This first volume contains only material on the basic tools of modern cryptography, that is, one-way functions, pseudorandomness, and zero-knowledge proofs. These basic tools are used in the construction of the basic applications (to be covered in the second volume). The latter will cover encryption, signatures, and general cryptographic protocols. In this appendix we provide brief summaries of the treatments of these basic applications.

Encryption: Brief Summary

Both private-key and public-key encryption schemes consist of three efficient algorithms: key generation, encryption, and decryption. The difference between the two types of schemes is reflected in the definition of security: The security of a public-key encryption scheme should also hold when the adversary is given the encryption key, whereas that is not required for private-key encryption schemes. Thus, public-key encryption schemes allow each user to broadcast its encryption key, so that any other user can send it encrypted messages (without needing to first agree on a private encryption key with the receiver). Next we present definitions of security for private-key encryption schemes. The public-key analogies can be easily derived by considering adversaries that get the encryption key as additional input. (For private-key encryption schemes, we can assume, without loss of generality, that the encryption key is identical to the decryption key.)

Definitions

For simplicity, we consider only the encryption of a single message; however, this message can be longer than the key (which rules out information-theoretic secrecy [200]). We present two equivalent definitions of security.