Boolean Functions and Cryptography

Abstract

Stream ciphers are commonly used for encrypting and decrypting messages. Stream ciphers have several advantages which make them suitable for some applications. Most notably, they are usually faster and have a lower hardware complexity than block ciphers. They are for instance appropriate when buffering is limited, since the binary digits are individually encrypted and decrypted. In stream cipher the encryption and the decryption consist in adding bitwise the input stream and a pseudo-random sequence generated by a pseudo-random generator taking as input a secret information, the secret key. Classical tools to produce such pseudo-random sequences, that are called keystream, are Linear Feedback Registers (LFSR). Stream ciphers can use several LFSR or a single LFSR. As indicated by its name, LFSR are linear and their linear systems are governed by linear relationships between their inputs and outputs. Since linear dependencies can relatively easily be analyzed, stream ciphers designed only with LFSR would be highly insecure.