One-Way Functions and Pseudorandomness

Abstract

There is a close relationship between encryption and randomness. The security of encryption algorithms usually depends on the random choice of keys and bit sequences. A famous example is Shannon’s result. Ciphers with perfect secrecy require randomly chosen key strings, which are of the same length as the encrypted message. In Chapter 9, we will study the classical Shannon approach to provable security, together with more recent notions of security. One main problem is that truly random bit sequences of sufficient length are not available in most practical situations. Therefore, one works with pseudorandom bit sequences. They appear to be random, but actually they are generated by an algorithm. Such algorithms are called pseudorandom bit generators. They output, given a short random input value (called the seed), a long pseudorandom bit sequence. Classical techniques for the generation of pseudorandom bits or numbers (see [Knuth98]) yield well-distributed sequences. Therefore, they are well-suited for Monte Carlo simulations. However, they are often cryptographically insecure. For example, in linear congruential pseudorandom number generators or linear feedback shift registers (see, e.g., [MenOorVan96]), the secret parameters and hence the complete pseudorandom sequence can be efficiently computed from a small number of outputs.