Decrypting legal dilemmas

It has become a truism that the speed of technological progress leaves law and policy scrambling to keep up. But in addition to creating new challenges, technological advances also enable new improvements to issues at the intersection of law and technology. In this thesis, I develop new cryptographic tools for informing and improving our law and policy, including specific technical innovations and analysis of the limits of possible interventions. First, I present a cryptographic analysis of a legal question concerning the limits of the Fifth Amendment: can courts legally compel people to decrypt their devices? Our cryptographic analysis is useful not only for answering this specific question about encrypted devices, but also for analyzing questions about the wider legal doctrine. The second part of this thesis turns to algorithmic fairness. With the rise of automated decision-making, greater attention has been paid to statistical notions of fairness and equity. In this part of the work, I demonstrate technical limits of those notions and examine a relaxation of those notions; these analyses should inform legal or policy interventions. Finally, the third section of this thesis describes several methods for improving zero-knowledge proofs of knowledge, which allow a prover to convince a verifier of some property without revealing anything beyond the fact of the prover's knowledge. The methods in this work yield a concrete proof size reduction of two plausibly post-quantum styles of proof with transparent setup that can be made non-interactive via the Fiat-Shamir transform: "MPC-in-the-head," which is a linear-size proof that is fast, low-memory, and has few assumptions, and "Ligero," a sublinear-size proof achieving a balance between proof size and prover runtime. We will describe areas where zero-knowledge proofs in general can provide new, currently-untapped functionalities for resolving legal disputes, proving adherence to a policy, executing contracts, and enabling the sale of information without giving it ...