CLOSED GALOIS FIELD CRYPTOGRAPHIC SYSTEM
First Claim
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[pk] to a Galois extension field GF[pk+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[pk+1];
wherein 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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Accused Products
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.
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Citations
24 Claims
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1. A method for encrypting a data sequence, comprising the steps of:
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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[pk] to a Galois extension field GF[pk+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[pk+1]; wherein 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, 10)
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11. A machine-readable medium having stored thereon instructions, which when executed by a machine, cause the machine to perform the following operations comprising:
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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[pk] to a Galois extension field GF[pk+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[pk+1]; wherein 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 (12, 13, 14, 15)
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16. A closed Galois field cryptographic (CGFC) system, comprising:
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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[pk] to a Galois extension field GF[pk+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[pk+1]; wherein 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 (17, 18, 19, 20, 21, 22, 23, 24)
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Specification