Throughput-efficient Lagrange coded private blockchain for secured IoT Systems

We develop a new Lagrange coded blockchain model for Internet-of-Things (IoT) systems based on Lagrange coded computing (LCC). In the model, a mining task assigned to a blockchain node (BN) is encoded with a specific encoding function. Thus, the final result, i.e., newly generated block or block verification result, can be decoded even when only some mining outputs returned by BNs are correct, while other outputs are erroneous or discarded due to delays. To be decoded correctly, the number of mining outputs returned prior to decoding must be at least a given decoding threshold. Then, security against malicious BNs and resilience against stragglers can be guaranteed if the number of mining tasks allocated to BNs is not less than the sum of decoding threshold, number of stragglers, and double of the number of malicious BNs. Unlike other IoT blockchains and LCC-based methods showing enhanced throughput but yielding poor security, our model can improve throughput without compromising on security. This is achieved through optimized load allocations when the higher loads (two or more mining tasks) are allocated to the fastest BNs leading to: 1) increased number of mining outputs returned prior to decoding required to meet the decoding threshold and 2) increased number of allocated mining tasks to strengthen security and resilience. To overcome the limitation of our model related to higher loads and, hence, higher mining costs to BNs, we develop a contract-theoretic mechanism that incentivizes each BN to complete its mining task through joint load and transaction fee allocations.