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Posts
(WIP) Some Secrets Shared
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In cryptography, secret sharing is the process of splitting a secret into pieces, called secret shares, so that no individual device stores the original secret but some group of devices can collectively recover that secret. Classic examples of situations involving secret sharing include missile launch codes and shared custody in the corporate setting; in both cases multiple individuals’ authorizations are required before any action can be taken. Recently, secret sharing has seen extensive use within multi-party computation (MPC) involving secret data, and private key management, where an individual or organization has cryptocurrency belonging to a secret key and they wish to split this key into \(n\) key shares such that some subset of \(t\) shares are required for using the key.
Schnorr Applications: MuSig
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Welcome to this week’s installment of the introductory Schnorr blog series! So far we have covered (in extreme depth) what Schnorr signatures are and why they work securely. If you didn’t follow or haven’t read the last two posts (detailing Schnorr’s security) you will still be able to read this post (and the remainder of this series) so long as you felt comfortable with the very first post in this series or have a good understanding of how Schnorr signatures work. In this post, we shall begin our exploration of variants of Schnorr signatures which enable countless application use cases, starting with MuSig.
Schnorr Security Part 2: From ID to Signature
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In the last blog post, we began laying out the groundwork for what will become an argument that Schnorr signatures are secure. We discovered the Schnorr Identity Protocol and proved that it is secure and correct (specifically Complete, Sound, and Honest-Verifier Zero-knowledge). It is very unlikely that this blog post will make much sense if you have not yet read the previous post, so go read it if you haven’t already.
Schnorr Security Part 1: Schnorr ID Protocol
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In the previous post of our introductory Schnorr series, we discussed the definition of Schnorr signatures and tried to build some intuition as to how Schnorr signatures work by looking at a sequence of choices that could have led us to the definition. In this post we will go even deeper and begin an argument for Schnorr’s security by deriving the signature scheme from yet another angle.
Introduction to Schnorr Signatures
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Welcome to the introductory Suredbits Schnorr blog series! In this post, I will explain what Schnorr signatures are and how they intuitively work. In the next post, I will present some evidence as to why this scheme is secure and correct. In the rest of this series, I will be diving into various signatures schemes that Schnorr easily enables and some of their use cases. Before you read on, I recommend you make sure you are comfortable with the following three ideas as I will assume some basic knowledge of them:
portfolio
Portfolio item number 1
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Short description of portfolio item number 1
Portfolio item number 2
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Short description of portfolio item number 2
publications
A Projective Representation of the Modular Group
Published in arXiv, 2020
In this paper, we calculate the trace and determinant of matrices representing the \(SL_2(\mathbb{Z})\)-action on \(\mathcal{W}_q\). This is the result of my undergraduate research under the supervision of Prof. Charles Frohman.
Consecutive Radio Labeling of Hamming Graphs
Published in arXiv, 2020
In this paper, we show provide a consecutive radio labeling for \(K_3^4\). This is the result of the research I conducted in high school under the supervision of Prof. Maggy Tomova.
Bitcoin Oracle Contracts: Discreet Log Contracts in Practice
Published in IEEE International Conference on Blockchain and Cryptocurrency, 2022
In this paper, we discuss the design of the Discreet Log Contract specification and its performance.
A Linear Representation for Constant Term Sequences mod \(p^a\) with Applications to Uniform Recurrence
Published in arXiv, 2025
In this paper, we show that, for a fixed prime \(p\), a fixed integer Laurent polynomial \(P\), arbitrary integer Laurent polynomial \(Q\), and arbitrary positive integer \(a\), the sequences \((\)ct[\(P^nQ\)] mod \(p^a)_{a, Q}\) are either all linearly recurrent or all 0 with frequency 1. We characterize when each of these cases occur.
Uniform Recurrence in the Motzkin Numbers and Related Sequences mod \(p\)
Published in The Electronic Journal of Combinatorics, 2025
In this paper, we characterize the primes, \(p\), for which sequences of the form ct[\(P^nQ\)] mod \(p\), where \(P\) is a symmetric trinomial, are uniformly recurrent.
The Automatic Study of Constant Term Sequences Modulo Prime Powers
Published in ProQuest, 2025
This is my PhD dissertation! The first three chapters provide exposition on automatic sequences, and the fourth chapter contains all of my research results.
Density and Symmetry in the Generalized Motzkin Numbers Modulo \(p\)
Published in Integers, 2026
In this paper, we prove some symmetries in the generalized central trinomial coefficients and generalized motzkin numbers, and then use these to characterize when these sequences are divisible by primes.
talks
Talk 1 on Relevant Topic in Your Field
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This is a description of your talk, which is a markdown file that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
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This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.