Fully homomorphic encryption

摘要

In one exemplary embodiment of the invention, a method and computer program include: receiving first and second ciphertexts having first and second data encrypted per an encryption scheme, the encryption scheme has public/secret keys and encryption, decryption, operation and refresh functions, the encryption function encrypts data, the decryption decrypts ciphertext, the operation receives ciphertexts and performs operation(s) on them, the refresh operates to prevent growth of the magnitude of noise for a ciphertext while reducing the modulus of the ciphertext without using the secret key, utilizing a modulus switching technique that involves transforming a first ciphertext c modulo q into a second ciphertext c′ modulo p while preserving correctness, the technique includes scaling by p/q and rounding, p

主权项

1. A non-transitory computer-readable storage medium storing program instructions, execution of the program instructions resulting in operations comprising:
transmitting by a requestor a query to a computer system; receiving at the computer system the query; accessing, at the computer system and from a memory of the computer system, a plurality of ciphertexts, where each of the input ciphertexts comprises data encrypted in accordance with an encryption scheme, where the encryption scheme uses a public key and a secret key and includes an encryption function, a decryption function, at least one operation function and a refresh function, where the encryption function operates to obtain ciphertext by encrypting data using the public key, where the decryption function operates using the secret key to decrypt ciphertext for data encrypted using the public key and obtain the data, where the at least one operation function receives at least two given ciphertexts and uses the public key to perform at least one operation on the at least two given ciphertexts and obtain a resulting ciphertext, where the refresh function operates to prevent growth of a magnitude of noise for a provided ciphertext while reducing a modulus of the provided ciphertext without using the secret key, where the refresh function utilizes a modulus switching technique that comprises transforming the provided ciphertext c modulo q into another ciphertext c′ modulo p while preserving correctness, where the modulus switching technique includes scaling by p/q and rounding, where pperforming operations on ciphertexts according to a circuit that corresponds to the query and the evaluation of which produces the one or more results that satisfy the query, wherein the operations use the at least one operation function to obtain a ciphertext result, and wherein at least some of the operations involve the plurality of input ciphertexts;reducing a noise level of the ciphertext result by using the refresh function; anddetermining the one or more results of the evaluation of the circuit at least by evaluating the circuit and iterating the performing the operations and the reducing the noise level multiple times during the evaluation of the circuit; sending by the computer system the one or more results of the evaluation of the circuit to the requestor; and receiving by the requestor the one or more results and decrypting by the requestor the one or more results to determine an answer to the query.