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Understanding Encryption through Calculus: A Polynomial Approach to Cryptography

This assignment explores the intersection of calculus and cryptography by using a polynomial function to encode messages. Students will create their own polynomial keys and then encrypt a message, transforming it into cipher text. For example, by solving for y values based on x inputs, these values can represent letters of the alphabet, allowing for secure communication. Students will also learn to decrypt messages using anti-derivative rules. This hands-on project aims to reinforce calculus concepts while applying them to practical cryptographic scenarios, serving as excellent exam preparation.

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Understanding Encryption through Calculus: A Polynomial Approach to Cryptography

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  1. Calculus Cryptology Caitlin Bryant Jennifer Davis Laura Tinney

  2. How it Works… • Given a simple polynomial for our key such as Find the y values when x is 1,2,3,4,……,25,26. (1-26 = Alphabet) • The y values found now become cipher text for the alphabet. For example, if we want to use the polynomial above and encrypt the word MATH, our cipher text to send would now be 2379,3,8420,584.

  3. Now suppose Alice wants to send Bob our encrypted message…. • In order for bob to decrypt the message Alice has sent, he must take the anti-derivative of the key polynomial he received. Ex: • Now all Bob has to do is plug in the numbers sent to him in for the ‘y’ value of his integrated polynomial to get the x values . • Now he can decipher his message using the table on the previous slide • Alice must take the derivative of our polynomial using the rules she has learned in Calculus class. • The message Bob receives should look something like this: (2379,3,84200,584)

  4. Homework: Review Worksheet • Students should create their own polynomial using the worksheets from “Finite Differences”. After this is complete, have each student encrypt their own message and send to a classmate. (Be sure to include the derivative) • Decrypt your classmates message using the derivative and anti-derivative rules we have learned in class so far. • This assignment will be used as a review for the AP Calculus Exam.

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