Homomorphic evaluation including key switching, modulus switching, and dynamic noise management

• US 9,608,817 B2
• Filed: 01/28/2016
• Issued: 03/28/2017
• Est. Priority Date: 02/17/2012
• Status: Expired due to Fees

• Current Assignee: International Business Machines Corporation, University of Bristol
• Original Assignee: International Business Machines Corporation
• Inventors: Gentry, Craig B., Halevi, Shai, Smart, Nigel P.
• Primary Examiner(s): Wang, Harris C
• Application Number:
  US15/008,921
• Publication Number:
  US 20160164670A1
• Time in Patent Office: 425 Days
• Field of Search: 380/28
• US Class Current: 1/1
• CPC Class Codes: H04L 2209/24 Key scheduling, i.e. generating round keys or sub-keys for block encryption
• CPC Class Codes: H04L 2209/34 Encoding or coding, e.g. Huffman coding or error correction
• CPC Class Codes: H04L 63/0442 wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption cryptographic mechanisms or cryptographic arrangements for public-key encryption H04L9/30
• CPC Class Codes: H04L 9/008 involving homomorphic encryption
• CPC Class Codes: H04L 9/0618 Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
• CPC Class Codes: H04L 9/08 Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords network architectures or network communication protocols for supporting key management in a packet data network H04L63/06
• CPC Class Codes: H04L 9/0838 Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these network architectures or network communication protocols for key exchange in a packet data network H04L63/061
• CPC Class Codes: H04L 9/16 the keys or algorithms being changed during operation
• CPC Class Codes: H04L 9/30 Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
• CPC Class Codes: H04L 9/38 Encryption being effected by mechanical apparatus, e.g. rotating cams, switches, keytape punchers

Abstract

Homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using a public key of an encryption scheme that also includes multiple secret keys. Each input ciphertext includes multiple real numbers that are kept with finite precision. Performing the homomorphic evaluation of the function includes performing operation(s). Performing each of one or more operations includes the following. A key-switching transformation is performed on selected ciphertext(s), including converting a first version of a selected ciphertext with respect to a first of the secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the secret keys and with some other number r′ bits of precision, r′>r. Each key switching transformation is performed prior to or after the operation(s) are evaluated. Results of the operation(s) are output.

Claims

1. A method, comprising:

performing, by a computing device, homomorphic evaluation of a function on one or more input ciphertexts, where the one or more input ciphertexts were encrypted using a public key of an encryption scheme that also comprises a plurality of secret keys, where each input ciphertext comprises a plurality of real numbers that are kept with finite precision, and where performing the homomorphic evaluation of the function comprises performing one or more operations, and where performing each of one or more operations comprises;

performing a key-switching transformation on selected ones of the one or more input ciphertexts, where performing key-switching transformation on a selected ciphertext comprises converting a first version of the selected ciphertext with respect to a first of the plurality of secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the plurality of secret keys and with some other number r′

bits of precision, where r′

>

r,

where each of the key switching transformations is performed prior to or after the one or more operations are evaluated; and

outputting one or more results of the one or more operations.

2. The method of claim 1, where r′

>

2r.

3. The method of claim 1, where performing the homomorphic evaluation further comprises, prior to performing the key switching transformation, decreasing a norm of the first version of the selected ciphertext, by representing every number in the selected ciphertext via a sum number d>

1 of smaller digits, and where r′

>

r+r/d.

4. The method of claim 1, where performing the homomorphic evaluation of the function further comprises performing the homomorphic evaluation of the function in order to evaluate a circuit comprising a plurality of levels.

5. The method of claim 4, where performing homomorphic evaluation of a function further comprises performing homomorphic evaluation of multiple functions in order to evaluate the circuit.

16. The method of claim 1, wherein:

the method further comprises receiving at the computing device a query from a requestor computer system;

the performing the homomorphic evaluation of the function is performed one or more times to evaluate a circuit using the query, the query corresponds to the input ciphertexts, and evaluation of the circuit produces one or more results; and

the method further comprises sending the one or more results of the evaluation of the circuit to the requestor computer system.

17. The method of claim 16, wherein:

the computing device comprises a server residing on the Internet;

the server comprises one or more communications components; and

the method further comprises communicating by the server with the requestor computer system over the Internet using the one or wore communications components.

