US 5,966,444 A · Method and system for establishing a cryptographic key agreement using linear protocols

Abstract

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.

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Claims20

Dependent claims

A method for establishing key agreement between a first device and a second device over a communication channel, comprising the steps of:

selecting a Euclidean space V.sub.1 with a finite dimension n and a Euclidean space V.sub.2 with a finite dimension m, space V.sub.1 having a dual space V.sub.1 *=V.sub.1, and space V.sub.2 * having a dual space V.sub.2 *=V.sub.2 ;
selecting a degenerate linear operator T represented by a mXn rectangular matrix A with rank less then n, mapping space V.sub.1 into space V.sub.2, and its conjugate operator T* represented by a matrix A.sup.t with rank less than m, mapping space V.sub.2 into space V.sub.1 ;
selecting in the first device, a secret element x in space V.sub.1 ;
selecting in the second device, a secret element y in the space V.sub.2 ;
sending the value Ax from the first device to the second device;
sending the value A.sup.t y from the second device to the first device;
computing in the first device the value of the functional (x, A.sup.t y);
computing in the second device the value of the functional (Ax, y);
using the value (x, A.sup.t y) as the encryption key when sending a message from the first device to the second device, or the decryption key for the first device when receiving a ciphertext from the second device;
and
using as an encryption key (Ax, y) when sending a message from the second device to the first device, or the decryption key for the second device when receiving a ciphertext from the first device.

8 more elements

Dependencies are inferred from the claim text.

Description7,539 words

Summary1,030 words

#1. Field of the Invention

#This invention relates generally to cryptography, and more particularly, to a method for achieving the establishing of key agreement between two communicating parties.

#2. Description of the Related Art

Brief description of the drawings12 figures

#FIG. 1 is a block diagram of a cryptographic system for establishing key agreement through an insecure communication channel.

#FIG. 2 is a spatial diagram showing the duality of the conjugate linear operators in topological linear spaces.

#FIG. 3 is a flow diagram of a general linear protocol for establishing key agreement between multiple communication devices.

Detailed description6,225 words

#As shown in FIG. 1, communication devices 10 and 30, having transceivers 45 and 49, establish key agreement over a communication channel 47. Communication device 10 includes a cryptographic subsystem 12, a secure key generator 18, and a source of a numerical quantity 22 ("quantity source"). Similarly, communication device 30 includes a cryptographic subsystem 32, a secure key generator 38, and a source of a numerical quantity 42. Cryptographic subsystems 12 and 32 receive plaintext at plaintext ports 13 and 33 and provides output ciphertext at ciphertext ports 14 and 34 using the keys generated by secure key generators 18 and 38. Quantity sources 22 and 42 can each be implemented by, for example, a random number generator.

#Upon establishing the key used in communication, i.e. achieving key agreement, ciphertext messages from cryptographic subsystem 12, represented by the character "M", are provided through a ciphertext port 14 to transceiver 45 to be transmitted to communication device 30 over a communication channel 47. Such a communication channel can be a telephone link, a radio link, a microwave link, a coaxial cable link, a fiber optic link, or any other suitable communication medium. At communication device 30, transceiver 49 receives the ciphertext and provides the ciphertext over ciphertext port 34 to cryptographic subsystem 32. Cryptographic subsystem 32 decrypts the ciphertext by converting the ciphertext M back to a plaintext message P.

#The key agreement protocol in accordance with this invention is achieved based on the property of linear spaces, linear operators, and linear functionals.

Facts

Application

08/761,455Filed 6 Dec 1996

Granted

12 Oct 1999

Term ended

6 Dec 2016

Estimated · how

20 years from earliest known nonprovisional domestic filing. Maintenance-fee lapses, terminal disclaimers and statutory extensions have not been checked. The continuity chain may be incomplete; this is not an enforceability determination. Patent term adjustment is unavailable; no adjustment was added.

Classification2 codes

H04L 9/0838
Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for…:…
H04L
Digital communication

Method and system for establishing a cryptographic key agreement using linear protocols

Life of this patent

Method and system for establishing a cryptographic key agreement using linear protocols

Life of this patent

Life of this patent

Abstract

Drawings

Drawings

Claims20

Description7,539 words

Drawings

Classification2 codes

Life of this patent

Description7,539 words