Sage Interactions - Cryptography - Under Construction

This page was be created at Sage Days 103, 7-10 August 2019 by Sarah Arpin, Catalina Camacho-Navarro, Holly Paige Chaos, Amy Feaver, Eva Goedhart, Rebecca Lauren Miller, Alexis Newton, and Nandita Sahajpal.

We would also like to acknowledge Katherine Stange, who allowed us to use some of the code from her cryptography course as a starting point for many of these interacts.

If you have cryptography-related interactions that you are interested in adding to this page, please do so. You can also contact Amy Feaver at firstname.lastname@kingsu.ca

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Shift Cipher

by Sarah Arpin, Alexis Newton

The shift cipher is a classical cryptosystem that takes plaintext and shifts it through the alphabet by a given number of letters. -EG

Shift Cipher Encryption

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#Last edited 8/7/19 2:45pm

print "Put your message in between the provided quotes (with no additional quotes or apostrophes!), and select your desired shift: "

@interact

def shift_cipher(message = input_box(default='"secrets"', width = 50), shift=slider(0,25,1,3)):

    A = AlphabeticStrings()

    S = ShiftCryptosystem(A)

    message = S.encoding(message)

    C = S.enciphering(shift, message)

    print "This is your encrypted text shifted by ",shift,":"

    print C

Shift Cipher Decryption

If you know that your message was encrypted using a shift cipher, you can use the known shift value to decrypt. If this is not known, brute force can be used to get 26 possible decrypted messages.

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#Last edited 8/7/19 2:56pm

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print "Enter the encrypted text in quotes, and enter a guess for the shift amount:"

@interact

def shift_decrypt(text = input_box('"KL"'), shift_by = input_box(0)):

    S = ShiftCryptosystem(AlphabeticStrings())

    ciphertext = S.encoding(text)

    decrypt = S.deciphering(shift_by,ciphertext)

    print "If the shift was by", shift_by,", then the original message was:"

    print decrypt

    decrypt = S.brute_force(ciphertext)

    print "These are the possibilities for the plaintext:"

    print decrypt

    decrypt = S.brute_force(ciphertext,ranking = "chisquare")

    print "These are the possibilities ranked by likelihood with the chi-squared function:"

    print decrypt

Affine Cipher

by Sarah Arpin, Alexis Newton

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# Last edited 8/7/2019 2:01pm

print "Put your message in between the provided quotes (with no additional quotes or apostrophes!), and select your desired a,b: "

print "Notice that the only choices for a can be numbers that are relatively prime to 26

print "This cipher will encipher the letters m of your message as a*m + b"

@interact

def affine_cipher(message = input_box(default='"secrets"', width = 50), a=[1,3,5,7,9,11,15,17,19,21,23], b =[0..25]):

    A = AlphabeticStrings()

    S = AffineCryptosystem(A)

    message = S.encoding(message)

    C = S.enciphering(a,b, message)

    print "This is your encrypted text:"

    print C

Substitution Cipher

by Catalina Camacho-Navarro

A simple cipher to encrypt messages in which each letter is assigned to another letter. Brute force or frequency analysis can be used to decrypt. -EG

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Playfair Cipher

A special type of substitution cipher in which the plaintext is broken up into two-letter digraphs with some restrictions. Those digraphs are encrypted using a Polybius square, (i.e. a 5x5 grid in which each letter of the alphabet is its own entry with the exception of ij which are placed together). The positions of the letters in the digraph determine how the digraph is encrypted.

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Frequency Analysis Decryption Tool

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Vigenère Cipher

by Holly Paige Chaos, Rebecca Lauren Miller, and Kate Stange

Using a secret code word, encrypt each letter by shifting it the corresponding letter in the code word. -EG

Vigenère Cipher Encryption

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#This encrypts your message: Final 8/7/19. Written by Rebecca Lauren Miller, Holly Paige Chaos, Kate Strange.

print "Put your message and codeword in quotes: "

@interact 

def vigenere_cipher(message = input_box(default ="'secrets hi'", width = 50), code_word = input_box(default="'cat'", width = 50)):

    A = AlphabeticStrings()

    message2 = A.encoding(message) 

    code_word2 = A.encoding(code_word) 

    system = VigenereCryptosystem(A,len(code_word2)) 

    ciphertext = system.enciphering(code_word2,message2) 

    print "Enciphered message:"

    print ciphertext

Vigenère Cipher Decryption

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#This decrypts your message: Final 8/7/19. Written by Rebecca Lauren Miller, Holly Paige Chaos, Kate Strange.

print "Put your message and codeword in quotes: "

@interact 

def vigenere_cipher(message = input_box(default ="'UEVTEMUHB'", width = 50), code_word = input_box(default="'cat'", width = 50)):

    A = AlphabeticStrings()

    message2 = A.encoding(message) 

    code_word2 = A.encoding(code_word) 

    system = VigenereCryptosystem(A,len(code_word2)) 

    ciphertext = system.deciphering(code_word2,message2) 

    print "Deciphered message:"

    print ciphertext

Hill Cipher

by Holly Paige Chaos and Rebecca Lauren Miller

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RSA

Named for the authors Rivest, Shamir, Aldeman, RSA uses exponentiation and modular arithmetic to encrypt and decrypt messages between two parties. Each of those parties has their own secret and public key. To see how it works, following along while Alicia and Bernadette share a message. -EG

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Diffe-Hellman Key Exchange

One-time Pad