6. A computer system, comprising:

one or more memories comprising computer-readable program code; and

one or more processors,

wherein the one or more processors are configured, responsive to execution of the computer-readable program code, to cause the computer system to perform;

performing homomorphic evaluation of a function on one or more input ciphertexts, where the one or more input ciphertexts were encrypted using a public key of an encryption scheme that also comprises a plurality of secret keys, where each input ciphertext comprises a plurality of real numbers that are kept with finite precision, and where performing the homomorphic evaluation of the function comprises performing one or more operations, and where performing each of one or more operations comprises;

performing a key-switching transformation on selected ones of the one or more input ciphertexts, where performing key-switching transformation on a selected ciphertext comprises converting a first version of the selected ciphertext with respect to a first of the plurality of secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the plurality of secret keys and with some other number r′

bits of precision, where r′

>

r,

where each of the key switching transformations is performed prior to or after the one or more operations are evaluated; and

outputting one or more results of the one or more operations.

7. The computer system of claim 6, where r′

>

2r.

8. The computer system of claim 6, where performing the homomorphic evaluation further comprises, prior to performing the key switching transformation, decreasing a norm of the first version of the selected ciphertext, by representing every number in the selected ciphertext via a sum number d>

1 of smaller digits, and where r′

>

r+r/d.

9. The computer system of claim 6, where performing the homomorphic evaluation of the function further comprises performing the homomorphic evaluation of the function in order to evaluate a circuit comprising a plurality of levels.

10. The computer system of claim 9, where performing homomorphic evaluation of a function further comprises performing homomorphic evaluation of multiple functions in order to evaluate the circuit.

18. The computer system of claim 6, wherein:

the one or more processors are further configured, responsive to execution of the computer-readable program code, to cause the computer system to perform;

receiving at the computer system a query from a requestor computer system;

the performing the homomorphic evaluation of the function is performed one or more times to evaluate a circuit using the query, the query corresponds to the input ciphertexts, and evaluation of the circuit produces one or more results; and

the one or more processors are further configured, responsive to execution of the computer-readable program code, to cause the computer system to perform;

sending the one or more results of the evaluation of the circuit to the requestor computer system.

19. The computer system of claim 18, wherein:

the computer system resides on the Internet;

the computer system comprises one or more communications components; and

the one or more processors are ifirther configured, responsive to execution of the computer-readable program code, to cause the computer system to perform;

communicating by the computer system with the requestor computer system over the Tnternet using the one or more communications components.

11. A computer program product comprising a non-transitory computer readable storage medium having program code embodied therewith, the program code readable and executable by a computer to cause the computer to perform:

performing homomorphic evaluation of a function on one or more input ciphertexts, where the one or more input ciphertexts were encrypted using a public key of an encryption scheme that also comprises a plurality of secret keys, where each input ciphertext comprises a plurality of real numbers that are kept with finite precision, and where performing the homomorphic evaluation of the function comprises performing one or more operations, and where performing each of one or more operations comprises;

performing a key-switching transformation on selected ones of the one or more input ciphertexts, where performing key-switching transformation on a selected ciphertext comprises converting a first version of the selected ciphertext with respect to a first of the plurality of secret keys and with some number r bits of precision to a second version of the selected ciphertext with respect to a second of the plurality of secret keys and with some other number r′

bits of precision, where r′

>

r,

where each of the key switching transformations is performed prior to or after the one or more operations are evaluated; and

outputting one or more results of the one or more operations.

12. The computer program product of claim 11, where r′

>

2r.

13. The computer program product of claim 11, where performing the homomorphic evaluation further comprises, prior to performing the key switching transformation, decreasing a norm of the first version of the selected ciphertext, by representing every number in the selected ciphertext via a sum number d>

1 of smaller digits, and where r′

>

r+r/d.

14. The computer program product of claim 11, where performing the homomorphic evaluation of the function further comprises performing the homomorphic evaluation of the function in order to evaluate a circuit comprising a plurality of levels.

15. The computer program product of claim 14, where performing homomorphic evaluation of a function further comprises performing homomorphic evaluation of multiple functions in order to evaluate the circuit.

20. The computer program product of claim 11, wherein:

the program code is readable and executable by a computer to cause the computer to perform;

receiving at the computing device a query from a requestor computer system;

the performing the homomorphic evaluation of the function is performed one or more times to evaluate a circuit using the query, the query corresponds to the input ciphertexts, and evaluation of the circuit produces one or more results; and

the program code is readable and executable by a computer to cause the computer to perform;

sending the one or more results of the evaluation of the circuit to the requestor computer system.