RESEARCH
Some current research projects are described below.
SPECIALIZATION OF ELLIPTIC SURFACES
Specialization is the process of selecting a specific elliptic curve from a family of elliptic curves, i.e. an elliptic surface. I aim to find effective ways to describe the relationship between the surface and its constituent curves. My results so far include describing an algorithm which can show a specialization map is injective and an extension to the specialization criteria of Gusić and Tadić. In the future, I hope to expand the effectiveness of my algorithm to be able to find all of the finitely many specialization maps which fail to be injective for a given elliptic surface.
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Publications:
[1] An algorithm for checking injectivity of specialization homomorphisms from elliptic surfaces, published in Journal of Number Theory: https://doi.org/10.1016/j.jnt.2021.11.002
[2] An extension to the Gusić-Tadić specialization criterion, submitted.
DECODING FAILURES IN BIKE
BIKE is a code-based key encapsulation cryptosystem that uses quasi-cyclic moderate density parity check (QC-MDPC) matrices as keys and the iterative Black-Grey-Flip decoder to decode messages. BIKE is a finalist in NIST's post-quantum cryptography standardization process, so ensuring its security is of great importance. It has been shown that if decoding fails frequently enough, one can use the decoding failures to recover the secret key. Several heuristic arguments have been made in support of BIKE's decoding failure rate being low enough to resist this attack, but there is currently no actual evidence. I am working with a team to further explore decoding failures in BIKE.
