Closed Galois Field Combination
First Claim
1. A method for combining at least two input sequences in a communications system to increase a repetition period of the at least two input sequences in a resource efficient manner, comprising:
- receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk];
mapping said first number sequence and said second number sequence to a Galois extension field GF[pk+1]; and
generating an output sequence by combining said first number sequence with said second number sequence utilizing 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 method is provided for combining two or more input sequences in a communications system to increase a repetition period of the input sequences in a resource-efficient manner. The method includes a receiving step, a mapping step, and a generating step. The receiving step involves receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]. The mapping step involves mapping the first and second number sequences to a Galois extension field GF[pk+1]. The generating step involves generating an output sequence by combining the first number sequence with the second number sequence utilizing a Galois field multiplication operation in the Galois extension field GF[pk+1]. p is a prime number. k is an integer. pk+1 defines a finite field size of the Galois extension field GF[pk+1].
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Citations
20 Claims
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1. A method for combining at least two input sequences in a communications system to increase a repetition period of the at least two input sequences in a resource efficient manner, comprising:
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receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]; mapping said first number sequence and said second number sequence to a Galois extension field GF[pk+1]; and generating an output sequence by combining said first number sequence with said second number sequence utilizing 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, 10, 11)
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12. A closed Galois field cryptographic (CGFC) system, comprising:
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a receiving means configured for receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]; a mapping means configured for mapping said first number sequence and said second number sequence to a Galois extension field GF[pk+1]; and a generating means configured for generating an output sequence by combining said first number sequence with said second number sequence utilizing 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 (13, 14, 15, 16, 17, 18, 19, 20)
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Specification