Fine-grained cryptography is the study of cryptographic objects that are required to be secure only against adversaries that are moderately more powerful than the honest parties. This weakening in security requirements opens up possibilities for meaningful cryptographic constructions in various settings using hardness assumptions that are considerably weaker than those used in standard cryptography.
In this thesis, we study these possibilities in two different settings:
1. First, we construct several unconditionally secure cryptographic primitives that are computable by and secure against constant-depth circuits. Under a reasonable complexity-theoretic assumption, we do the same for log-depth circuits.
2. Second, we present functions that are hard to compute on average for algorithms running in some fixed polynomial time, assuming widely-conjectured worst-case hardness of certain problems from the study of fine-grained complexity. We also construct a proof-of-work protocol based on this hardness and certain structural properties of our functions.