Current Research Project
Depth Bounded Quantum Cryptography
Quantum cryptography is a powerful tool for secure communication. However, it is not without its limitations in the ideal model. We are exploring how quantum cryptography can be more powerful in the a somewhat realistic model where the adversary has limited quantum resources.
Formal Proofs for Transformers
Transformers have taken the world by storm recently. However, they are not without their flaws. Specifically, proving any general statement, even when restricting to a specific model, is quite challenging. We are leveraging existing work and new techniques to prove formal statements about the behavior of specific transformers given their weights.
Past Research
Effective Distance Preservation of Weight Reduced Codes and Higher Dim HGPs
Good quantum error correcting codes often have high weight stabilizer. This results in more expensive measurements and as such, a higher effective error rate. Starting with Hasting's work, we show effective distance preservation for weight reduced codes and higher dimensional hypergraph product codes. See the paper on arXiv.
Multiparty Secret Leader Election
Work done while at the Ethereum Foundation with Mark Simkin to improve communication cost of secret leader election for multiple leaders. The work resulted in a novel data independent and oblivious priority queue.
Addressing Stopping Failures for Small Set Flip Decoding of Hypergraph Product Codes
Work done with Anirudh Krishna and Michael Beverland to improve speed and decrease word error rates for hypergraph product codes (also known as quantum expander codes). Work had an order of magnitude improvement in decoding rates and speed. The paper was presented at a poster in QIP 2024. The paper can be found on arXiv.
Weighted Secret Sharing from the Wiretap Channel
With Fabrice Benhamouda and Shai Halevi, we introduced a novel connection between weighted secret sharing and wiretap channels. Achieving a ramped weighted secret sharing scheme, we eliminate dependence on the number of parties and use little public information. The paper was presented at Information-Theoretic Cryptography (ITC) 2023 and the paper can be found on ePrint.
3D Turtles and Drawing Math
A fun side project, I explored whether a sequence of movements to an object generated by rational numbers will form a closed path. Surprisingly, the question of closure is initmatly connected to discrete logs and roots of a very specific multinomial with coefficients of +/- 1. The paper can be found on Github. With a friend (Shiva Peri), we also created a visualization which creates some rather beautiful shapes. We also posted an interactive website to play around with parameters.
