  As blockchain technology and cryptocurrency become increasingly mainstream,
ever-increasing energy costs required to maintain the computational power
running these decentralized platforms create a market for more energy-efficient
hardware. Photonic cryptographic hash functions, which use photonic integrated
circuits to accelerate computation, promise energy efficiency for verifying
transactions and mining in a cryptonetwork. Like many analog computing
approaches, however, current proposals for photonic cryptographic hash
functions that promise similar security guarantees as Bitcoin are susceptible
to systematic error, so multiple devices may not reach a consensus on
computation despite high numerical precision (associated with low photodetector
noise). In this paper, we theoretically and experimentally demonstrate that a
more general family of robust discrete analog cryptographic hash functions,
which we introduce as LightHash, leverages integer matrix-vector operations on
photonic mesh networks of interferometers. The difficulty of LightHash can be
adjusted to be sufficiently tolerant to systematic error (calibration error,
loss error, coupling error, and phase error) and preserve inherent security
guarantees present in the Bitcoin protocol. Finally, going beyond our
proof-of-concept, we define a ``photonic advantage'' criterion and justify how
recent developments in CMOS optoelectronics (including analog-digital
conversion) provably achieve such advantage for robust and digitally-verifiable
photonic computing and ultimately generate a new market for decentralized
photonic technology.
