Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions

Reduced complexity turbo decoders

Turbo codes are a class of forward error correction codes, which have outperformed all the previously known error coding schemes. The strength of this scheme lies in the parallel concatenation of component codes and their iterative decoding algorithm. Although turbo codes have found their way in a number of future wireless communications standards, their efficient implementation in hardware and software is still being actively researched. This study therefore focuses on the design of efficient turbo decoders. The dissertation begins with the description of encoding and decoding of turbo codes. Sliding window implementations of decoding algorithms, which are used to reduce the memory requirements in turbo decoders, are presented. The contribution of this work is the proposed modifications to the conventional sliding window implementations of SOVA, bi-directional SOVA and Max-Log-MAP based turbo decoders. The proposed modifications allow multiple bits to be released in a single decoding window thus reducing the computational complexity and increasing the decoding speed of turbo decoders. A performance and complexity comparison of these decoder implementations is also presented