WO-2026095522-A1 - AUTHENTICATION SYSTEM AND METHOD USING ELLIPTIC EQUATION

WO2026095522A1WO 2026095522 A1WO2026095522 A1WO 2026095522A1WO-2026095522-A1

Abstract

An authentication system using an elliptic equation, according to an embodiment of the present application, comprises: a first apparatus that generates ellipse information regarding a predefined elliptic equation; and a second apparatus that is provided to communicate with the first apparatus, receives at least a portion of the ellipse information, transmits, to the first apparatus, credential information generated on the basis of geometric properties of an ellipse defined in the received ellipse information, and is authenticated by the first apparatus, wherein the first apparatus may authenticate the second apparatus by using the credential information received from the second apparatus.

Inventors

PARK, SOO YONG
SEO, JUNG WON
LEE, JU HUI
LEE, KANG HO
JOO, Yun Jae

Assignees

서강대학교 산학협력단

Dates

Publication Date: 20260507
Application Date: 20251027
Priority Date: 20241101

Claims (12)

In an authentication system using elliptic equations, A first device for generating elliptical information regarding a predefined elliptical equation; and A second device configured to communicate with the first device, receiving at least a portion of the ellipse information, transmitting proof information generated based on the geometric properties of the ellipse defined in the received ellipse information to the first device, and performing authentication by the first device; An authentication system in which the first device performs authentication for the second device using the certification information received from the second device.
In paragraph 1, The above ellipse includes a first focus, a second focus, and a first point on the ellipse, and The first device transmits information of the first point to the second device as part of the elliptical information, and The second device is an authentication system that calculates the sum of the lengths of the three sides of a focal triangle formed by the first focal point, the second focal point, and the first point as the proof information.
In paragraph 1, The second device selects a second point on the ellipse, generates angle information corresponding to the second point as proof information, and transmits it to the first device. An authentication system in which the first device identifies the location of the second point based on the received angle information and performs authentication for the second device based on the identified location.
In paragraph 3, An authentication system in which the second device generates a symmetric key based on the selected second point and transmits encrypted attribute data, encrypted using the generated symmetric key, to the first device.
In paragraph 4, An authentication system wherein the first device calculates the second point based on the received angle information, restores the symmetric key based on the calculated second point, and decrypts the encrypted attribute data using the restored symmetric key.
In paragraph 1, An authentication system in which the above elliptical information is generated and managed through a blockchain-based smart contract.
In paragraph 1, An authentication system in which the first device is a service provider server and the second device is a service user terminal.
In an authentication method using elliptic equations, (a) A step in which the first device generates elliptical information regarding a predefined elliptical equation; (b) a step in which the first device transmits at least a portion of the elliptical information to the second device; (c) A step in which the second device generates proof information based on the geometric properties of the ellipse defined in the received ellipse information; (d) the second device transmitting the generated proof information to the first device; and (e) a step in which the first device performs authentication for the second device using the received authentication information; comprising an authentication method.
In paragraph 8, The above ellipse includes a first focus, a second focus, and a first point on the ellipse, and The above (c) step is, An authentication method comprising the step of the second device calculating the sum of the lengths of the three sides of a focal triangle formed by the first focal point, the second focal point, and the first point as the proof information.
In paragraph 8, The above (c) step is, An authentication method comprising the step of the second device selecting a second point on the ellipse and generating angle information corresponding to the selected second point as proof information.
In Paragraph 10, After step (c) above, (c-1) A step in which the second device generates a symmetric key based on the selected second point; (c-2) A step in which the second device encrypts attribute data using the generated symmetric key to generate encrypted attribute data; and (c-3) A step of the second device transmitting the encrypted attribute data to the first device; further comprising an authentication method.
In Paragraph 11, The above step (e) is, (e-1) A step in which the first device calculates the second point based on the received angle information; (e-2) A step in which the first device restores the symmetric key based on the calculated second point; and (e-3) A step in which the first device decrypts the encrypted attribute data using the restored symmetric key and verifies the decrypted attribute data; an authentication method comprising.

Description

Authentication system and method using elliptic equations The present invention relates to an authentication system and method using an elliptic equation. In the modern online environment, personal information protection and identity management are emerging as critical issues. Anonymity is a technical and social concept that conceals an individual's identity or prevents identification; by enabling online users to operate without exposing their personal information, it reduces the risk of data leakage or theft. This anonymity plays an important role in enhancing individual privacy while simultaneously promoting free expression and participation online. With the increasing importance of anonymity in recent years, there is a growing demand for technologies that go beyond simply concealing identities to verify the accuracy and integrity of information without directly disclosing sensitive data. This trend is particularly pronounced in fields such as online financial transactions, identity authentication, and blockchain, where accurate verification is required without infringing upon personal information. To address these demands, Zero-Knowledge Proof (ZKP) technology is gaining attention. ZKP provides a method to verify the authenticity of specific information without disclosing the information itself. Consequently, it is emerging as a powerful technological tool capable of guaranteeing information integrity while maintaining user anonymity. FIG. 1 is a diagram illustrating the configuration of an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 2 is a diagram illustrating an example of an elliptic equation and a focal triangle through an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 3 is a diagram illustrating an example of a notation method of an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 4 is a diagram illustrating an algorithm representing a simple authentication process of an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 5 is a diagram illustrating an algorithm representing the attribute authentication process of an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 6 is a diagram illustrating an overview of an online public opinion survey scenario that performs authentication through an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 7 is a diagram illustrating an overview of a data transaction scenario that performs authentication through an authentication system using an elliptic equation according to one embodiment of the present invention. FIG. 8 is a diagram illustrating the flow of an authentication method using an elliptic equation according to one embodiment of the present invention. The objectives and effects of the present invention, and the technical configurations for achieving them, will become clear by referring to the embodiments described in detail below in conjunction with the accompanying drawings. In describing the present invention, if it is determined that a detailed description of known functions or configurations may unnecessarily obscure the essence of the invention, such detailed description will be omitted. However, this is not intended to limit the invention to specific embodiments, and it should be understood that it includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention. Furthermore, the terms described below are defined considering their functions in the present invention, and these may vary depending on the intentions or practices of the user or operator. However, the present invention is not limited to the embodiments disclosed below but may be implemented in various different forms. These embodiments are provided merely to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined only by the scope of the claims. Therefore, such definition should be based on the content throughout this specification. The terms used in this application are used merely to describe specific embodiments and are not intended to limit the invention. The singular expression includes the plural expression unless the context clearly indicates otherwise. In this application, terms such as "comprising" or "having" are intended to specify the presence of the features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof. Unless otherwise defined, all terms us