Homomorphic encryption

Abstract

Systems, methods, and computer-readable storage devices storing instructions for homomorphic encryption via finite ring isomorphisms are provided. An example method includes selecting a polynomial f(x) of exact degree n with small coefficients in a ring Fq[x] and selecting a polynomial h(y) of exact degree n in a ring Fq[y]. The method includes constructing an isomorphism from the ring Fq[x]/(f(x)) to the ring Fq[y]/(h(y)) and constructing an inverse isomorphism from the ring Fq[y]/(h(y)) to the ring Fq[x]/(f(x)). The method includes encrypting a message using said isomorphism from the ring Fq[x]/(f(x)) to the ring Fq[y]/(h(y)) and transmitting the encrypted message to a remote computer. The method also includes receiving one or more encrypted response messages from the remote computer based at least in part on the transmitted message and decrypting the one or more encrypted response messages.

1 - 20 . (canceled) 
     
     
         21 . A system comprising:
 a computing device, the computing device configured to encrypt data using a secret isomorphism to generate a first encrypted message;   a remote computing device, the remote computing device configured to receive the encrypted message, perform calculations on the first encrypted message without decrypting the first encrypted message, and send the results back to the computing device in second encrypted message; and   a network communicatively linking the computing device and the remote computing device.   
     
     
         22 . The system of  claim 21 , wherein the network is selected from the group consisting of a Local Area Network, a Wide Area Network, a cellular network and a public network. 
     
     
         23 . The system of  claim 21 , wherein the computing device comprises:
 a processor;   a memory;   an application; and   a cryptography engine.   
     
     
         24 . The system of  claim 23 , wherein the application comprises a computer program that performs one or more functions and interacts with confidential data. 
     
     
         25 . The system of  claim 24 , wherein the confidential data is selected from the group consisting of health data, genetic data, security data, and financial data. 
     
     
         26 . The system of  claim 23 , wherein the cryptography engine is configured to encrypt unencrypted data decrypt encrypted data. 
     
     
         27 . The system of  claim 26 , the cryptography engine is further configured to generate a secret isomorphism that is usable to encrypt data and a secret inverse isomorphism that is usable to decrypt data encrypted using the secret isomorphism. 
     
     
         28 . The system of  claim 27 , wherein the secret isomorphism is from a private-basis ring to a public-basis ring. 
     
     
         29 . The system of  claim 28 , wherein the secret inverse isomorphism is from the public-basis ring to the private-basis ring. 
     
     
         30 . The system of  claim 27 , wherein the remote computing device comprises a services engine. 
     
     
         31 . The system of  claim 30 , wherein the services engine is configured to perform computing services for the computing device based on the first encrypted message received from the computing device. 
     
     
         32 . The system of  claim 31 , wherein the computing services include a service to perform calculations on the first encrypted message that are usable in performing genetic analysis. 
     
     
         33 . The system of  claim 26 , wherein the cryptography engine is further configured to perform leveled homomorphic encryption. 
     
     
         34 . The system of  claim 33 , wherein the leveled homomorphic encryption imposes a limit on a number of computations that can be performed on ciphertext before numerical error overcomes data in the ciphertext.