Improved Nose-Hoover system with ergodicity

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By adding external forces to the Nosé-Hoover system and designing circuits, the encryption security hidden dangers caused by system multi-stability are solved, and the system traversality and encryption security are improved.

CN119628819APending Publication Date: 2025-03-14SHANDONG POLICE ACAD

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Patent Information

Application Number: CN202411798118.3
Authority / Receiving Office: CN · China
Patent Type: Applications(China)
Current Assignee / Owner
Filing Date: 2024-12-09
Publication Date: 2025-03-14

AI Technical Summary

Technical Problem

In the field of information encryption, the Nosé-Hoover system may exhibit non-chaotic behavior under different initial conditions due to multiple stability problems, resulting in security risks in the encryption process.

Method used

By adding an external force term to the Nosé-Hoover system, an improved Nosé-Hoover system with traversality was constructed, and a circuit consisting of three channel circuits was designed to ensure that the system can enter a chaotic state under different initial conditions.

Benefits of technology

The traversality of the Nosé-Hoover system is realized, ensuring that it always enters a chaotic state during the information encryption process, and improving the security of encryption technology.

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Abstract

A circuit of the system is composed of three channel circuits, and the first channel circuit and the third channel circuit are each composed of a direct-current voltage source, a battery pack, an operational amplifier, a multiplier, a resistor, a capacitor and an analog ground. The second channel circuit is composed of a direct-current voltage source, an operational amplifier, a multiplier, a resistor, a capacitor and an analog ground. The research shows that the ergodicity plays a significant role in improving the security of the encryption algorithm based on the Nose-Hoover system. However, the Nosee-Hover system with ergodicity at present is extremely rare. Aiming at the current situation, an external force item is introduced into the Noseme-Hoover system, and the improved Noseme-Hoover system with ergodicity is provided. In addition, the invention also provides circuit simulation of the system, which has profound significance for promoting wide expansion of the system in practical application.

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Description

Technical Field

[0001] The invention relates to the field of conservative chaotic systems, and in particular to an improved Nosé-Hoover system with ergodicity. Background Art

[0002] As a classic conservative chaotic system, the Nosé-Hoover system has rich dynamic behaviors, which make it have potential application value in the field of cryptography. However, existing studies have shown that the Nosé-Hoover system has multi-stability, that is, under different initial conditions, the system may exhibit different dynamic behaviors, including chaotic motion, invariant torus or periodic orbits, etc. This multi-stability means that the Nosé-Hoover system does not have ergodicity. In information encryption applications based on the Nosé-Hoover system, if the selected initial conditions fail to lead the system into a chaotic state, but fall into an invariant torus or other non-chaotic behaviors, the encryption process may have security risks, making the information easy to be cracked or attacked. Based on this situation, the present invention proposes an improved Nosé-Hoover system with ergodicity by adding an external force term to the Nosé-Hoover system, and gives the circuit design of the system.

[0003] In view of the important position of the Nosé-Hoover system in the field of information encryption, in-depth research on the ergodic Nosé-Hoover system will not only help enrich the research scope of chaos theory, but also have far-reaching significance for improving the security of encryption technology. Summary of the invention

[0004] The object of the present invention is to provide an improved Nosé-Hoover system with ergodicity.

[0005] In order to achieve the above object, the solution of the present invention is:

[0006] 1. An improved Nosé-Hoover system with ergodicity, characterized in that:

[0007] (1) An improved Nosé-Hoover system (i) with ergodicity is:

[0008]

[0009] Where x, y, z are state variables;

[0010] (2) A circuit constructed based on system (i), the system comprising three channel circuits: the first channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, a battery pack V1, an operational amplifier U1A, an operational amplifier U4A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1 and an analog ground; the second channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U2A, an operational amplifier U5A, a resistor R5, a resistor R6, a resistor R7, a resistor R8, a multiplier A1, a capacitor C2 and an analog ground; the third channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, a battery pack V2, an operational amplifier U3A, an operational amplifier U6A, a resistor R9, a resistor R10, a resistor R11, a resistor R12, a multiplier A2, a capacitor C3 and an analog ground;

[0011] (3) The positive electrode of the battery pack V1 in the first channel circuit is grounded; the negative electrode of the battery pack V1 is connected to the negative input terminal of the operational amplifier U1A through the resistor R2; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the capacitor C1; the output terminal of the operational amplifier U1A outputs an x signal; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U4A through the resistor R3; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U2A in the second channel circuit through the resistor R6; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R4; the output terminal of the operational amplifier U4A outputs a -x signal; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD;

