  With the increasing popularity of the cloud, clients oursource their data to
clouds in order to take advantage of unlimited virtualized storage space and
the low management cost. Such trend prompts the privately oursourcing
computation, called \emph{multiparty cloud computation} (\MCC): Given $k$
clients storing their data in the cloud, how can they perform the joint
functionality by contributing their private data as inputs, and making use of
cloud's powerful computation capability. Namely, the clients wish to oursource
computation to the cloud together with their private data stored in the cloud,
which naturally happens when the computation is involved with large datasets,
e.g., to analyze malicious URLs. We note that the \MCC\ problem is different
from widely considered concepts, e.g., secure multiparty computation and
multiparty computation with server aid.
  To address this problem, we introduce the notion of \emph{homomorphic
threshold proxy re-encryption} schemes, which are encryption schemes that enjoy
three promising properties: proxy re-encryption -- transforming encrypted data
of one user to encrypted data of target user, threshold decryption --
decrypting encrypted data by combining secret key shares obtained by a set of
users, and homomorphic computation -- evaluating functions on the encrypted
data. To demonstrate the feasibility of the proposed approach, we present an
encryption scheme which allows anyone to compute arbitrary many additions and
at most one multiplications.
