Data encryption and decryption method using a public key

• US 20050117745A1
• Filed: 10/08/2004
• Published: 06/02/2005
• Est. Priority Date: 10/08/2003
• Status: Abandoned Application

• Current Assignee: Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: Jung, Tae-chul, Krouk, Evgeny, Lee, Kyung-hee, Bezzateev, Sergey, Fomin, Alexey
• Application Number:
  US10/960,630
• Publication Number:
  US 20050117745A1
• Time in Patent Office: Days
• US Class Current: 380/30
• CPC Class Codes: H04L 9/304 based on error correction codes, e.g. McEliece

Abstract

A data encryption method using a public key includes encoding data into a first code using a first public key, selecting a predetermined error vector, encoding the selected error vector into a second code using a second public key, and generating a ciphertext by adding the first and second codes. A corresponding decryption method includes performing first decoding of the ciphertext using a first set of a plurality of secret keys, determining locations of errors in the result of the first decoding using a second set of the plurality of secret keys and declaring erasures to the locations, performing second decoding according to a predetermined decoding algorithm and correcting a predetermined number of errors and the declared erasures, and detecting data from a result of correcting the errors and erasures.

Claims

1. A data encryption method, comprising:

encoding data into a first code using a first public key;

selecting a predetermined error vector;

encoding the selected error vector into a second code using a second public key; and

generating a ciphertext by adding the first and second codes.

2. The method as claimed in claim 1, wherein the first public key is an encoded matrix generated by a product of a generator matrix of an error correcting code and a non-singular matrix.

3. The method as claimed in claim 1, wherein the error vector is an arbitrary error vector selected from a custom error set.

4. The method as claimed in claim 3, wherein the error vector has a weight less than or equal to a number of errors correctable by an error correcting code.

5. The method as claimed in claim 1, wherein the second public key is generated by the following equation:

Second public key=(I+A) FV

where I is a unit matrix, A is a generator matrix of an anticode, F is a permutation matrix, and V is a non-singular matrix generating the first public key.

6. A decryption method for receiving and decrypting a ciphertext, the decryption method comprising:

performing first decoding of the ciphertext using a first set of a plurality of secret keys;

determining locations of errors in the result of the first decoding using a second set of the plurality of secret keys and declaring erasures to the locations;

performing second decoding according to a predetermined decoding algorithm and correcting a predetermined number of errors and the declared erasures; and

detecting data from a result of correcting the errors and erasures, wherein the ciphertext is generated by encoding data into a first code using a first public key, selecting a predetermined error vector, encoding the selected error vector into a second code using a second public key, and adding the first and second codes.

7. The method as claimed in claim 6, wherein the plurality of secret keys comprise a generator matrix of an error correction code forming the first public key, a non-singular matrix, a generator matrix of an anticode forming the second public key, and a permutation matrix.

8. The method as claimed in claim 7, wherein the erasures are determined from the generator matrix of the anticode.

9. A data encryption and decryption method, comprising:

encoding data into a first code using a first public key;

selecting a predetermined error vector;

encoding the selected error vector into a second code using a second public key;

generating a ciphertext by adding the first and second codes;

performing first decoding of the ciphertext using a first set of a plurality of secret keys;

determining locations of errors in the result of the first decoding using a second set of the plurality of secret keys and declaring erasures to the locations;

performing second decoding according to a predetermined decoding algorithm and correcting a predetermined number of errors and the declared erasures; and

detecting the data from the result of correcting the errors and erasures.

11. The method as claimed in claim 9, wherein the error vector is an arbitrary error vector selected from a custom error set.

12. The method as claimed in claim 11, wherein the error vector has a weight less than or equal to a number of errors correctable by an error correcting code.

13. The method as claimed in claim 9, wherein the second public key is generated by the following equation:

Second public key=(I+A) FV

where I is a unit matrix, A is a generator matrix of an anticode, F is a permutation matrix, and V is a non-singular matrix generating the first public key.

14. The method as claimed in claim 9, wherein the plurality of secret keys comprise a generator matrix of an error correction code forming the first public key, a non-singular matrix, a generator matrix of an anticode forming the second public key, and a permutation matrix.

15. The method as claimed in claim 14, wherein the erasures are determined from the generator matrix of the anticode.

10. The method as claimed in 9, wherein the first public key is an encoded matrix generated by a product of a generator matrix of an error correcting code and a non-singular matrix.