Cryptography

The History and Mathematics of Codes and Code Breaking

Expository Essay - The Hill Cipher #1

Here's Danielle's paper on the Hill cipher [PDF].

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Expository Essay - The Hill Cipher #2

2 Comments

  1. Tanner Strickland

    After reading this essay, what stood out to me as the most interesting aspect was the Hill cipher's impact on the field of cryptology. I was surprised to find out that the first method of enciphering plaintext that relied heavily on mathematics involved using matrices. I thought this fact was unexpected, and I realized that it is a very practical use for matrices.

    The method of enciphering and deciphering plaintext was very clear to me throughout the explanation in the essay. The Hill cipher could be very confusing if it were not explained clearly, but Danielle used good figures to illustrate the steps of enciphering and gave basic explanations to anyone who is unfamiliar with matrices. Also, the paper flowed smoothly, with a well-written introduction that engages the reader's attention.

    My only question after reading this essay is about the historical background related to the Hill cipher. I would like to know why Hill was motivated to create the cipher and more details about how the public initially reacted to Hill's idea.

    After reading Danielle's essay about the Hill cipher, I associated the mathematics involved with creating the Hill cipher to those involved in creating a decimation cipher. Although the Hill cipher is more complex, both ciphers involve multiplying numerical values that represent letters by some sort of constant, then using the mod26 fuction to get the numerical value of the cipher letter.

  2. John Zeleznak

    My favorite part about you essay was how you emphasized the Hill cipher's significance in the field of cryptography in both your introduction and conclusion. It really seemed to give your writing a purpose and made the paper a lot more entertaining. I also want to commend you on your explanation of matrices and how it was used. It was a difficult topic to try and break down into its basic principles, but you succeeded in making the math of the Hill cipher easy to understand for even the most mathematically challenged person. You definitely gave an explanation for why there was not a ton of historical information on the Hill cipher (the lack of use and the fact that it became obsolete fairly quickly). However, if you would have talked about why it was invented by Hill and how he came up with the cipher, it might have given your essay a little more balance between the math and history of the code. I did notice some correlation between math we've used in class and the math found in the Hill cipher, including the use of mod26 in order to decipher the code. You also briefly talked about how this code ushered in the movement that led to some of the more mechanical forms of encryption that we have discussed this year. Overall, your paper was well organized, enlightening, and fun to read. Great job!

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