Abstract Algebra Course
Dive into groups, rings, fields, and modular arithmetic, then apply them directly to cryptographic algorithms like RSA and Diffie-Hellman. This course transforms abstract algebraic theory into practical computations, security analysis, and proof methods ideal for mathematicians and developers working in secure systems.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This course offers a quick and practical journey from fundamental concepts of groups, rings, and fields to actual cryptographic algorithms. Learners will explore permutations, modular arithmetic, finite fields, and protocols such as RSA, Diffie-Hellman, and elliptic curves, gaining skills in proofs, complexity analysis, and implementation for enhanced security and accuracy in professional tasks.
Elevify advantages
Develop skills
- Master finite groups to handle permutations and bitwise operations efficiently.
- Gain fluency in modular arithmetic for implementing rings, fields, and secure computations.
- Build foundational cryptography skills by constructing RSA, Diffie-Hellman, and elliptic curve systems manually.
- Apply algebraic structures to optimise algorithms, reduce search times, and verify correctness.
- Develop insights into security by evaluating algebraic vulnerabilities, parameters, and complexity balances.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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