LectureVPublicKeyCryptography详解.PDFVIP

Lecture V : Public Key Cryptography Internet Security: Principles Practices John K. Zao, PhD (Harvard) SMIEEE Amir Rezapoor Computer Science Department, National Chiao Tung University Spring 2012 2 Internet Security 鈥 Public Key Cryptography Spring 2012 Outline 飦 Functional Components 飦禣ne-Way Functions 飦禣ne-Way Trapdoor Functions 飦 Cryptographic Systems 飦禗iffie-Hellman (Key Agreement) Algorithm 飦禦SA Algorithm 飦禗igital Signature Algorithm 3 Internet Security 鈥 Public Key Cryptography Spring 2012 One -Way Function Definition : A one-to-one mapping 鈭€x 鈭圫, 鈭 y 鈭圫 | y = f (x) of which 飩 Forward Mapping f is computationally feasible 飩 Inverse Mapping f -1 is computationally infeasible Characteristics : Cryptographically Strong / Secure 飩 Inverse Infeasibility f -1 is computationally infeasible 飩 Collision Improbability Given a, b 鈭圫, P ( f (a) = f (b) ) 鈮 #(S)/2 Example : 飩 Modular Exponentiation 飩 Message Digest (Cryptographically Strong Hashing) 4 Internet Security 鈥 Public Key Cryptography Spring 2012 One -Way Trapdoor Function Definition : A one-to-one parameterized mapping 鈭€x 鈭圫, 鈭 y 鈭圫 | y = f (x) k of which 飩 Forward Mapping fk is computationally feasible if k is known 飩 Inverse Mapping f -1 is k 飦稢omputationally infeasible if k is unknown, but 飦稢omputationally feasible if k is known Question : Does such function ever exist ? Diffie and Hellman thought so ! Diffie, w. and Hellman, M.E., 鈥淣ew Directions in Cryp