Compressible (F)HE with Applications to PIR

A request is received for specific information that can be determined using data in a database on a first computer system. Either at least some of the data is encrypted or the request is encrypted. The first computer system does not have a decryption key to decrypt the encrypted data or request. The first computer system performs compressible HE operations on the data to determine compressed ciphertext(s) that correspond to the specific information. The operations include using a first uncompressed HE scheme and a second compressed HEscheme. The first HE scheme is used on the data to create other multiple ciphertexts and the second HE scheme is used on the other multiple ciphertexts to pack the other multiple ciphertexts into fewer ciphertexts that are compressed. Both the HE schemes use a same secret key. The first computer system sends a response including compressed ciphertext(s) corresponding to the specific information.