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Unformatted text preview: 11COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 2.1, pp. 4354Intro to Crypto and ModVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen21Godfrey Harold Hardyb. 1877. d. 1947was a prominent British mathematician,known for his achievements innumber theory and mathematical analysis.fromhttp://en.wikipedia.org/wiki/G.H.Hardy22Godfrey Harold Hardyb. 1877. d. 1947was a prominent British mathematician,known for his achievements innumber theory and mathematical analysis.fromhttp://en.wikipedia.org/wiki/G.H.HardyIn his 1940 autobiographyA Mathematician’s Apology, Hardy wrote23Godfrey Harold Hardyb. 1877. d. 1947was a prominent British mathematician,known for his achievements innumber theory and mathematical analysis.fromhttp://en.wikipedia.org/wiki/G.H.HardyIn his 1940 autobiographyA Mathematician’s Apology, Hardy wrote”The great modern achievments of applied mathematics have been inrelativity and quantum mechanics, and these subjects are, at present,almost as ‘useless’ as the theory of numbers.”24Godfrey Harold Hardyb. 1877. d. 1947was a prominent British mathematician,known for his achievements innumber theory and mathematical analysis.fromhttp://en.wikipedia.org/wiki/G.H.HardyIn his 1940 autobiographyA Mathematician’s Apology, Hardy wrote”The great modern achievments of applied mathematics have been inrelativity and quantum mechanics, and these subjects are, at present,almost as ‘useless’ as the theory of numbers.””... then the great bulk of higher mathematics isuseless.ModernGeometry and algebra,the theory of numbers, the theory of aggregatesand functions, relativity, quantum mechanics – no one of them standsthe test much better than another, . . .”and31If he could see the world now, G.H. Hardy wouldbe spinning in his grave.Number theory, introduced in this lecture, isthe basis of modern coding theory.Computer security and ecommerce would beimpossiblewithout it.32If he could see the world now, G.H. Hardy wouldbe spinning in his grave.Number theory, introduced in this lecture, isthe basis of modern coding theory.Computer security and ecommerce would beimpossiblewithout it.relativity and quantum theory turned out to be prettyuseful as well . . ..33If he could see the world now, G.H. Hardy wouldbe spinning in his grave.Number theory, introduced in this lecture, isthe basis of modern coding theory.Computer security and ecommerce would beimpossiblewithout it.relativity and quantum theory turned out to be prettyuseful as well . . ..At one point, not long ago, the largest employer of mathematicians in the United States, and therefore probably theworld, was the National Security Agency (NSA). The NSA isthe largest spy agency in the US – bigger than the CIA – andhas the responsibility for code design and breaking.41(Euclid’s Division Theorem)Letnbe apositiveinteger. Then foreveryintegerm,there existuniqueintegersqandrsuch thatm=nq+rand≤r < n.42...
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 M.J.Golin
 Computer Science, Cryptography, Alice, Bob iii

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