Pseudorandom Number Generation and Stream Ciphers

Chapter 7

PSEUDORANDOM NUMBER GENERATION AND STREAM CIPHERS

o Principles of Pseudorandom Number Generation

·         The Use of Random Numbers TRNGs, PRNGs, and PRFs PRNG Requirements Algorithm Design

o Pseudorandom  Number Generators

·         Linear Congruential Generators Blum Blum Shub Generator

o Pseudorandom Number Generation Using a Block   Cipher

·         PRNG Using Block Cipher Modes of Operation ANSI X9.17 PRNG

·         Stream Ciphers

·         RC4

·         Initialization of S

·         Stream Generation

·         Strength of RC4

o True Random Number  Generators

·         Entropy Sources Skew

KEY POINTS

◆      A capability with application to a number of cryptographic functions is random or pseudorandom number generation. The principle requirement for this capability is that the generated number stream be unpredictable.

◆      A stream cipher is a symmetric encryption algorithm in which ciphertext output is produced bit-by-bit or byte-by-byte from a stream of plaintext input. The most widely used such cipher is RC4.

An important cryptographic function is cryptographically strong pseudorandom num- ber generation. Pseudorandom number generators (PRNGs) are used in a variety of cryptographic and security applications. We begin the chapter with a look at the basic principles of PRNGs and contrast these with true random number generators (TRNGs).1 Next, we look at some common PRNGs, including PRNGs based on the use of a symmetric block cipher.

The chapter then moves on to the topic of symmetric stream ciphers, which are based on the use of a PRNG. The chapter next examines the most important stream cipher, RC4. Finally, we examine TRNGs.