TWC:Small: Design and Analysis of Symmetric Key Ciphers

This project concerns symmetric key cryptography. It includes continued collaboration between the PI and M. Goresky and C. Carlet. Its goal is the development of new approaches in the design and analysis of symmetric key cryptosystems - both block and stream ciphers. A major portion of the funding is directed toward the education and training of graduate students in Kentucky. Broader Impact. This grant will benefit society by helping design and implement high speed cryptographic devices. It will advance science while promoting teaching, training and learning and will broaden participation of an underrepresented group by supporting two female PhD students. Block and stream ciphers are essential tools for sending all but the smallest amounts of data securely. They are used for moderate to high volumes of data, such as JPEG files, video on demand, and digital telephony. In such ciphers, linear components such as linear feedback shift registers and bit permutations are used because they are extremely fast and can produce excellent randomness properties. Yet these components are vulnerable to attacks exploiting linearity. To avoid this, nonlinear Boolean functions are used as filters in various ways. The purpose of this grant is to find new approaches to the design of block and stream ciphers and to study nonlinear functions and pseudorandom sequence generators for cryptography. History indicates the cryptosystems now used will need replacement at some point. We must be ready with tools for designing new systems. The innovations from this grant will hasten the development of those tools and will help provide a work force that has the knowledge to use them. Pseudorandom sequence generators are used in other areas, for example as spreading codes in spread spectrum systems, for frequency-hopping in radar and radio systems for protection against jamming, as codewords in error-correcting codes, in large simulations and other quasi-Monte Carlo applications. This work will likely have an impact in these areas as well as cryptography. The principal investigator is one of only a few university faculty members in Kentucky actively involved in cryptographic research. This grant will help support the education of young researchers in this vital field, including graduate students from the underrepresented state of Kentucky. Intellectual Merit. In a block cipher, the input is modified through a series of rounds. Each round commonly consists of linear mixing operations plus some highly nonlinear function applied to small blocks of input symbols and a static key. Nonlinearity and statistical randomness properties of the functions lead to resistance to various attacks, but the static key enables various types of attack. In a typical stream cipher fast pseudorandom sequence generators are used. Their outputs are inputs to a nonlinear combining function whose output is used as a keystream. The keystream is then added symbol by symbol to the message to produce the cipher. The statistical randomness of the keystream protects against attacks based on statistical bias, and the complexity of the combining function, as measured by various nonlinearity measures, protects against known attacks. We propose to (1) develop new designs of block ciphers with time varying keys using pseu- dorandom sequence generators and new architectures of Feistel networks; (2) study the effect of replacing LFSRs by FCSRs stream ciphers; (3) study measures of randomness of Boolean functions (e.g., bentness, resilience, strict avalanche, and correlation immunity based on new generalizations of the Walsh transform.); (4) further analyze AFSRs, e.g. the solution of the register synthesis problem for more general classes of AFSRs, a step in understanding the security of a large class of stream ciphers; and (5) develop more efficient implementations of sequence generators.