Other Public-Key Cryptosystems

Chapter 10

OTHER PUBLIC-KEY CRYPTOSYSTEMS

            Diffie-Hellman Key Exchange

The Algorithm

Key Exchange Protocols Man-in-the-Middle Attack

            Elgamal Cryptographic System

            Elliptic Curve Arithmetic

Abelian Groups

Elliptic Curves over Real Numbers Elliptic Curves over Zp

Elliptic Curves over GF(2m)

            Elliptic Curve Cryptography

Analog of Diffie-Hellman Key Exchange Elliptic Curve Encryption/Decryption Security of Elliptic Curve Cryptography

            Pseudorandom Number Generation Based on an Asymmetric   Cipher

PRNG Based on RSA

PRNG Based on Elliptic Curve Cryptography

KEY POINTS

◆     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(2 Power m) have been developed.

This chapter begins with a description of one of the earliest and simplest PKCS: Diffie- Hellman key exchange. The chapter then looks at another important scheme, the ElGamal PKCS. Next, we look at the increasingly important PKCS known as elliptic curve cryptography. Finally, the use of public-key algorithms for pseudorandom num- ber generation is examined.