Wireless Mobile Internet Security, 2nd Edition

Chapter 6

Asymmetric Public-Key Cryptosystems

Public-key cryptography became public soon after Whitefield Diffie and Martin Hellman (1976) proposed the innovative concept of an exponential key exchange scheme. Since 1976, numerous public-key algorithms have been proposed, but many of them have since been broken. Of the many algorithms that are still considered to be secure, most are impractical.

Only a few public-key algorithms are both secure and practical. Of these, only some are suitable for encryption. Others are only suitable for digital signatures. Among these numerous public-key cryptography algorithms, only four algorithms, RSA (1978), ElGamal (1985), Schnorr (1990), and ECC (1985), are considered to be suitable for both encryption and digital signatures. Another public-key algorithm that is designed to only be suitable for secure digital signatures is DSA (Digital Signature Algorithm; 1991). The designer should bear in mind that the security of any encryption scheme depends on the length of the key and the computational work involved in breaking a cipher.

6.1 Diffie–Hellman Exponential Key Exchange

In 1976, Diffie and Hellman proposed a scheme using the exponentiation modulo q (a prime) as a public key exchange algorithm. Exponential key exchange takes advantage of easy computation of exponentials in a finite field GF(q) with a prime q compared with the difficulty of computing logarithms over GF(q) with q elements . Let q be a prime number and a primitive element of the ...