Design and Analysis of Symmetric Cryptographic Primitives

Abstract

Stream ciphers are well-known primitives that are used to ensure privacy over a com munication channel. The central theme of a stream cipher is a keystream generator that produces a pseudorandom bit sequence. In such algorithms, the keystream bits are usually XORed with the plaintext bits to produce the ciphertext bits. Therefore, the design and analysis of new keystream generators are important. This thesis presents the design and analysis of several word-oriented keystream generators. The word-based LFSR also known as the multiple recursive matrix method (MRMM) is very attractive as it possesses most of the randomness properties like LFSR. It also takes advantage of modern word-based processors and thus increases the throughput. We intro duce a generalized form of the feedback function for word-oriented feedback shift registers (WFSRs) along with some special cases. A necessary and sufficient condition for nonsingular WFSR is also provided. Like LFSR, the major drawback of MRMM is that it has very low linear complexity. In order to address the low linear complexity drawback in MRMM, the concept of several bit oriented generators has been introduced. First, word-oriented shrinking and self-shrinking generators are studied where the lower bound for the period as well as for the linear com plexity of the bitstream is shown to be exponential. Further experimentation and research have resulted in the identification and then mathematical verification of the exact period of self-shrinking generators. Different word-based cascade systems along with their periods are studied. We provide experimental results on avalanche property on the states of all cascade systems and then analyze the statistical results of the keystream. We present a cryptanalytic attack on the cascade systems and suggest its countermeasure. In the later part of the thesis, we extend the idea of bit-oriented alternating step generators and nonlinear combination generators to the respective word-oriented generators.