Computational Group Theory and Quantum-Era Cryptography

Authors

  • Michael N. John  Department of Mathematics, Akwa Ibom State University, Nigeria
  • Udoaka O. G.  Department of Mathematics, Akwa Ibom State University, Nigeria

DOI:

https://doi.org/10.32628/IJSRSET2310556

Keywords:

Computational Group theory, Lattice, Cryptography, Quantum computers, Encryption, Decryption, Polycyclic group

Abstract

This paper provides an overview of the significant role of computational group theory in cryptography. Group theory plays a crucial role in various cryptographic applications, such as key exchange, encryption, and digital signatures. This paper examines the fundamental concepts, algorithms, and applications of computational group theory in cryptography, using polycyclic groups with a focus on key findings and recent developments in quantum-era cryptography.

References

  1. Fraleigh, J. B. (2003). A First Course in Abstract Algebra. Pearson.
  2. Shoup, V. (1996). Lower bounds for discrete logarithms and related problems. Advances in Cryptology - CRYPTO '96.
  3. Diffie, W., & Hellman, M. E. (1976). New Directions in Cryptography. IEEE Transactions on Information Theory.
  4. Koblitz, N. (1987). Elliptic Curve Cryptosystems. Mathematics of Computation.
  5. Peikert, C. (2016). Lattice Cryptography for the Internet. arXiv:1612.00988.
  6. Pollard, J. M. (1978). Monte Carlo Methods for Index Computation (Mod p). Mathematics of Computation.
  7. Schoof, R. (1995). Counting Points on Elliptic Curves over Finite Fields. Journal of the London Mathematical Society.
  8. Bernstein, D. J., Lange, T., & Schwabe, P. (2016). Post-Quantum Cryptography. Springer.
  9. Brakerski, Z., & Vaikuntanathan, V. (2014). Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages. Advances in Cryptology - CRYPTO '11.
  10. Michael N. John & Udoaka O. G (2023). Algorithm and Cube-Lattice-Based Cryptography. International journal of Research Publication and reviews, Vol 4, no 10, pp 3312-3315 October 2023.
  11. Groth, J., Sahai, A., & Waters, B. (2008). Pairing-Based Cryptography: A Survey. Advances in Cryptology - EUROCRYPT '08, 2-16.
  12. Ajtai, M. (1996). Public-Key Cryptosystems from Lattice Reduction Problems. STOC '96, 99-108.
  13. Goldwasser, S., & Rackoff, C. (1989). A Group Theoretic Framework for Cryptographic Applications. Advances in Cryptology - CRYPTO '85, 368-383.
  14. Alagiannis, I., et al. "Lattice-based cryptography as a Post-Quantum candidate." Journal of Cryptographic Engineering (2014)
  15. Derek F. Holt, Handbook of Computational Group theory. In the series ‘Discrete Mathematics and its Application’,Chapman & Hall/CRC 2005, xvi + 514 p.
  16. Udoaka O. G. & Frank E. A. (2022). Finite Semi-group Modulo and Its Application to Symmetric Cryptography, International Journal of Pure Mathematics DOI: 10.46300/91019.2022.9.13.
  17. Udoaka, O. G. (2022). Generators and inner automorphism. THE COLLOQUIUM -A Multi-disciplinary Thematc Policy Journal www.ccsonlinejournals.com. Volume 10, Number 1 , Pages 102 -111 CC-BY-NC-SA 4.0 International Print ISSN : 2971-6624 eISSN: 2971-6632

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Published

2023-11-03

Issue

Section

Research Articles

How to Cite

[1]
Michael N. John, Udoaka O. G. "Computational Group Theory and Quantum-Era Cryptography" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 10, Issue 6, pp.01-11, November-December-2023. Available at doi : https://doi.org/10.32628/IJSRSET2310556