Secure replication-based outsourced computation using smart contracts

The replication-Based Outsourced Computation (RBOC) mechanism allows a client to outsource the same computing job to multiple contractors and the honest contractors will get paid in the incentivized system based on the fact that a majority of contractors will honestly perform the computation. As self-executing contracts, smart contracts are utilized in the decentralized blockchain networks to execute coded programs automatically transparently, and publicly. It is natural to apply smart contracts to RBOC to improve performance by setting smart contracts as the converter between the client and contractors to reduce the load on the client. However, it is infeasible to directly combine these two blocks together because the data including returned computing results from contractors in the decentralized blockchain are in the form of plaintexts such that some lazy contractors could copy others' results as their own and still get paid, which will compromise the security of RBOC. The existing public-key encryption with equality test (PKEET) is a promising candidate solution to stop the above lazy contractors, where the results are encrypted by PKEET and then transferred without hindering smart contracts to compare the equality of underlying results. Unfortunately, we found that the advanced lazy contractors can still compromise security by forging ciphertexts to pass the equality test only with the encrypted results of other contractors. In this paper, to achieve security against lazy contractors, we introduce the notion of PKEET against lazy encryptors (PKEET-LE). Besides the fundamental property of PKEET that performs equality test on ciphertexts without decryption, PKEET-LE additionally realizes the security against the lazy encryptors who aim to forge a ciphertext for a given one to pass the equality test between them without the knowledge of the underlying plaintext. We further propose a concrete and practical PKEET-LE construction along with formal security proof. Finally, we conduct a performance evaluation to demonstrate that our PKEET-LE scheme is efficient and practical in the RBOC system using smart contracts.