The Beautiful Deception: How 256 Bits Pretend to be Infinity
Alexander Towell
TL;DR
The paper argues that true random oracles are impossible to implement on real machines and demonstrates this through OracleDigest, which fails in memory, persistence, reproducibility, and distributability. It then introduces LazyDigest, a 256-bit deterministic construction that, via lazy evaluation and cryptographic hardness, yields sequences indistinguishable from infinite randomness to any computationally bounded observer. The work develops extended constructions, security pillars, and an algebra of operations, grounding the approach in information theory, Kolmogorov complexity, and computational randomness. It further explores philosophical implications of randomness, practical applications such as deterministic test data and memory-hard KDFs, and outlines future directions toward quantum resistance, formal verification, and broader cryptographic use, arguing for a constructivist view where finite, computable objects realize effectively infinite behavior.
Abstract
How do you store infinity in 256 bits? This paper explores the fundamental deception at the heart of computational cryptography: using finite information to simulate infinite randomness. We prove why true random oracles are impossible, then show how lazy evaluation creates a beautiful lie -- a finite automaton that successfully pretends to be infinite. We reveal that ``randomness'' in cryptography is actually computational hardness in disguise, demonstrating through Python implementations how 256 bits of entropy can generate sequences indistinguishable from infinite randomness to any computationally bounded observer.How do you store infinity in 256 bits? This paper explores the fundamental deception at the heart of computational cryptography: using finite information to simulate infinite randomness. We prove why true random oracles are impossible, then show how lazy evaluation creates a beautiful lie -- a finite automaton that successfully pretends to be infinite. We reveal that ``randomness'' in cryptography is actually computational hardness in disguise, demonstrating through Python implementations how 256 bits of entropy can generate sequences indistinguishable from infinite randomness to any computationally bounded observer.