With the emergence of cloud computing services, a resource-constrained client can outsource its computationally-heavy tasks to cloud providers. Because such service providers might not be fully trusted by the client, the need to verify integrity of the returned computation result arises. The ability to do so is called verifiable delegation or verifiable outsourcing. Furthermore, the data used in the computation may be sensitive and it is often desired to protect it from the cloud throughout the computation. In this work, we put forward solutions for verifiable outsourcing of matrix multiplications that favorably compare with the state of the art. Our goal is to minimize the cost of verifying the result without increasing overhead associated with other aspects of the scheme. In our scheme, the cost of verifying the result of computation uses only a single modulo exponentiation and the number of modulo multiplications linear in the size of the output matrix. This cost can be further reduced to avoid all cryptographic operations if the cloud is rational. A rational cloud is neither honest nor arbitrarily malicious, but rather economically motivated with the sole purpose of maximizing its monetary reward. We extend our core constructions with several desired features such as data protection, public verifiability, and computation chaining.
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