Fully Homomorphic Encryption

A method, comprising:

• receiving a first ciphertext and a second ciphertext, where the first ciphertext comprises first data encrypted in accordance with an encryption scheme and the second ciphertext comprises second data encrypted in accordance with the 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 ciphertexts and uses the public key to perform at least one operation on the at least two ciphertexts and obtain a resulting ciphertext, where the refresh function operates to prevent growth of the magnitude of noise for a ciphertext while reducing the modulus of the ciphertext without using the secret key, where the refresh function utilizes a modulus switching technique that comprises transforming a first ciphertext c modulo q into a second ciphertext c′ modulo p while preserving correctness, where the modulus switching technique includes scaling by p/q and rounding, where p<q, where the encryption scheme enables homomorphic operations to be performed on ciphertexts encoded and operated on in accordance with the encryption scheme;
• performing at least one operation on the first ciphertext and the second ciphertext, using the at least one operation function, to obtain a third ciphertext;
• and
• reducing a noise level of the third ciphertext by using the refresh function.

An apparatus, comprising:

• at least one processor configured to receive a first ciphertext and a second ciphertext, where the first ciphertext comprises first data encrypted in accordance with an encryption scheme and the second ciphertext comprises second data encrypted in accordance with the 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 ciphertexts and uses the public key to perform at least one operation on the at least two ciphertexts and obtain a resulting ciphertext, where the refresh function operates to prevent growth of the magnitude of noise for a ciphertext while reducing the modulus of the ciphertext without using the secret key, where the refresh function utilizes a modulus switching technique that comprises transforming a first ciphertext c modulo q into a second ciphertext c′ modulo p while preserving correctness, where the modulus switching technique includes scaling by p/q and rounding, where p<q, where the encryption scheme enables homomorphic operations to be performed on ciphertexts encoded and operated on in accordance with the encryption scheme;
• and
• at least one memory configured to store the first ciphertext and the second ciphertext, where the at least one processor is further configured to perform at least one operation on the first ciphertext and the second ciphertext, using the at least one operation function, to obtain a third ciphertext;
• and to reduce a noise level of the third ciphertext by using the refresh function.

An apparatus, comprising:

• means for receiving a first ciphertext and a second ciphertext, where the first ciphertext comprises first data encrypted in accordance with an encryption scheme and the second ciphertext comprises second data encrypted in accordance with the 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 ciphertexts and uses the public key to perform at least one operation on the at least two ciphertexts and obtain a resulting ciphertext, where the refresh function operates to prevent growth of the magnitude of noise for a ciphertext while reducing the modulus of the ciphertext without using the secret key, where the refresh function utilizes a modulus switching technique that comprises transforming a first ciphertext c modulo q into a second ciphertext c′ modulo p while preserving correctness, where the modulus switching technique includes scaling by p/q and rounding, where p<q, where the encryption scheme enables homomorphic operations to be performed on ciphertexts encoded and operated on in accordance with the encryption scheme;
• means for performing at least one operation on the first ciphertext and the second ciphertext, using the at least one operation function, to obtain a third ciphertext;
• and
• means for reducing a noise level of the third ciphertext by using the refresh function.

A computer-readable storage medium storing program instructions, execution of the program instructions resulting in operations comprising:

• receiving a first ciphertext and a second ciphertext, where the first ciphertext comprises first data encrypted in accordance with an encryption scheme and the second ciphertext comprises second data encrypted in accordance with the 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 ciphertexts and uses the public key to perform at least one operation on the at least two ciphertexts and obtain a resulting ciphertext, where the refresh function operates to enable slow growth of the magnitude of noise for a ciphertext while maintaining the modulus of the ciphertext constant without using the secret key, where the encryption scheme enables homomorphic operations to be performed on ciphertexts encoded and operated on in accordance with the encryption scheme;
• performing at least one operation on the first ciphertext and the second ciphertext, using the at least one operation function, to obtain a third ciphertext;
• and
• reducing a noise level of the third ciphertext by using the refresh function.