Series Vol. 10 , 17 November 2023
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With the rapid development of the digital age, information security, from personal data to national security, is becoming increasingly crucial. Information security primarily refers to the computation and processing of diverse information in computer systems and information exchange networks in order to safeguard information security. Cryptography is the technical foundation for achieving these objectives. In the early stages of education, advanced mathematics, linear algebra, probability theory, and other fundamental disciplines must be studied, although the practical application of modern algebra, cryptography, number theory, and mathematical knowledge will vary. This study explores the application of current algebra in cryptography, including both traditional and modern cryptographic applications, using a literature review approach. By comparing images from various eras, the researchers discovered that images were classed as "traditional" and "modern" at various times. Moreover, the likelihood of both traditional and modern images being identified throughout the modern era is comparatively higher.
modern algebra, cryptography, information security
1. Victor Shoup. A Computational Introduction to Number Theory and Algebra. Cambridge University Press, 2015.
2. Neal Koblitz. Algebraic Aspects of Cryptography. Springer, 1998.
3. J.-J. Quisquater and L. Guillou. How to Explain Zero-Knowledge Protocols to Your Children. Advances in cryptology—CRYPTO’89 Proceedings, Springer, 1989, pp. 628-631.
4. David Joyner. Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys. The Johns Hopkins University Press, 2002.
5. Serge Vaudenay. A Classical Introduction to Cryptography: Applications for Communications Security, Springer, 2005.
6. Michiel Kosters. Algorithmic Number Theory: 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006, Proceedings. Springer-Verlag, Berlin, Heidelberg, 2006.
7. Scott Aaronson. Quantum Computing, post-quantum cryptography, and the quest for quantum supremacy. National Science Review, Volume 4, Issue 3, May 2017, Pages 293–299.
8. Gary L. Mullen and Daniel Panario. Handbook of Finite Fields. CRC Press, 2013.
9. Tanja Lange, Daniel J. Bernstein, and Peter Schwabe. Post-Quantum Cryptography. Springer, 2009.
10. Nigel P. Smart. Cryptography: An Introduction. McGraw-Hill, Springer, 2004, pp 50.
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.