  New cryptographic techniques such as homomorphic encryption (HE) allow
computations to be outsourced to and evaluated blindfolded in a resourceful
cloud. These computations often require private data owned by multiple
participants, engaging in joint evaluation of some functions. For example,
Genome-Wide Association Study (GWAS) is becoming feasible because of recent
proliferation of genome sequencing technology. Due to the sensitivity of
genomic data, these data should be encrypted using different keys. However,
supporting computation on ciphertexts encrypted under multiple keys is a
non-trivial task. In this paper, we present a comprehensive survey on different
state-of-the-art cryptographic techniques and schemes that are commonly used.
We review techniques and schemes including Attribute-Based Encryption (ABE),
Proxy Re-Encryption (PRE), Threshold Homomorphic Encryption (ThHE), and
Multi-Key Homomorphic Encryption (MKHE). We analyze them based on different
system and security models, and examine their complexities. We share lessons
learned and draw observations for designing better schemes with reduced
overheads.
