The notion of Best-of-Both-Worlds introduced in the work of Ishai et al. (CRYPTO 2006) investigated whether an MPC protocol can simultaneously provide two incomparable security guarantees: guaranteed output delivery against an honest majority and security with abort against a dishonest majority and provided tight upper and lower bounds in the presence of computationally bounded, i.e., PPT adversaries. Another line of works starting from the work of Chaum (CRYPTO 1989) considered protocols that simultaneously achieved security against an unbounded adversary corrupting a minority of the parties and security against arbitrary corruption by a PPT adversary. In this work, we generalize previous work to investigate a fundamental challenge of designing an MPC in a multiverse where security is specified with respect to (1) GOD, (2) fairness, (3) security w.r.t. unbounded adversaries, and (4) security with abort. The work of Lucas et al. (PODC 2010) resolved this question when considering threshold adversaries; however, the case of general adversary structures remains open. Our main result completely characterizes when a protocol can simultaneously achieve all properties. Namely, given adversary structures $$\mathcal{Z}_{\textsf{GOD}}, \mathcal{Z}_{\textsf{fair}},\mathcal{Z}_{\textsf{S}}$$ and $$\mathcal{Z}_{\textsf{C}}$$ , we provide tight upper and lower bounds for when an MPC protocol can provide GOD, fairness, and security with abort respectively for unbounded and PPT adversaries w.r.t. these adversary structures.

In addition to storage and computing power, cloud providers ensure confidentiality of user data through the use of various encryption technologies. The need to decrypt the data before it can be operated upon exposes a possible security hole which could be exploited by untrustworthy system administrators. Homomorphic encryption allows operations on encrypted data without the need to first decrypt it making it attractive for cloud computing. However, it incurs significant overhead of storage and computation and is therefore infeasible in practice. Somewhat homomorphic schemes have been proposed to handle specific applications - one such scheme, the Zhou Wornell Scheme, operates on vectors of integers. We demonstrate that this scheme is vulnerable to plaintext recovery attacks for a range of vector sizes. We explore the trade-offs between plaintext vector length, public key size and security. Increasing vector length increases security but at the cost of greatly increased public key size. We suggest a way of reducing the size of the public key by up to 90%. Finally, we propose a variant of this scheme which is secure against plaintext recovery attacks.