtained from another permutation by repeated swapping, this elementary approach enables us to, in principle, obtain any key. To compute a score, we could look for dictionary words =-=[12]-=-, but given a sufficiently long ciphertext, an alternative approach is to use English digram frequencies (and, possibly, trigrams and higher-order-grams). We discuss English letter frequencies and Eng... |

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Citation Context ...uristic search is that it can be much faster than a brute force approach. However, there is no guarantee that a heuristic algorithm 7will find an optimal solution, or even a reasonable approximation =-=[15]-=-. But for most substitution ciphers, an exhaustive search is out of the question, so it is natural to consider heuristic techniques. Hill climbing is an an iterative technique that can be viewed as a ... |

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Citation Context ...ing local maxima. Figure 2: Hill Climbing [9] Hill climbing works well on many substitution ciphers, including some polyalphabetic cipher machines, such as the World War II-era Japanese Purple cipher =-=[20]-=-. For substitution ciphers, the closer a putative key is to the actual key, the closer the corresponding putative plaintext is to the actual plaintext. This is the crucial 8feature that enables a hil... |

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Citation Context ...ngs” might be due to the fact that a thick-tipped pen was used, and several of the symbols are similar. Also, the final 18 symbols appear to be filler used to make the cipher fit a predetermined grid =-=[6]-=-. The frequency distribution for the Zodiac 408 plaintext is given in Table 12. The letters J, Q, and Z do not appear in the plaintext. 6.2 Zodiac 340 Cipher The unsolved Zodiac 340, which appears in ... |

1 |
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Citation Context ...rd hill climb algorithm, multiple initial guesses will increase our chance of finding a satisfactory solution, since we can then choose the best of the resulting local maxima. Figure 2: Hill Climbing =-=[9]-=- Hill climbing works well on many substitution ciphers, including some polyalphabetic cipher machines, such as the World War II-era Japanese Purple cipher [20]. For substitution ciphers, the closer a ... |

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Citation Context ...re have been many proposed solutions to the Zodiac 340, but none of the “solutions” published to date holds up under scrutiny. For recent examples of proposed solutions, see [18] or [22]. The website =-=[14]-=- gives a good analysis of the flaws in the supposed solution [18]. 37Figure 22: Zodiac 408 Cipher [19] It is possible that the Zodiac 340 is a homophonic substitution combined with another encryption... |

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Citation Context ...November 8, 1969 [16]. There have been many proposed solutions to the Zodiac 340, but none of the “solutions” published to date holds up under scrutiny. For recent examples of proposed solutions, see =-=[18]-=- or [22]. The website [14] gives a good analysis of the flaws in the supposed solution [18]. 37Figure 22: Zodiac 408 Cipher [19] It is possible that the Zodiac 340 is a homophonic substitution combin... |