Applied Cryptography: Protocols, Algorithms, and Source Code in C, Second Edition

CHAPTER 19

Public-Key Algorithms

19.1 BACKGROUND

The concept of public-key cryptography was invented by Whitfield Diffie and Martin Hellman, and independently by Ralph Merkle. Their contribution to cryptography was the notion that keys could come in pairs—an encryption key and a decryption key—and that it could be infeasible to generate one key from the other (see Section 2.5). Diffie and Hellman first presented this concept at the 1976 National Computer Conference [495]; a few months later, their seminal paper “New Directions in Cryptography” was published [496]. (Due to a glacial publishing process, Merkle's first contribution to the field didn't appear until 1978 [1064].)

Since 1976, numerous public-key cryptography algorithms have been proposed. Many of these are insecure. Of those still considered secure, many are impractical. Either they have too large a key or the ciphertext is much larger than the plaintext.

Only a few algorithms are both secure and practical. These algorithms are generally based on one of the hard problems discussed in Section 11.2. Of these secure and practical public-key algorithms, some are only suitable for key distribution. Others are suitable for encryption (and by extension for key distribution). Still others are only useful for digital signatures. Only three algorithms work well for both encryption and digital signatures: RSA, ElGamal, and Rabin. All of these algorithms are slow. They encrypt and decrypt data much more slowly than symmetric algorithms; ...