SYLLABUS – MA 4550 – Combinatorial and Cryptographic Properties of Boolean Functions,
NPS, Dr. Pante Stanica

LECTURE:  

INSTRUCTOR: Dr. Pante STANICA, 268 Spanagel, 656-2714,
                   pstanica@nps.edu, http://faculty.nps.edu/pstanica/index.htm
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OFFICE HOURS: T,Th  12:00-12:40am; M/W 10:00-10:40pm (or come by if my door is open).
(Be aware that office hours are not a substitute for regular class time)

TEXT: Cryptographic Boolean Functions and Applications (Elsevier-Academic Press); by T.W. Cusick, P. Stanica, 2009. 

PREREQUISITE: MA3025, or equivalent exposure to elementary propositional and predicate logic and mathematical proof. A bit of probability knowledge will help, but I'll go over some topics in class.
 

MATERIAL TO BE COVERED (and Objectives for the course—subject to be adjusted along the way):
* Fourier Analysis of Boolean Functions: Hamming weights, Walsh transform, linear feedback shift registers (LFSRs)                           
* Avalanche and Propagation Criteria: Strict/Global Avalanche – counting and constructions                                                                                      

* Correlation Immunity (CI) and Resiliency: counting and constructions, LFSRs and CI, trade-offs                                                                          

* Bent Boolean Functions: known constructions (Rothaus, Dillon, Dobbertin, Carlet), cryptographic properties, open questions                

* Symmetric and Rotation Symmetric Boolean Functions                          

* Stream Cipher Design: bit generators, nonlinear combiners, LFSRs, algebraic attacks                                                                                      

* Block Ciphers Review: Data Encryption Standard, Advanced Encryption Standard                                                                

* Cayley Graphs: Graph Theory approaches to cryptographic, Boolean Functions                                                                                   

 
CLASS ATTENDANCE AND ENVIRONMENT:  You should do every attempt to arrive on time and attend each class. You are responsible for the material covered in missed classes. I do not tolerate any rude behavior; however, I encourage constructive comments on the material and/or lecture. We have to maintain a class environment conducive to learning therefore I am against bringing “active” cell phones, pagers, and other similar disruptive devices into the classroom.

 

NOTES: MA4550 course will discuss the Fourier analysis of Boolean functions and the relevant combinatorics with an eye toward cryptography and coding theory. Particular topics will include avalanche features of Boolean functions, correlation immunity and resiliency, bentness, trade-offs among cryptographic criteria and real-life applications in the designs of stream and block ciphers.