Mathematical Foundations for Cryptography
Master cryptographic mathematics, including number theory and algorithms, to understand and implement secure encryption systems and protocols.
Master cryptographic mathematics, including number theory and algorithms, to understand and implement secure encryption systems and protocols.
This foundational course explores the mathematical principles crucial for understanding cryptography and cryptanalysis. Students learn fundamental concepts including prime numbers, modular arithmetic, Euler's theorems, and primality testing. The course provides comprehensive coverage of mathematical tools essential for both symmetric and asymmetric cryptographic methods.
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English
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What you'll learn
Master prime numbers and modular arithmetic
Understand multiplicative inverses and GCD
Apply Euler's theorems and functions
Implement Chinese Remainder Theorem
Perform primality testing
Calculate discrete logarithms
Skills you'll gain
This course includes:
3.5 Hours PreRecorded video
9 quizzes
Access on Desktop
FullTime access
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There are 4 modules in this course
This course provides a comprehensive introduction to the mathematical foundations essential for cryptography. The curriculum covers fundamental concepts from number theory, including prime numbers and modular arithmetic, progressing to advanced topics like Euler's theorems and primality testing. Students learn through theoretical concepts and practical applications of mathematical principles in cryptographic systems.
Integer Foundations
Module 1 · 3 Hours to complete
Modular Exponentiation
Module 2 · 3 Hours to complete
Chinese Remainder Theorem
Module 3 · 3 Hours to complete
Primality Testing
Module 4 · 3 Hours to complete
Fee Structure
Instructors
Expert in Computer Security and Assistant Professor at UCCS
Dr. Sang-Yoon Chang is an Assistant Professor in the Computer Science department at the University of Colorado Colorado Springs (UCCS). He specializes in computer security and computer networks, with a particular focus on wireless networks, edge computing, and cyber-physical systems. His research aligns closely with advancements in the Internet of Things (IoT) and aims to enhance the security and efficiency of networked systems. Dr. Chang has a strong academic background, having earned both his Bachelor’s and Ph.D. degrees in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign.In addition to his research, Dr. Chang teaches several courses related to cryptography and network security, including "Asymmetric Cryptography and Key Management" and "Cryptography and Information Theory." His work has garnered attention for its relevance in today's technology landscape, particularly as it pertains to secure communications in increasingly interconnected environments.
Lecturer in Engineering and Cryptography
William Bahn is a lecturer with a strong academic background in engineering and cryptography. He holds a Bachelor of Science in Engineering Physics and a Master of Engineering in Engineering Systems, both from the Colorado School of Mines. Bahn further advanced his education by earning a Ph.D. in Electrical Engineering from the University of Colorado Colorado Springs.With his expertise in electrical engineering and cryptography, Bahn teaches specialized courses focused on the mathematical and conceptual foundations of secure communications. His courses include Classical Cryptosystems and Core Concepts and Mathematical Foundations for Cryptography, providing students with a comprehensive understanding of cryptographic techniques and the underlying mathematical principles essential for secure systems.Bahn’s academic and research interests are centered on cryptography, making him a valuable instructor for students pursuing advanced studies in the field of secure communications and information security.
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