Homomorphic encryption constitutes a powerful cryptographic method that enables data aggregation in distributed applications over large datasets, such as electronic voting, electronic wallets, secure auctions, lotteries and secret sharing. At the same time, as attack trends move towards the lower levels of the computation stack and new threats continue to emerge, the lack of trust in contemporary computing paradigms keeps increasing. Since, homomorphic encryption helps preserve the confidentiality of sensitive information, it offers a powerful countermeasure against contemporary and future privacy threats, while allowing meaningful processing even though the data remains unreadable. Nevertheless, when homomorphic primitives are mapped to hardware circuits to improve performance, they become vulnerable to random faults and soft errors since homomorphic operations are malleable by construction and do not provide any explicit assurance towards data integrity. In this chapter, we present a fault tolerance methodology that protects homomorphic aggregation circuits through concurrent detection of random errors in homomorphic ALUs and encrypted values stored in memory. Our approach establishes the theoretical foundations to extend residue numbering to additive homomorphic operations, which enables lightweight fault detection with detection rates of more than 99.98% for ALU operations, and 100% for clustered faults and single bitflips in memory values. Using an efficient modular reduction algorithm, our method incurs a performance overhead between 3.6 and 8%, for a minimal area penalty.