Signal Processing Techniques in Cryptography

Security of cryptographic symmetric primitives is studied in this thesis. Pseudorandomness characteristics of cryptographic sequences are analyzed, resulting in new methods for constructing sequences with high linear complexity. Connections between nonlinear complexity and other cryptographic criteria are also established, whereas a new recursive algorithm for efficiently computing the minimal feedback shift register which generates a given sequence is provided. Furthermore, security issues of cryptographic Boolean functions that are used in cryptographic systems as components of sequence generators are studied; on this direction, new efficient formulas for determining best quadratic approximations of several classes of Boolean functions are derived, leading to new design principles that should be considered in the construction of secure cryptosystems.