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
The certificate sequence of courses is as
- 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
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.
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.
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
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.
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