Cryptography and Security

As more systems and devices connect to the internet, the risk of malicious cyber attacks and data breaches grows exponentially. Recent years have seen several high-profile data breaches impacting billions of users’ personal information. In 2022 alone, over 4 billion records were exposed in data breaches according to cybersecurity company Varonis. The increasing prevalence of…

Harnessing the Power of Quantum Superposition Quantum superposition is a fundamental principle of quantum mechanics in which a quantum system can exist in multiple states simultaneously. This contrasts with classical systems that can only exist in a single, definite state. Quantum superposition enables exponentially greater information density and parallelism compared to classical systems. A key…

Defining Relative Randomness Relative randomness formalizes the intuitive notion that some probability distributions exhibit more randomness deficiencies than others. We introduce a rigorous approach for quantifying and comparing the randomness properties of probability distributions. Let $X$ and $Y$ be discrete probability distributions. We say $X$ is relatively more random than $Y$, denoted $X \succ_{rr} Y$,…

Randomness refers to the lack of pattern or predictability in events or data. True randomness involves events that cannot be predicted even with complete knowledge of the system. Pseudorandomness refers to data that appears random but is actually generated by a deterministic algorithm. Understanding the difference between true and pseudorandomness is important for many areas…

The Promise of Quantum Computers Quantum computers utilize the strange properties of quantum mechanics like superposition and entanglement to perform computations. This allows them to encode information as quantum bits (qubits) and potentially process it in parallel, enabling exponential speedups over classical computers for certain algorithms. By leveraging the counterintuitive principles of quantum physics, quantum…

Locally decodable codes (LDCs) are a special type of error-correcting code that enable the extraction of individual message symbols by only querying a small subset of the encoded symbols. Unlike traditional decoding which requires reading the entire codeword, LDCs allow for localized decoding whereby each symbol can be recovered by looking at a few codeword…

The Complexity Class Conundrum Defining the key complexity classes BPP, RP, and co-RP is critical for understanding the relationships between them. BPP, or Bounded-error Probabilistic Polynomial time, contains decision problems solvable in polynomial time by a probabilistic Turing machine with an error probability bounded by 1/3 for all instances. RP, or Randomized Polynomial time, denotes…

The Declining State of Support for Basic Research Foundational research, also known as basic or fundamental research, aims to advance fundamental knowledge without an explicit commercial application. This open-ended, curiosity-driven investigation has historically catalyzed transformative technological and scientific breakthroughs. However, recent analyses indicate diminishing support for the unfettered exploration central to foundational inquiry. Assessing this…

The Lack of Diversity in TCS Research Current demographic data illustrates a concerning lack of gender, racial, and socioeconomic diversity within theoretical computer science (TCS) research. Studies show over 75% of tenured TCS professors in the United States identify as male, while underrepresented racial minorities comprise less than 5% of tenure-track faculty. Additionally, those from…

In algorithm analysis, the complexity of an algorithm refers to the amount of computational resources required for the algorithm to run as a function of the size of its input. Two important measures of complexity are average-case complexity and worst-case complexity. Average-case complexity analyzes the expected running time of an algorithm over all possible inputs…