Shift Registers (LFSR) and Stream Ciphers

Shift registers are at the heart of cryptography, error‐correction, and information theory. In cryptography, they are the main tools for generating long pseudo‐random sequences which can be used as keys in symmetric cryptography. In error correction, as we will see, the linear feedback shift registers (LFSRs) are the basic building blocks for the theory of cyclic linear codes. According to Schneier, “most practical stream‐cipher designs center around LFSRs,” and “stream ciphers based on shift registers have been the workhorse of military cryptography since the beginning of electronics.” This chapter provides a thorough analysis of LFSRs. It also discusses issues related to the celebrated Berlekamp–Massey algorithm. The Vernam cipher is a stream cipher in which the secret message is encrypted bit by bit. For a block cipher, such as Advanced Encryption Standard, the message is first divided up into blocks of a fixed length before encryption.