Investigation of Supersingular Elliptic Curves in Quantum-Resistant CryptographyAn
This thesis seeks to explore some of the theory and concepts underlying the security of SIDH, especially as it relates to finding supersingular elliptic curves, generating isogeny graphs, and implementing SIDH. As elliptic curves and SIDH may be an unfamiliar topic to many readers, the paper begins by providing a brief introduction to elliptic curves, isogenies, and the SIDH Protocol. Next, the paper investigates more efficient methods of generating supersingular elliptic curves, which are important for visualizing the isogeny graphs in the algorithm and the setup of the protocol. Afterwards, the paper focuses on isogeny maps of various degrees, attempting to visualize isogeny maps similar to those used in SIDH. Finally, the paper looks at an implementation of SIDH in PARI/GP and work is done to see the effects of using isogenies of degree greater than 2 and 3 on the security, runtime, and practicality of the algorithm.]]>autSteele, Aaron JthsJones, JohndgcChildress, NancyctbComputer Science and Engineering ProgramctbSchool of Mathematical and Statistical SciencesctbComputer Science and Engineering ProgramctbBarrett, The Honors Collegeenghttps://hdl.handle.net/2286/R.I.6334438 pages116182906561628716197148348ajsteeleIn Copyright2021-05TextCryptographyquantumMathematicsElliptic Curves