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## Active learning in E-learning: a case study to teach elliptic curve cryptosystem, its fast computational algorithms and authentication protocols for resource constraint RFID-sensor integrated mobile devices

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Elliptic curve cryptosystem (ECC) is a public key-based cryptosystem. All algorithms in ECC are based on point addition and point doubling arithmetic operations. This explains the active learning process and its usages in teaching elliptic curve cryptography-based contents to undergraduate and graduate students. Here, the emphasis is given to mathematical contents that make the cryptography concepts easy to understand. Mathematical concepts mainly include point addition and doubling with examples. Further, technical observations are made while teaching these contents. For example, to reduce computation cost, there is a need for fast computations method in point addition and doubling operations. Thus, the fast computational algorithms are important to understand with examples for reducing the cost in ECC arithmetic operations. These algorithms reduce the number of steps required to perform cryptography operations by reducing compute addition and doubling operations. Group authentication is one of the major application domains of ECC. This work presents the ECC-based authentication protocols that provide authentication using encryption/decryption, digital signature, and other cryptography primitives. In observations, it is found that the proposed approach is much better quantitatively and quantitatively compared to traditional teaching.

Chapter Contents:

• 13.1 Introduction
• 13.2 Related work
• 13.3 The methodology of active learning process
• 13.4 Introduction to elliptic curve cryptography
• 13.4.1 Elliptic curve operations
• 13.4.1.2 Point doubling
• 13.4.2 Fast point multiplication algorithms
• 13.4.2.1 Double and add algorithm
• 13.4.2.2 𝒲-Windowed algorithm
• 13.4.2.3 Fixed-base doubling and addition method
• 13.5 Elliptic curve cryptography (ECC)-based authentication protocols
• 13.6 Experimental results
• 13.7 Conclusion
• References

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