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Cryptology with Spreadsheets A Computer Course for Everyone Jim Belk Texas A&M University

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The Course MATH 135: The Art of Secret Writing Cornell University, Spring 2005 Humanities students fulfilling a math/computer science requirement. No prerequisites Invitation to Cryptology by Thomas H. Barr

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The Book Shift Ciphers, Affine Ciphers Substitution Ciphers Transposition Ciphers Vigenère Ciphers Hill Ciphers Chapter 1: History and Examples Chapter 2: Classical Ciphers

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The Book Chapter 1: History and Examples Chapter 2: Classical Ciphers Chapter 3: Computer Cryptology Chapter 4: Public-Key Cryptography (RSA, Diffie-Hellman, zero-knowledge proofs) Chapter 5: Additional Topics

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Why Spreadsheets? Goals: Emphasize numeracy and computer literacy. Similar to programming, but easier to work with and debug. Useful—spreadsheets are the primary mathematical software available on most PC’s.

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Example: Shift Cipher Simple alphabetic shift: y = x + c (mod 26) MOD(A1, B1): computes the remainder when A1 is divided by B1 CODE(A1): returns the ASCII code for the character in cell A1 CHAR(A1): returns the character whose ASCII code is the value in cell A1 Useful Commands:

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Example: Shift Cipher MOD(A1, B1): computes the remainder when A1 is divided by B1 CODE(A1): returns the ASCII code for the character in cell A1 CHAR(A1): returns the character whose ASCII code is the value in cell A1 Shift by 5: CHAR( MOD( CODE(A1) – CODE(“A”) + 5, 26) + CODE(“A”) )

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Homework 1 Problem 1: The ciphertext: ZSZKV DPKYL DSRKP FLJZI was obtained using a shift cipher. Use a spreadsheet to try all possible keys and decipher the message.

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Homework 1

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Problem 2: Similar, but the students must decode an affine cipher, i.e. y = ax + b (mod 26)

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Later Projects 1.Decode a Substitution Cipher Determine the letter frequencies for a 993-character ciphertext.

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Later Projects 1.Decode a Substitution Cipher Determine the letter frequencies for a 993-character ciphertext. Find common digraphs and trigraphs.

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Later Projects 1.Decode a Substitution Cipher Determine the letter frequencies for a 993-character ciphertext. Find common digraphs and trigraphs. Decode the message.

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Later Projects 1.Decode a Substitution Cipher 2.Decode a Vigenère Cipher Figure out how to import a 6,351-character ciphertext into Excel. Use the Friedman test to estimate the length of the keyword. Use the Kasiski test to find the keyword length. Determine the key.

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Later Projects 1.Decode a Substitution Cipher 2.Decode a Vigenère Cipher 3.Statistical analysis of the English language. Copy 100,000 characters from the internet. Figure out how to remove spaces and punctuation. Count the letter frequencies and digraph frequencies.

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Later Projects 1.Decode a Substitution Cipher 2.Decode a Vigenère Cipher 3.Statistical analysis of the English language. 4.RSA-related: Find the prime factorization of 43,428,539,417. Compute 1281 3645 MOD 4703. Use the Fermat primality test. Implement the Euclidean algorithm. Break RSA.

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Section 4.4: The RSA Cryptosystem Practice HW Handwritten and Maple Exercises p. 11-13 at end of class notes.

Section 4.4: The RSA Cryptosystem Practice HW Handwritten and Maple Exercises p. 11-13 at end of class notes.

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