Colin Dougherty PUBLIC KEY CRYPTOGRAPHY What is 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 �NP complete problems
Public Key Cryptography � Diffie-Hellman �Public Key exchange system �Subset-sum problem � Rivest, Shamir and Adleman �Factoring very large numbers
RSA Example � Random Primes: p = 47 and q = 73 � 1. 79769313486231590772930519078 e+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
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
Digital Signing � Alice � Bob Signature = hashd mod n checks Alice’s Signature hashe mod n
Key Dissemination � Public Key Infrastructure (PKI) � Certificate Authorities (CA) �Enterprise Solution • +
Summary � Public Key Cryptography �Public and Private Keys �Encryption and Decryption �Key Exchange �Digital Signatures
Homework Problem � Find a polynomial time solution to the factorization problem. • OR � Who authored the paper on RSA?
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 �
Colin Dougherty PUBLIC KEY CRYPTOGRAPHY
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