[0012] (4) The output of the multiplier A1 in the second channel circuit is connected to the negative input terminal of the operational amplifier U2A through the resistor R5; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C2; the output terminal of the operational amplifier U2A outputs the y signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U5A through the resistor R7; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A2 in the third channel circuit; the positive input terminal of the operational amplifier U2A is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the operational amplifier The negative power supply terminal of U2A is connected to the DC voltage source VDD; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U5A through the resistor R8; the output terminal of the operational amplifier U5A outputs a -y signal; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U1A in the first channel circuit through the resistor R1; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A1 in the second channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD;

[0013] (5) The output of the multiplier A2 in the third channel circuit is connected to the negative input terminal of the operational amplifier U3A through the resistor R10; the positive electrode of the battery pack V2 is grounded; the negative electrode of the battery pack V2 is connected to the negative input terminal of the operational amplifier U3A through the resistor R9; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U3A through the capacitor C3; the output terminal of the operational amplifier U3A outputs the z signal; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U6A through the resistor R11; the output of the operational amplifier U3A is connected to the second channel circuit The X input terminal of the multiplier A1 is connected; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R12; the output terminal of the operational amplifier U6A outputs a -z signal; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

[0014] 2. According to claim 1, an improved Nosé-Hoover system with ergodicity is characterized in that: the models of the operational amplifiers U1A, U2A, U3A, U4A, U5A, and U6A are all LF347N.

[0015] 3. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: the multipliers A1 and A2 are both AD633.

[0016] 4. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: the DC voltage source VCC is 15V and VDD is -15V.

[0017] 5. An improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: the voltage of the battery pack V1 is 0.5V and the resistance is 0.1Ω; the voltage of the battery pack V2 is 1V and the resistance is 0.1Ω.

[0018] 6. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that the capacitance values of the capacitors C1, C2, and C3 are all 10nF.

[0019] 7. An improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: the resistance values of the resistors R1, R2, R5, R6, R9, and R10 are all 100kΩ; the resistance values of the resistors R3, R4, R7, R8, R11, and R12 are all 10kΩ.

[0020] After adopting the above scheme, the present invention is provided with three channel circuits, the input ends and output ends of the three channel circuits are connected to each other, forming an improved Nosé-Hoover system with ergodicity. The circuit has the following beneficial effects:

[0021] (1) The circuit structure is simple and easy to implement;

[0022] (2) The conservative chaos generated by the circuit is ergodic. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a circuit diagram of the present invention.

[0024] Figure 2 It is the XY phase diagram of the present invention.

[0025] Figure 3 It is the XZ phase diagram of the present invention.

[0026] Figure 4 It is the YZ phase diagram of the present invention. DETAILED DESCRIPTION

[0027] The technical solutions and beneficial effects of the present invention are described in detail below in conjunction with the accompanying drawings. Figure 1-Figure 4 .

[0028] 1. The present invention proposes an improved Nosé-Hoover system with ergodicity, which has 6 terms in total, including 2 constant terms, 2 linear terms, and 2 quadratic terms.

[0029] (1) The improved Nosé-Hoover system model involved in the present invention is as follows:

[0030]

[0031] Where x, y, z are state variables.

[0032] (2) Figure 1 As shown, the simulation circuit involved in the present invention is composed of three channel circuits: the first channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, a battery pack V1, an operational amplifier U1A, an operational amplifier U4A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1 and an analog ground; the second channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U2A, an operational amplifier U5A, a resistor R5, a resistor R6, a resistor R7, a resistor R8, a multiplier A1, a capacitor C2 and an analog ground; the third channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, a battery pack V2, an operational amplifier U3A, an operational amplifier U6A, a resistor R9, a resistor R10, a resistor R11, a resistor R12, a multiplier A2, a capacitor C3 and an analog ground;

[0033] (3) The positive electrode of the battery pack V1 in the first channel circuit is grounded; the negative electrode of the battery pack V1 is connected to the negative input terminal of the operational amplifier U1A through the resistor R2; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the capacitor C1; the output terminal of the operational amplifier U1A outputs an x signal; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U4A through the resistor R3; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U2A in the second channel circuit through the resistor R6; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R4; the output terminal of the operational amplifier U4A outputs a -x signal; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD;

[0034] (4) The output of the multiplier A1 in the second channel circuit is connected to the negative input terminal of the operational amplifier U2A through the resistor R5; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C2; the output terminal of the operational amplifier U2A outputs the y signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U5A through the resistor R7; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A2 in the third channel circuit; the positive input terminal of the operational amplifier U2A is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the operational amplifier The negative power supply terminal of U2A is connected to the DC voltage source VDD; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U5A through the resistor R8; the output terminal of the operational amplifier U5A outputs a -y signal; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U1A in the first channel circuit through the resistor R1; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A1 in the second channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD;

