tailieunhanh - Chapter 10: Symmetric-Key Cryptography

Objectives of Chapter 7: To distinguish between two cryptosystems; to introduce trapdoor one-way functions and their use in asymmetric-key cryptosystems; to introduce the knapsack cryptosystem as one of the first ideas in asymmetric-key cryptography; to discuss the RSA cryptosystem. | Chapter 10 Symmetric-Key Cryptography Chapter 10 Objectives To distinguish between two cryptosystems symmetric-key and asymmetric-key To introduce trapdoor one-way functions and their use in asymmetric-key cryptosystems To introduce the knapsack cryptosystem as one of the first ideas in asymmetric-key cryptography To discuss the RSA cryptosystem To discuss the Rabin cryptosystem To discuss the ElGamal cryptosystem To discuss the elliptic curve cryptosystem 10-1 INTRODUCTION 10-1 INTRODUCTION S mme ric and asymmetric-key cryptography will exist in parallel and continue to serve the community. We actually believe that they are complements of each other the advantages of one can compensate for the disadvantages of the other. Topics discussed in this section Keys General Idea Need for Both Trapdoor One-Way Function Knapsack Cryptosystem Symmetric and asymmetric-key cryptography will exist in parallel and continue to serve the community. We actually believe that they are complements of each other the advantages of one can compensate for the disadvantages of the other. Note 1 Symmetric-key cryptography is based on sharing secrecy asymmetric-key cryptography is based on personal secrecy. Figure Locking and unlocking in asymmetric-key cryptosystem 1 Continued Need for Both Plaintext Ciphertext Unlike in symmetric-key cryptography plaintext and ciphertext are treated as integers in asymmetric-key cryptography. There is a very important fact that is sometimes misunderstood The advent of asymmetric-key cryptography does not eliminate the need for symmetric-key cryptography. Encryption Decryption C f Kpublic P P g K i . C Trapdoor One-Way Function The main idea behind asymmetric-key cryptography is the concept of the trapdoor one-way function. I Functions Figure A function as rule mapping a domain to a range Continued One-Way Function OWF 1. f is easy to compute. 2. f-1 is .