Public Key CryptographyWhat is Cryptography?ApplicationsSlide 4RSA ExampleRSA ContinuedDigital SigningKey DisseminationSummaryHomework ProblemReferencesSlide 12Colin DoughertyWhat is Cryptography?PrivateSymmetric keyExample: AESPublic Asymmetric keysExample: RSAApplicationsReal WorldSpies, NSA, CIAFinancial InstitutionsAlice, Bob and EveComputer SciencePrimes, factoring, hashingRandomnessNP complete problemsPublic Key CryptographyDiffie-Hellman Public Key exchange systemSubset-sum problemRivest, Shamir and Adleman Factoring very large numbersRSA ExampleRandom Primes: p = 47 and q = 731.79769313486231590772930519078e+308n = p * q = 3431φ = (p – 1) * (q – 1) = 3312 1<e<n and relatively prime to φ; e = 425Modular inverse of e: d = 1769RSA ContinuedEncrypt: plaintext = 707c = me mod nc = 707425 (mod 3431) = 2142Decrypt: cipher text = 2142m = cd mod nm = 21421769 (mod 3431) = 707Digital SigningAlice Signature = hashd mod nBob checks Alice’s Signature hashe mod nKey DisseminationSummaryPublic Key CryptographyPublic and Private KeysEncryption and DecryptionKey ExchangeDigital SignaturesHomework ProblemReferencesModern Language Association (MLA): "cryptography." The American Heritage® Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company, 2004. Rivest, R. L., Shamir, A., Adleman, L. A.: A method for obtaining digital signatures and public-key cryptosystems; Communications of the ACM, Vol.21, Nr.2, 1978, S.120-126.Diffie, W., and Hellman, M. New directions in cryptography. IEEE Trans. Inform.Theory IT-22, (Nov. 1976), 644-654.A. K. Dewdney: The New Turing OmnibusColin
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