This paper introduces a new notion of secure multiparty computation (MPC) called on-the-fly MPC, which allows users to perform arbitrary computations on encrypted data stored in a cloud server without prior knowledge of the function or participants. The cloud server can perform the computation non-interactively, and users only need to decrypt the result at the end. The key innovation is the use of multikey fully homomorphic encryption (FHE), which enables computations on data encrypted under multiple unrelated keys. The authors construct a multikey FHE scheme based on the NTRU encryption scheme, which is efficient and has been previously used for single-key FHE. They show that this scheme can be extended to multikey FHE, allowing for secure computations on data from multiple users. The paper also discusses the security of the protocol against semi-malicious and malicious adversaries, and shows that a completely non-interactive solution is impossible. The authors conclude that their approach provides a practical and efficient solution for on-the-fly MPC.This paper introduces a new notion of secure multiparty computation (MPC) called on-the-fly MPC, which allows users to perform arbitrary computations on encrypted data stored in a cloud server without prior knowledge of the function or participants. The cloud server can perform the computation non-interactively, and users only need to decrypt the result at the end. The key innovation is the use of multikey fully homomorphic encryption (FHE), which enables computations on data encrypted under multiple unrelated keys. The authors construct a multikey FHE scheme based on the NTRU encryption scheme, which is efficient and has been previously used for single-key FHE. They show that this scheme can be extended to multikey FHE, allowing for secure computations on data from multiple users. The paper also discusses the security of the protocol against semi-malicious and malicious adversaries, and shows that a completely non-interactive solution is impossible. The authors conclude that their approach provides a practical and efficient solution for on-the-fly MPC.