TWC: Small: Design and Analysis of Symmetric Key Ciphers

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Pseudorandom sequences (PRS) exhibit a statistical randomness and are widely used in applications where randomness is needed and PRS generation can be effectively done. Many everyday applications in digital computing and communication require randomness to operate correctly. For example, these include secure network communications, global positioning systems, and even weather prediction simulations. Yet, few general generators of high quality pseudorandom sequences are known. This research will develop algorithms and software tools to make high quality usable pseudorandom sequences, particularly, which would lead to improvements in performance and security over current symmetric key ciphers. This project concerns the design of high speed mechanisms for data encryption: Feistel networks, a widely used architecture for block ciphers; Boolean functions, building blocks for both block ciphers and stream ciphers; and feedback-with-carry shift registers (FCSRs) and generalizations (AFSRs), generators of sequences with many desirable properties. Many basic properties of FCSRs have been determined and they have been used in stream ciphers and quasi-Monte Carlo. We propose to (1) develop new designs of block ciphers with new Feistel-like networks or time varying keys using PRS generators; (2) study stream ciphers with FCSRs replacing LFSRs; (3) study measures of randomness of Boolean functions; (4) further analyze AFSRs, e.g. solve the register synthesis problem for more general AFSRs; and (5) develop efficient implementations of sequence generators.