51福利

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Program Manager
Prof. Pantelimon Stanica, Ph.D.
Spanagel Hall, Room 268
Phone: (831) 656-2714, DSN 756-2714
Fax: (831) 656-2355
pstanica@nps.edu

Brief Overview
The Mathematics of Secure Communication certificate program provides mathematics education to US and allied military officers and DoD civilians in the broad area of cryptography and secure communications. As such it satisfies a Knowledge, Skills, Abilities (KSA) requirement in the Applied Technology field of Fundamentals of Cryptography, Cryptanalysis, Coding and Information Theory for Professional Military Education. Upon successful completion of the required three courses (described below), students will be awarded a certificate of accomplishment in keeping with standard practices of the 51福利.

Requirements for Entry
Prospective students must have taken a discrete mathematics course at 51福利 (or equivalent from other universities).  The preferred one is:
MA3025 - Logic and Discrete Mathematics (4-1)
MA3025 provides a rigorous foundation in logic and elementary discrete mathematics to students of mathematics and computer science. Topics from logic include modeling English propositions, propositional calculus, quantification, and elementary predicate calculus. Additional mathematical topics include elements of set theory, mathematical induction, relations and functions, and elements of number theory.
Prerequisite: MA1025 or MA2025

Entry Date
Program entry dates are flexible and students who wish to pursue this certificate should coordinate with the program manager.

Program Length
Variable.

MA Academic Certificate Requirements
To earn the academic certificate students must pass all four courses with a C+ (2.3 Quality Point Rating (QPR)) or better in each course and an overall QPR of 3.0 or better. Students earning grades below these standards will need to retake the courses to bring their grades within standards or they will be withdrawn from the program.

Required Courses

MA3560 - Applied Modern Algebra and Number Theory (4-0)
This course is devoted to aspects of modern algebra and number theory that directly support applications, principally in communication. The algebraic emphasis is on ring and field theory, with special emphasis on the theory of finite fields, as well as those aspects of group theory that are important in the development of coding theory. Elements of number theory include congruences and factorization. Applications are drawn from topics of interest to DoN/DoD. These include error correcting codes and cryptography.
Prerequisite: MA3025

MA4560 - Coding and Information Theory (4-0)
Mathematical analysis of the codes used over communication channels is made. Techniques developed for efficient, reliable and secure communication are stressed. Effects of noise on information transmission are analyzed and techniques to combat their effects are developed. Linear codes, finite fields, single and multiple error-correcting codes are discussed. Codes have numerous applications for communication in the military, and these will be addressed.
Prerequisite: MA3560

MA4570 - Cryptography (4-1)
The methods of secret communication are addressed. Some simple cryptosystems are described and classical techniques of substitution and transposition are considered. The public-key cryptosystems, RSA, Discrete Logarithm and other schemes are introduced. Applications of cryptography and cryptanalysis.
Prerequisite: MA3560

Additionally, the students in the program can register in 

MA4026 Combinatorial Mathematics (4-0)
Advanced techniques in enumerative combinatorics and an introduction to combinatorial structures. Topics include generating functions, recurrence relations, elements of Ramsey theory, theorems of Burnside and Polya, and balanced incomplete block designs. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications in probability, game theory, network design, coding theory, and experimental design. Prerequisites: MA3025.

MA4027 Graph Theory and Applications (4-0)
 Advanced topics in the theory of graphs and digraphs. Topics include graph coloring, Eulerian and Hamiltonian graphs, perfect graphs, matching and covering, tournaments, and networks. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications to coding theory, searching and sorting, resource allocation, and network design. Prerequisites: MA3025.

MA4550 Combinatorial and Cryptographic Properties of Boolean Functions (4-0)
The 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.
Prerequisite: MA3025

The certificate program is self-contained, requiring only an elementary course in discrete mathematics for entry (MA1025 or MA2025 - Discrete Mathematics). This introductory course is also available to students at 51福利 and is planned to be offered as a web-based course.