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Fully Homomorphic Encryption has become a hot research topic in light of the privacy concerns related to the emerging cloud computing paradigm. Existing fully homomorphic schemes are not truly practical due to their high computational complexities and huge message expansions. Targeting the construction of a homomorphic encryption scheme that is implementable for at least certain class of applications, this paper proposes a Somewhat Homomorphic public key encryption scheme, which can be viewed as a variant of the scheme devised by Van Dijk et.al, extended to larger message space. The proposed scheme is compact, semantically secure with significantly smaller public key, and is capable of encrypting integer plaintexts rather than single bits, with comparatively lower message expansion and computational complexities.