Cryptology with SpreadsheetsA Computer Course for EveryoneJim BelkTexas A&M University

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

The BookChapter 1: History and ExamplesChapter 2: Classical CiphersShift Ciphers, Affine CiphersSubstitution CiphersTransposition CiphersVigenre CiphersHill Ciphers

The BookChapter 1: History and ExamplesChapter 2: Classical CiphersChapter 3: Computer CryptologyChapter 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.Usefulspreadsheets are the primary mathematical software available on most PCs.

Example: Shift CipherSimple alphabetic shift:y = x + c (mod 26)MOD(A1, B1): computes the remainder when A1 is divided by B1CODE(A1): returns the ASCII code for the character in cell A1CHAR(A1): returns the character whose ASCII code is the value in cell A1Useful Commands:

Example: Shift CipherShift by 5:CHAR( MOD( CODE(A1) CODE(A) + 5 , 26) + CODE(A) )MOD(A1, B1): computes the remainder when A1 is divided by B1CODE(A1): returns the ASCII code for the character in cell A1CHAR(A1): returns the character whose ASCII code is the value in cell A1

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

Homework 1

Homework 1

Homework 1Problem 2:Similar, but the students must decode an affinecipher, i.e.y = ax + b (mod 26)

Later ProjectsDecode a Substitution CipherDetermine the letter frequencies for a 993-character ciphertext.

Later ProjectsDecode a Substitution CipherDetermine the letter frequencies for a 993-character ciphertext.Find common digraphs and trigraphs.

Later ProjectsDecode a Substitution CipherDetermine the letter frequencies for a 993-character ciphertext.Find common digraphs and trigraphs.Decode the message.

Later ProjectsDecode a Substitution Cipher2.Decode a Vigenre CipherFigure 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 ProjectsDecode a Substitution Cipher2.Decode a Vigenre CipherStatistical 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 ProjectsDecode a Substitution Cipher2.Decode a Vigenre CipherStatistical analysis of the English language.RSA-related:Find the prime factorization of 43,428,539,417.Compute 12813645 MOD 4703.Use the Fermat primality test.Implement the Euclidean algorithm.Break RSA.