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John von Neumann 1903-1957, Garrett Birkhoff 1911-1996
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Mathematics of Secure Communication
certificate program


The Mathematics of Secure Communication certificate program comprises four courses (see below). Upon successful completion of the coursework, students will be awarded a certificate of accomplishment in keeping with standard practices of the Naval Postgraduate School. The purpose for its development is to provide Mathematics education to Naval 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 cryptology and cryptanalysis for Professional Military Education.

The certificate program will be further supported by collaborations between the Applied Mathematics departments of NPS and San Diego State University through an EPA signed in FY02 by both schools.

Please note that one of these courses involved in the certificate program (MA3560) is to be amended from a 3-0 to 4-0. This change reflects incorporation of Number Theory subject matter in support of further courses in the sequence.

The certificate sequence of courses is as follows:

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

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 (4-0)
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 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 NPS and is planned to be offered as a web-based course.