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Public Key Cryptography

Colin Dougherty. Public Key Cryptography. What is Cryptography?. Private Symmetric key Example: AES Public Asymmetric keys Example: RSA. Applications. Real World Spies, NSA, CIA Financial Institutions Alice, Bob and Eve Computer Science Primes, factoring, hashing Randomness

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Public Key Cryptography

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  1. Colin Dougherty Public Key Cryptography

  2. What is Cryptography? • Private • Symmetric key • Example: AES • Public • Asymmetric keys • Example: RSA

  3. Applications • Real World • Spies, NSA, CIA • Financial Institutions • Alice, Bob and Eve • Computer Science • Primes, factoring, hashing • Randomness • NP complete problems

  4. Public Key Cryptography • Diffie-Hellman • Public Key exchange system • Subset-sum problem • Rivest, Shamir and Adleman • Factoring very large numbers

  5. RSA Example • Random Primes: p = 47 and q = 73 • 1.79769313486231590772930519078e+308 • n = p * q = 3431 • φ = (p – 1) * (q – 1) = 3312 • 1<e<n and relatively prime to φ; e = 425 • Modular inverse of e: d = 1769

  6. RSA Continued • Encrypt: plaintext = 707 • c = me mod n • c = 707425 (mod 3431) = 2142 • Decrypt: cipher text = 2142 • m = cd mod n • m = 21421769 (mod 3431) = 707

  7. Digital Signing • Alice Signature = hashd mod n • Bob checks Alice’s Signature hashe mod n

  8. Key Dissemination • Public Key Infrastructure (PKI) • Certificate Authorities (CA) • Enterprise Solution • +

  9. Summary • Public Key Cryptography • Public and Private Keys • Encryption and Decryption • Key Exchange • Digital Signatures

  10. Homework Problem • Find a polynomial time solution to the factorization problem. • OR • Who authored the paper on RSA?

  11. References • Modern 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 Omnibus

  12. Colin Dougherty Public Key Cryptography

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