[Page 289]Chapter 10. Key Management; Other Public-Key Cryptosystems 10.1 Key Management | Distribution of Public Keys Distribution of Secret Keys Using Public-Key Cryptography | 10.2 Diffie-Hellman Key Exchange | The Algorithm Key Exchange Protocols Man-in-the-Middle Attack | 10.3 Elliptic Curve Arithmetic | Abelian Groups Elliptic Curves over Real Numbers Elliptic Curves over Zp Elliptic Curves over GF(2m) | 10.4 Elliptic Curve Cryptography | Analog of Diffie-Hellman Key Exchange Elliptic Curve Encryption/Decryption Security of Elliptic Curve Cryptography | 10.5 Recommended Reading and Web Sites | 10.6 Key Terms, Review Questions, and Problems | Key Terms Review Questions Problems |
[Page 290]No Singhalese, whether man or woman, would venture out of the house without a bunch of keys in his hand, for without such a talisman he would fear that some devil might take advantage of his weak state to slip into his body. The Golden Bough, Sir James George Frazer Key Points Public-key encryption schemes are secure only if the authenticity of the public key is assured. A public-key certificate scheme provides the necessary security. A simple public-key algorithm is Diffie-Hellman key exchange. This protocol enables two users to establish a secret key using a public-key scheme based on discrete logarithms. The protocol is secure only if the authenticity of the two participants can be established. Elliptic curve arithmetic can be used to develop a variety of elliptic curve cryptography (ECC) schemes, including key exchange, encryption, and digital signature. For purposes of ECC, elliptic curve arithmetic involves the use of an elliptic curve equation defined over a finite field. The coefficients and variables in the equation are elements of a finite field. Schemes using Zp and GF(2m) have been developed.
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This chapter continues our overview of public-key encryption. We examine key distribution and management for public-key systems, including a discussion of Diffie-Hellman key exchange. Finally, we provide an introduction to elliptic curve cryptography. |