Abstract
The public key of the integer homomorphic encryption scheme which was proposed by Van Dijk et al. is long, so the scheme is almost impossible to use in practice. By studying the scheme and Coron’s public key compression technique, a scheme which is able to encrypt n bits plaintext once was obtained. The scheme improved the efficiency of the decrypting party and increased the number of encrypting parties, so it meets the needs of cloud computing better. The security of the scheme is based on the approximate GCD problem and the sparse-subset sum problem.
Highlights
Full homomorphic encryption (FHE) was proposed by Rivest, Adleman, and Dertouzos in 1978 [1]
The public key of the integer homomorphic encryption scheme which was proposed by Van Dijk et al is long, so the scheme is almost impossible to use in practice
The scheme improved the efficiency of the decrypting party and increased the number of encrypting parties, so it meets the needs of cloud computing better
Summary
Full homomorphic encryption (FHE) was proposed by Rivest, Adleman, and Dertouzos in 1978 [1] This encryption method can perform operations on ciphertext. With such characteristics, the data can be encrypted and handed over to the cloud for processing, which utilizes the computing power of the cloud, and reduces the amount of local computing and ensures the security of the data [2] [3]. In view of the above problems, this paper studies Coron’s public key compression technology, shortens the size of the public key, expands the plaintext space in the scheme to n bits, and expands the number of encryption parties to achieve multiple encryption methods. The public key size of this scheme is O λ5
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