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

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Presentation transcript:

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

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

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

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

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.

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:

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”) )

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.

Homework 1

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

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

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

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

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.

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.

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 MOD Use the Fermat primality test. Implement the Euclidean algorithm. Break RSA.