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.
4.6
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English
پښتو, বাংলা, اردو, 3 more
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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
Assistant Professor in Computer Science
Sang-Yoon Chang is an Assistant Professor in the Computer Science Department at the University of Colorado Colorado Springs (UCCS). His research focuses on critical areas of computer security and computer networks, particularly in wireless networks, edge computing, and cyber-physical systems. His work intersects with the burgeoning fields of the Internet of Things (IoT) and cyber-physical systems, making significant contributions to the security of these evolving technologies.Professor Chang's expertise in cryptography and network security is evident in the courses he teaches, which include Asymmetric Cryptography and Key Management, Classical Cryptosystems and Core Concepts, Cryptographic Hash and Integrity Protection, Cryptography and Information Theory, Mathematical Foundations for Cryptography, and Symmetric Cryptography. These courses reflect his deep knowledge in securing digital communications and ensuring the integrity of systems, particularly in the context of emerging technologies such as IoT and edge computing.Through his teaching and research, Professor Chang is committed to advancing the understanding and implementation of robust security mechanisms for modern computing systems and infrastructures.
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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4.6 course rating
321 ratings
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