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Feng Q Hao

Chuan K Yuan

Chung Nan Chang

A method for establishing key agreement between two communicating parties using a general linear protocol in finite and infinite dimensional spaces. Two topological linear spaces, in particular Euclidean spaces, and a non-trivial degenerate linear operator are selected. Each party respectively selects a secret element, and exchanges with the other party an image under the transformation of a matrix. Key agreement is therefore mutually established between the two communicating parties having the same cryptographic key. Various illustrative embodiments of the general linear operator are disclosed, including a rectangular matrix, a square matrix, a symmetric matrix, a skew symmetric matrix, an upper triangular square matrix, a lower triangular square matrix, a special type of skew symmetric matrix to generate a modified cross product protocol, a series of matrices to generate a sequential key protocol, and a combination of circulant matrices.

Method and system for establishing a cryptographic key agreement using

Using the present cryptographic key exchange protocol, a first of two cryptographic units selects quantities 'A' and 'B.' That same unit then applies a mathematical function '.PHI..sub.1 ' to A and B to compute a third quantity 'C.'. A and B and the function .PHI..sub.1 posses the property that knowing A or B, and C, and the function .PHI..sub.1, it is mathematically impossible to compute the unknown quantity B or A. The first unit then transmits A together C to the second unit while retaining B. The second unit selects a fourth quantity 'D' and then applies a second mathematical function .PHI..sub.2 to A and D to compute a quantity 'E' which the second unit transmits to the first unit while retaining D. The quantities A and D and the function .PHI..sub.2 must posses the property that knowing D and E, and the function .PHI..sub.2, it is mathematically impossible to compute the unknown quantity D. Then the second unit applies a third mathematical function '.PSI..sub.2 ' to D and C to compute the secure key 'K.' The first unit upon receiving the quantity E then applies a fourth mathematical function .PSI..sub.1 to B and E to also compute the secure key K.

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Feng Q Hao