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The control of future power grids is migrating from a centralized to a distributed/decentralized scheme to enable a massive penetration of distributed energy resources and bring extreme enhancements of autonomous operations in terms of grid resilience, security, and reliability. Most effort has been on the design of distributed/decentralized controllers; however, the guarantees of the proper execution of the controls are also essential but relatively less emphasized. A common assumption is that local controllers would fully follow the designated controller dynamics based on the data received from communication channels. Such an assumption could be risky because proper execution of the controller dynamics is then built on trust in secure communication and computation. On the other hand, it is impractical for a verifier to repeat all the computations involved in the controls to verify the computational integrity. In this work, we leverage a type of cryptography technology, known as zero-knowledge scalable transparent arguments of knowledge to verify the computational integrity of control algorithms, such that verifiers can check the computational integrity with much less computational burden. The method presented here converts the challenge of data integrity into a subset of computational integrity. In this proof-of-concept paper, our focus will be on projected linear dynamics that are commonly seen in distributed/decentralized power system controllers. In particular, we have derived polynomial conditions in the context of zk-STARKs for the projected linear dynamics.