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Fully homomorphic encryption (FHE) is a "holy grail" of cryptography. However, it is not yet adopted in practice because no known scheme is efficient. In this paper, we mainly focus on how to reduce the public key sizes in FHE. Based on Dijk et al.'s FHE scheme (DGHV) and Gentry's fully homomorhpic technology, we propose two schemes with shorter public keys by encrypting with a combination of the public key elements to replace a linear form in DGHV scheme and a quadratic form in Coron et al.'sdoi:10.14257/ijsia.2014.8.6.31 fatcat:bdtckdmtebahnc4ihj5t4l32vm