Linear transformation for symmetric-key ciphers
First Claim
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1. A method of generating a linear transformation matrix A for use in a symmetric-key cipher, the method including:
- generating a binary [n,k,d] error-correcting code, represented by a generator matrix Gε
Z2k×
n in a standard form G=(Ik∥
B), with B ∥
Z2k×
(n−
k), where k<
n<
2k, and d is the minimum distance of the binary error-correcting code;
extending matrix B with 2k−
n columns such that a resulting matrix C is non-singular, and deriving matrix A from matrix C.
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Abstract
A method of generating a linear transformation matrix A for use in a symmetric-key cipher includes generating a binary [n,k,d] error-correcting code, where k<n <2k, and d is the minimum distance of the binary error-correcting code. The code is represented by a generator matrix GεZ2k×n in a standard form G=(Ik∥B), with BεZ2k×(n−k). The matrix B is extended with 2k−n columns such that a resulting matrix C is non-singular. The linear transformation matrix A is derived from matrix C. Preferably, the error correcting code is based on an XBCH code.
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Citations
8 Claims
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1. A method of generating a linear transformation matrix A for use in a symmetric-key cipher, the method including:
-
generating a binary [n,k,d] error-correcting code, represented by a generator matrix Gε
Z2k×
n in a standard form G=(Ik∥
B), with B ∥
Z2k×
(n−
k), where k<
n<
2k, and d is the minimum distance of the binary error-correcting code;
extending matrix B with 2k−
n columns such that a resulting matrix C is non-singular, andderiving matrix A from matrix C. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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Specification