Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
individual
Campus
Daytona Beach
Authors' Class Standing
Lola Torres, Senior
Lead Presenter's Name
Lola Torres
Lead Presenter's College
DB College of Arts and Sciences
Faculty Mentor Name
Sirani Perera
Abstract
Secure communication for space-based systems requires cryptographic methods that remain both reliable and efficient under strict computational constraints. This work investigates a low-complexity polynomial ring learning algorithm designed for quantum space assets, including satellite–ground communication systems. The project focuses on post-quantum cryptographic principles, where encryption and decryption rely heavily on repeated polynomial operations; this can be computationally expensive with constrained platforms. This is addressed with reformulating polynomial multiplication as a structured linear transformation on coefficient vectors. By representing these operations as matrices with a cyclic structure, the structure allows the use of the discrete Fourier transform (DFT); this will simplify the complex convolution-based operations into element-wise computations in a transformed domain. The Fast Fourier Transform (FFT) is then used to efficiently perform these transformations as well as reduce any computational complexity that can be compared to direct methods. This approach not only accelerates the algorithm but also provides a deeper understanding of linking Fourier based methods. The results demonstrate that combining polynomial ring represented with matrix-based methods and Fourier transforms enables efficient and scalable cryptographic implementations. This framework is best for constrained environments such as satellites, highlighting that both performance and security are critical. The work emphasizes how polynomial ring structures can be utilized to develop advanced encryption and decryption techniques for secure communication in emerging quantum space systems.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Data Science Commons, Dynamical Systems Commons, Navigation, Guidance, Control and Dynamics Commons
Low-complexity Polynomial Ring Learning for Quantum Space Assets
Secure communication for space-based systems requires cryptographic methods that remain both reliable and efficient under strict computational constraints. This work investigates a low-complexity polynomial ring learning algorithm designed for quantum space assets, including satellite–ground communication systems. The project focuses on post-quantum cryptographic principles, where encryption and decryption rely heavily on repeated polynomial operations; this can be computationally expensive with constrained platforms. This is addressed with reformulating polynomial multiplication as a structured linear transformation on coefficient vectors. By representing these operations as matrices with a cyclic structure, the structure allows the use of the discrete Fourier transform (DFT); this will simplify the complex convolution-based operations into element-wise computations in a transformed domain. The Fast Fourier Transform (FFT) is then used to efficiently perform these transformations as well as reduce any computational complexity that can be compared to direct methods. This approach not only accelerates the algorithm but also provides a deeper understanding of linking Fourier based methods. The results demonstrate that combining polynomial ring represented with matrix-based methods and Fourier transforms enables efficient and scalable cryptographic implementations. This framework is best for constrained environments such as satellites, highlighting that both performance and security are critical. The work emphasizes how polynomial ring structures can be utilized to develop advanced encryption and decryption techniques for secure communication in emerging quantum space systems.