[0035] (5) The output of the multiplier A2 in the third channel circuit is connected to the negative input terminal of the operational amplifier U3A through the resistor R10; the positive electrode of the battery pack V2 is grounded; the negative electrode of the battery pack V2 is connected to the negative input terminal of the operational amplifier U3A through the resistor R9; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U3A through the capacitor C3; the output terminal of the operational amplifier U3A outputs the z signal; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U6A through the resistor R11; the output of the operational amplifier U3A is connected to the second channel circuit The X input terminal of the multiplier A1 is connected; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R12; the output terminal of the operational amplifier U6A outputs a -z signal; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

[0036] 2. In the three channel circuits, the operational amplifiers U1A, U2A, U3A, U4A, U5A, and U6A are all LF347N; the multipliers A1 and A2 are all AD633; the DC voltage sources VCC are 15V, and VDD are -15V; the voltage of the battery pack V1 is 0.5V, and the resistance is 0.1Ω; the voltage of the battery pack V2 is 1V, and the resistance is 0.1Ω; the capacitance values of the capacitors C1, C2, and C3 are all 10nF; the resistance values of the resistors R1, R2, R5, R6, R9, and R10 are all 100kΩ; the resistance values of the resistors R3, R4, R7, R8, R11, and R12 are all 10kΩ.

[0037] Of course, the above description is not a limitation of the invention, and the invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the invention also belong to the protection scope of the invention.

Claims

1. An improved Nosé-Hoover system with ergodicity, characterized in that: (1) An improved Nosé-Hoover system (i) with ergodicity is: Where x, y, z are state variables; (2) A circuit constructed based on system (i), the system comprising three channel circuits: the first channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, a battery pack V1, an operational amplifier U1A, an operational amplifier U4A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a capacitor C1 and an analog ground; the second channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U2A, an operational amplifier U5A, a resistor R5, a resistor R6, a resistor R7, a resistor R8, a multiplier A1, a capacitor C2 and an analog ground; the third channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, a battery pack V2, an operational amplifier U3A, an operational amplifier U6A, a resistor R9, a resistor R10, a resistor R11, a resistor R12, a multiplier A2, a capacitor C3 and an analog ground; (3) The positive electrode of the battery pack V1 in the first channel circuit is grounded; the negative electrode of the battery pack V1 is connected to the negative input terminal of the operational amplifier U1A through the resistor R2; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the capacitor C1; the output terminal of the operational amplifier U1A outputs an x signal; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U4A through the resistor R3; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U2A in the second channel circuit through the resistor R6; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R4; the output terminal of the operational amplifier U4A outputs a -x signal; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD; (4) The output of the multiplier A1 in the second channel circuit is connected to the negative input terminal of the operational amplifier U2A through the resistor R5; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C2; the output terminal of the operational amplifier U2A outputs the y signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U5A through the resistor R7; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A2 in the third channel circuit; the positive input terminal of the operational amplifier U2A is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the operational amplifier The negative power supply terminal of U2A is connected to the DC voltage source VDD; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U5A through the resistor R8; the output terminal of the operational amplifier U5A outputs a -y signal; the output of the operational amplifier U5A is connected to the negative input terminal of the operational amplifier U1A in the first channel circuit through the resistor R1; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A1 in the second channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD; (5) The output of the multiplier A2 in the third channel circuit is connected to the negative input terminal of the operational amplifier U3A through the resistor R10; the positive electrode of the battery pack V2 is grounded; the negative electrode of the battery pack V2 is connected to the negative input terminal of the operational amplifier U3A through the resistor R9; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U3A through the capacitor C3; the output terminal of the operational amplifier U3A outputs the z signal; the output of the operational amplifier U3A is connected to the negative input terminal of the operational amplifier U6A through the resistor R11; the output of the operational amplifier U3A is connected to the second channel circuit The X input terminal of the multiplier A1 is connected; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R12; the output terminal of the operational amplifier U6A outputs a -z signal; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

2. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The operational amplifiers U1A, U2A, U3A, U4A, U5A and U6A are all of model LF347N.

3. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The multipliers A1 and A2 are both AD633.

4. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The DC voltage sources VCC and VDD are both 15V and -15V, respectively.

5. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The voltage of the battery pack V1 is 0.5V and the resistance is 0.1Ω; The voltage of the battery pack V2 is 1V and the resistance is 0.1Ω.

6. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The capacitance values of the capacitors C1, C2 and C3 are all 10 nF.

7. The improved Nosé-Hoover system with ergodicity according to claim 1, characterized in that: The resistance values of the resistors R1, R2, R5, R6, R9, and R10 are all 100 kΩ; the resistance values of the resistors R3, R4, R7, R8, R11, and R12 are all 10 kΩ.