Cryptography at The University of South Carolina Douglas B. Meade

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Cryptography at The University of South Carolina Douglas B. Meade

Cryptography as an application in …  Number Theory (M ATH 580)  Course homepage:  RSA Encryption Algorithm  (Numerical) Linear Algebra (M ATH 526 )  Course homepage:  Hill Substitution Cypher

Cryptography as its own course  Cryptography  Cross-listed as C SCE 557 and M ATH 587  Course homepage:  Syllabus:

Cross-listing between C SCE & M ATH  Computer science/engineering students …  see relevant and interesting applications of mathematics  learn some new mathematics  motivated to take more mathematics courses

Cross-listing between C SCE & M ATH  Mathematics students …  see cutting-edge application of mathematics  appreciate importance of computational mathematics  exposed to practical issues related to implementing mathematics (Gnu MultiPrecision library)  motivated to take more computer science courses

Hill Substitution Cypher  Reference: Linear Algebra and Its Applications, David C. Lay, Addison-Wesley, updated 3 rd edition,  Case Study (electronic supplement)

Hill Substitution Cypher  Preparation 1. Specify alphabet and cypher/decypher array p = # characters in alphabet 2. Select key matrix M invertible mod p: det M <> = mod p 3. Compute inverse key matrix M -1 M = I mod p 4. Share cypher/decypher array and M -1

Hill Substitution Cypher  Encryption 1. Convert message to numeric code + vectorize 2. Encode using key matrix e = Mv mod p 3. Convert numeric vector to string in alphabet

Hill Substitution Cypher  Decryption 1. Convert encoded string to numeric code + vectorize 2. Decode using inverse key matrix v = M -1 e mod p 3. Convert numeric vector to string in alphabet

Hill Substitution Cypher  Implementation  Maple supports modular linear algebra supports modular linear algebra embedded components eliminate need to know any Maple to use [worksheet] [MapleNet] embedded components eliminate need to know any Maple to use [worksheet] [MapleNet]worksheetMapleNetworksheetMapleNet  MATLAB does not support modular linear algebra does not support modular linear algebra