CLOSED GALOIS FIELD CRYPTOGRAPHIC SYSTEM

• US 20090279688A1
• Filed: 05/06/2008
• Published: 11/12/2009
• Est. Priority Date: 05/06/2008
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J., Chester, David B.
• Granted Patent: US 8,139,764 B2
• Time in Patent Office: Days
• US Class Current: 380/28
• CPC Class Codes: H04L 2209/04 Masking or blinding
• CPC Class Codes: H04L 2209/34 Encoding or coding, e.g. Huffman coding or error correction
• CPC Class Codes: H04L 9/0668 producing a non-linear pseudorandom sequence

Abstract

A cryptographic system (CS) comprised of generators (502), (504), (510), an encryption device (ED), and a decryption device (DD). The generator (502) generates a data sequence (DS) including payload data. The generator (504) generates an encryption sequence (ES) including random numbers. The ED (506) is configured to perform a CGFC arithmetic process. As such, the ED is comprised of a mapping device (MD) and an encryptor. The MD is configured to map the DS and ES from Galois field GF[p^k] to Galois extension field GF[p^k+1]. The encryptor is configured to generate an encrypted data sequence (EDS) by combining the DS and ES utilizing a Galois field multiplication operation in Galois extension field GF[p^k+1]. The generator (510) is configured to generate a decryption sequence (DS). The DD (508) is configured to generate a decrypted data sequence by performing an inverse of the CGFC arithmetic process utilizing the EDS and DS.

Claims

1. A method for encrypting a data sequence, comprising the steps of:

generating a data sequence comprising payload data;

generating an encryption sequence comprising random numbers;

mapping said data sequence and said encryption sequence from a Galois field GF[p^k] to a Galois extension field GF[p^k+1]; and

generating an encrypted data sequence by performing a CGFC arithmetic process, said CGFC arithmetic process including combining said data sequence with said encryption sequence utilizing a Galois field multiplication operation in said Galois extension field GF[p^k+1];

wherein p is a prime number, k is an integer value, and p^k+1 defines a finite field size of said Galois extension field GF[p^k+1].

2. The method according to claim 1, further comprising selecting said random numbers of said encryption sequence to be pseudo-random numbers or pseudo-chaotic random numbers.

3. The method according to claim 1, further comprising expressing said data sequence and said encryption sequence in a p-adic number system representation or a mixed-radix number system representation.

4. The method according to claim 1, further comprising selecting each of said data sequence and said encryption sequence to be comprised of at least two digits expressed in a weighted number system.

5. The method according to claim 1, further comprising combining said data sequence and said encryption sequence by selectively performing a plurality of Galois field multiplication operations using a distinct subset of digits from each of said data sequence and said encryption sequence.

6. The method according to claim 1, further comprising mapping said data sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said data sequence and mapping said encryption sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said encryption sequence.

7. The method according to claim 1, further comprising generating a decryption sequence comprising random numbers and expressed in a Galois field GF[p^k].

8. The method according to claim 7, further comprising selecting said random numbers of said decryption sequence to be pseudo-random numbers or pseudo-chaotic random numbers.

9. The method according to claim 7, wherein said decryption sequence is an inverted sequence based on said encryption sequence.

10. The method according to claim 7, generating a decrypted data sequence by performing an inverse of said CGFC arithmetic process utilizing said encrypted data sequence and said decryption sequence.

11. A machine-readable medium having stored thereon instructions, which when executed by a machine, cause the machine to perform the following operations comprising:

generating a data sequence comprising payload data;

generating an encryption sequence comprising random numbers;

mapping said data sequence and said encryption sequence from a Galois field GF[p^k] to a Galois extension field GF[p^k+1]; and

generating an encrypted data sequence by performing a CGFC arithmetic process, said CGFC arithmetic process including combining said data sequence with said encryption sequence utilizing a Galois field multiplication operation in said Galois extension field GF[p^k+1];

wherein p is a prime number, k is an integer value, and p^k+1 defines a finite field size of said Galois extension field GF[p^k+1].

12. The machine-readable medium according to claim 11, further comprising instructions to cause the operation of combining said data sequence and said encryption sequence by selectively performing a plurality of Galois field multiplication operations using a distinct subset of digits from each of said data sequence and said encryption sequence.

13. The machine-readable medium according to claim 11, further comprising instructions to cause the operation of mapping said data sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said data sequence and mapping said encryption sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said encryption sequence.

14. The machine-readable medium according to claim 11, further comprising instructions to cause the operation of receiving a signal comprising said encrypted data sequence and generating a decryption sequence comprising random numbers and expressed in a Galois field GF[p^k] subsequent to receiving said signal.

15. The machine-readable medium according to claim 14, further comprising instructions to cause the operation of generating a decrypted data sequence by performing an inverse of said CGFC arithmetic process utilizing said encrypted data sequence and said decryption sequence.

16. A closed Galois field cryptographic (CGFC) system, comprising:

a first generator configured for generating a data sequence comprising payload data;

a second generator configured for generating an encryption sequence comprising random numbers; and

an encryption device coupled to said first and second generators and configured for performing a CGFC arithmetic process, said encryption device comprising (a) a mapping device configured for mapping said data sequence and said encryption sequence from a Galois field GF[p^k] to a Galois extension field GF[p^k+1] and (b) an encryptor configured for generating an encrypted data sequence by combining said data sequence with said encryption sequence utilizing a Galois field multiplication operation in said Galois extension field GF[p^k+1];

wherein p is a prime number, k is an integer value, p^k is defines a finite field size of said Galois field GF[p^k], and p^k+1 defines a finite field size of said Galois extension field GF[p^k+1].

17. The CGFC system according to claim 16, wherein said encryptor is further configured for combining said data sequence and said encryption sequence by selectively performing a plurality of Galois field multiplication operations using a distinct subset of digits from each of said data sequence and said encryption sequence.

18. The CGFC system according to claim 16, wherein said encryption sequence is a pseudo random number sequence or a pseudo-chaotic random number sequence.

19. The CGFC system according to claim 16, wherein said mapping device is further configured for mapping said data sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said data sequence.

20. The CGFC system according to claim 16, wherein said mapping device is further configured for mapping said encryption sequence to said Galois extension field GF[p^k+1] by performing an Affine transformation of said encryption sequence.

21. The CGFC system according to claim 16, further comprising a third generator configured for generating a decryption sequence expressed in a Galois field GF[p^k].

22. The CGFC system according to claim 21, wherein said decryption sequence is comprised of pseudo-random numbers or pseudo-chaotic random numbers.

23. The CGFC system according to claim 21, wherein said decryption sequence is an inverted sequence based on said encryption sequence.

24. The CGFC system according to claim 21, further comprising a decryption device coupled to said third generator and configured for generating a decrypted data sequence by performing an inverse of said CGFC arithmetic process utilizing said encrypted data sequence and said decryption sequence.