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In this chapter we provide formal definitions for verifiable computing schemes and their relevant properties. More precisely, first, we define verifiable computing schemes in general and privately verifiable computing schemes and publicly verifiable computing schemes in particular. Then, we provide a definition for weak and adaptive security. Following, we discuss the different types of privacy protection, i.e. input privacy w.r.t. the server, input privacy w.r.t. the verifier, output privacy w.r.t. the server, output privacy w.r.t. the verifier and give a definition for each property. Finally, we define efficiency distinguishing between efficiency and amortized efficiency. Many verifiable computing schemes presented in the subsequent chapters are constructed with the help of cryptographic primitives that come with additional definitions for the underlying hardness assumptions. However, since these are very specific to the individual solutions they are presented in Appendix A.
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