Efficient homomorphic encryption scheme for bilinear forms

摘要

In one exemplary embodiment, a computer readable storage medium tangibly embodying a program of instructions executable by a machine for performing operations including: receiving information B to be encrypted as a ciphertext C in accordance with an encryption scheme having an encrypt function; and encrypting B in accordance with the encrypt function to obtain C, the scheme utilizes at least one public key A, where B, C, and A are matrices, the encrypt function receives as inputs A and B and outputs C as C←AS+pX+B(mod q), S is a random matrix, X is an error matrix, p is in integer, q is an odd prime number. In other exemplary embodiments, the encryption scheme includes a decrypt function that receives as inputs at least one private key T (a matrix) and C and outputs B as B=T−1·(TCTt mod q)·(Tt)−1 mod p.

主权项

1. An apparatus comprising:
at least one storage medium configured to store information B to be encrypted as a ciphertext C in accordance with an encryption scheme that comprises an encrypt function; and at least one processor configured to use an encryption scheme that is homomorphic and supports computing bilinear forms, the at least one processor configured to encrypt the information B in accordance with the encrypt function of the encryption scheme to obtain the ciphertext C, where the encryption scheme utilizes at least one public key A, where the information B, the ciphertext C, and the at least one public key A are matrices, where the encrypt function receives as inputs the at least one public key A and the information B and outputs the ciphertext C as C←AS+pX+B(mod q), where S is a random matrix, where X is an error matrix, where p is an integer, where q is an odd prime number; and wherein the at least one processor is further configured to output the ciphertext C, to send the outputted ciphertext over a network to a remote computer which uses the outputted ciphertext in one or more homomorphic operations, and to receive a result of the one or more homomorphic operations from the remote computer, and wherein the at least one processor is further configured to perform decryption of the result of the one or more homomorphic operations received from the remote computer to create plaintext.