As blockchain technology and cryptocurrency become increasingly mainstream, photonic computing has emerged as an efficient hardware platform that reduces ever-increasing energy costs required to verify transactions in decentralized cryptonetworks. To reduce sensitivity of these verifications to photonic hardware error, we propose and experimentally demonstrate a cryptographic scheme, LightHash, that implements robust, low-bit precision matrix multiplication in programmable silicon photonic networks. We demonstrate an error mitigation scheme to reduce error by averaging computation across circuits, and simulate energy-efficiency-error trade-offs for large circuit sizes. We conclude that our error-resistant and efficient hardware solution can potentially generate a new market for decentralized photonic blockchain.