Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homo- morphically processing a vector of plaintexts as a single ciphertext.  present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisional problem, the Decisional Approximate-GCD problem, whereas the sec- ond variant is based on the more classical computational Error-Free Approximate-GCD problem but requires additional public key elements.  also show how to perform arbitrary permutations on the underly- ing plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance even with the bootstrapping procedure:  describe an implementation of the homomorphic evaluation of AES, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al. at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme.
['Jung Hee Cheon', 'Jean-Sébastien Coron', 'Jinsu Kim', 'Moon Sung Lee', 'Tancrède Lepoint', 'Mehdi Tibouchi', 'Aaram Yun']
I am writing a research paper on a idea Batch Fully Homomorphic Encryption over the Integers
[{"from": "human", "value": "I am writing a research paper on a idea Batch Fully Homomorphic Encryption over the Integers"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homo- morphically processing a vector of plaintexts as a single ciphertext.  present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisional problem, the Decisional Approximate-GCD problem, whereas the sec- ond variant is based on the more classical computational Error-Free Approximate-GCD problem but requires additional public key elements.  also show how to perform arbitrary permutations on the underly- ing plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance even with the bootstrapping procedure:  describe an implementation of the homomorphic evaluation of AES, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al. at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme."}]