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So You Want to Break Codes: Careers in Government for Mathematicians

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So You Want to Break Codes: Careers in Government for Mathematicians Edray Herber Goins Department of Mathematics Purdue University September 22, 2011 MA 10800: Mathematics As A Profession And A Discipline
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So You Want to Break Codes: Careers in Government for Mathematicians Edray Herber Goins Department of Mathematics Purdue University September 22, 2011 MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 1/28 Outline of Talk 1 Challenge Problem 2 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research 3 Shift Cipher ASCII and Unicode Examples Affine Cipher 4 MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 2/28 Challenge Problem! MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 3/28 BANJO is to FERNS as PECAN is to [? ] MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 4/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Where Are Such Problems Useful? MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 5/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 6/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research 9800 Savage Road, Ft. George G. Meade, MD MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 7/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Main Building MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 8/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Secure Entrance to Main Building MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 9/28 Facts About NSA Challenge Problem What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research The /Central Security Service (NSA/CSS) is a cryptologic intelligence agency of the United States Department of Defense responsible for the collection and analysis of foreign communications and foreign signals intelligence, as well as protecting U.S. government communications and information systems, which involves cryptanalysis and cryptography. NSA s mission is to collect information that constitutes foreign intelligence or counterintelligence while not acquiring information concerning the domestic activities of United States persons. NSA has declared that it relies on the FBI to collect information on foreign intelligence activities within the borders of the USA, while confining its own activities within the USA to the embassies and missions of foreign nations. Largest employer of mathematicians in the world. In fact, NSA has invested many millions of dollars in academic research. MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 10/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research To Work for NSA, Must I Live in Maryland? MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 11/28 Opportunities at NSA What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Director s Summer Program (DSP) Institute for Defense Analyses (IDA) Center for Communications Research (CCR) Princeton, NJ La Jolla, CA MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 12/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Director s Summer Program MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 13/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Institute for Defense Analyses MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 14/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Center for Communications Research in Princeton, NJ MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 15/28 What is NSA? Director s Summer Program Institute for Defense Analyses Center for Communications Research Center for Communications Research in La Jolla, CA MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 16/28 Shift Cipher ASCII and Unicode Examples Affine Cipher What Kind of Mathematics Happens at NSA? MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 17/28 Shift Cipher ASCII and Unicode Examples Affine Cipher Caesar Cipher MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 18/28 Shift Cipher ASCII and Unicode Examples Affine Cipher American Standard Code for Information Interchange Unicode MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 19/28 Example of Caesar Cipher Shift Cipher ASCII and Unicode Examples Affine Cipher MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 20/28 Converting a String to a Number Shift Cipher ASCII and Unicode Examples Affine Cipher MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 21/28 Converting a Number to a String Shift Cipher ASCII and Unicode Examples Affine Cipher MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 22/28 Shift Cipher ASCII and Unicode Examples Affine Cipher Mathematical Sciences Research Institute Undergraduate Program MSRI-UP MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 23/28 Affine Cipher Challenge Problem Shift Cipher ASCII and Unicode Examples Affine Cipher Plaintext Ciphertext N 1, N 2,...,N n M 1, M 2,...,M n {a 1, a 2,..., a n } (λ,ν) {c 1,c 2,..., c n } with c k = λa k +ν N = n a k b k 1 k=1 (λ,ν) M = n c k b k 1 k=1 = λn +ν bn 1 b 1 MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 24/28 Solution to Challenge Problem! MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 25/28 BANJO is to FERNS as PECAN is to TIGER MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 26/28 Mathematica Code MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 27/28 Questions? MA 10800: Mathematics As A Profession And A Discipline So You Want to Break Codes 28/28
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