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.
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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 Chapter 10 To introduce the knapsack cryptosystem as one of the first ideas in asymmetric-key cryptography Symmetric-Key To discuss the RSA cryptosystem Cryptography To discuss the Rabin cryptosystem To discuss the ElGamal cryptosystem To discuss the elliptic curve cryptosystem10.1 10.2 10- 10-1 INTRODUCTION 10 10--1 INTRODUCTION Symmetric and asymmetric asymmetric--key cryptography will exist in Symmetric and asymmetric- asymmetric-key cryptography will exist in parallel and continue to serve the community community.. We actually parallel and continue to serve the community community.. We actually believe that they are complements of each other;other; the believe that they are complements of each other other;; the advantages of one can compensate for the disadvantages of advantages of one can compensate for the disadvantages of the other. other. the other other.. Topics discussed in this section: Note 10.1.1 Keys 10.1.2 General Idea Symmetric-key cryptography is based on sharing secrecy; 10.1.3 Need for Both asymmetric-key cryptography is based on personal secrecy. 10.1.4 Trapdoor One-Way Function 10.1.5 Knapsack Cryptosystem10.3 10.4 10.1.1 Keys 10.1.2 General Idea Asymmetric key cryptography uses two separate keys: one private and one public. Figure 10.2 General idea of asymmetric-key cryptosystem Figure 10.1 Locking and unlocking in asymmetric-key cryptosystem10.5 10.6 1 10.1.2 Continued 10.1.3 Need for Both Plaintext/Ciphertext There is a very important fact that is sometimes Unlike in symmetric-key cryptography, plaintext and misunderstood: The advent of asymmetric-key cryptography ciphertext are treated as integers in asymmetric-key does not eliminate the need for symmetric-key cryptography. cryptography. Encryption/Decryption C = f (Kpublic , P) P = g(Kprivate , C)10.7 10.8 10.1.4 Trapdoor One-Way Function 10.1.4 Continued The main idea behind asymmetric-key cryptography is the One-Way Function (OWF) concept of the trapdoor one-way function. 1. f is easy to compute. 2. f −1 is difficult to compute. Functions Trapdoor One-Way Function (TOWF) Figure 10.3 A function as rule mapping a domain to a range 3. Given y and a trapdoor, x can be computed ...