Closed galois field cryptographic system
First Claim
1. A method for encrypting a data sequence, comprising the steps of:
- generating, by an electronic circuit, a payload data sequence comprising a plurality of first digits expressed as members of a Galois field GF[pk];
generating, by an electronic circuit, an encryption sequence comprising a plurality of second digits expressed as members of said Galois field GF[pk];
mapping, by an electronic circuit, said payload data sequence and said encryption sequence from said Galois field GF[pk] to a Galois extension field GF[pk+1], said mapping achieved by performing a first Affine transformation using said plurality of first digits and a second Affine transformation using said plurality of second digits; and
generating, by an electronic circuit, an encrypted data sequence by performing a CGFC arithmetic process, said CGFC arithmetic process including combining first results of said first Affine transformation with second results of said second Affine transformation;
wherein said first results and said second results are combined using a Galois field multiplication operation in said Galois extension field GF[pk+1], where p is a prime number, k is an integer value, and pk+1 defines a finite field size of said Galois extension field GF[pk+1].
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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[pk] to Galois extension field GF[pk+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[pk+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.
137 Citations
20 Claims
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1. A method for encrypting a data sequence, comprising the steps of:
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generating, by an electronic circuit, a payload data sequence comprising a plurality of first digits expressed as members of a Galois field GF[pk]; generating, by an electronic circuit, an encryption sequence comprising a plurality of second digits expressed as members of said Galois field GF[pk]; mapping, by an electronic circuit, said payload data sequence and said encryption sequence from said Galois field GF[pk] to a Galois extension field GF[pk+1], said mapping achieved by performing a first Affine transformation using said plurality of first digits and a second Affine transformation using said plurality of second digits; and generating, by an electronic circuit, an encrypted data sequence by performing a CGFC arithmetic process, said CGFC arithmetic process including combining first results of said first Affine transformation with second results of said second Affine transformation; wherein said first results and said second results are combined using a Galois field multiplication operation in said Galois extension field GF[pk+1], where p is a prime number, k is an integer value, and pk+1 defines a finite field size of said Galois extension field GF[pk+1]. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A device comprising a machine-readable non-transitory medium, having stored thereon a computer program for data communication, the computer program having a plurality of code sections, the code sections executable by a processor to cause the processor to perform the steps of:
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generating a payload data sequence comprising a plurality of first digits expressed as members of a Galois field GF[pk]; generating an encryption sequence comprising a plurality of second digits expressed as members of said Galois field GF[pk]; mapping said payload data sequence and said encryption sequence from said Galois field GF[pk] to a Galois extension field GF[pk+1], said mapping achieved by performing a first Affine transformation using said plurality of first digits and a second Affine transformation using a plurality of second digits; and generating an encrypted data sequence by performing a CGFC arithmetic process, said CGFC arithmetic process including combining first results of said first Affine transformation with second results of said second Affine transformation; wherein said first results and said second results are combined using a Galois field multiplication operation in said Galois extension field GF[pk+1], where p is a prime number, k is an integer value, and pk+1 defines a finite field size of said Galois extension field GF[pk+1]. - View Dependent Claims (11, 12, 13)
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14. A closed Galois field cryptographic (CGFC) system, comprising:
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a first generator configured to generate a payload data sequence comprising a plurality of first digits expressed as members of a Galois field GF[pk]; a second generator configured to generate an encryption sequence comprising a plurality of second digits expressed as members of a Galois field GF[pk]; and an encryption device coupled to said first and second generators and configured to perform a CGFC arithmetic process, said encryption device comprising (a) a mapping device configured to map said payload data sequence and said encryption sequence from said Galois field GF[pk] to a Galois extension field GF[pk+1], said mapping achieved by performing a first Affine transformation using said plurality of first digits and a second Affine transformation using said plurality of second digits, and (b) an encryptor configured to generate an encrypted data sequence by combining first results of said first Affine transformation with second results of said second Affine transformation; wherein said first results and said second results are combined using a Galois field multiplication operation in said Galois extension field GF[pk+1], where p is a prime number, k is an integer value, pk is defines a finite field size of said Galois field GF[pk], and pk+1 defines a finite field size of said Galois extension field GF[pk+1]. - View Dependent Claims (15, 16, 17, 18, 19, 20)
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Specification