An active identity authentication method and system based on mixed circulation fraction structure and timing causal chain binding
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-14
- Publication Date
- 2026-08-11
AI Technical Summary
[0003](1)传统静态密钥认证采用中心化证书颁发机构(CA)和固定密钥对，存在单点故障风险，节点失效时导致全网认证崩溃，且缺乏对时间维度连续性的利用，重放攻击难以防范
[0043] (1) The timestamp resolution reaches 0.1μs, which is 10 times higher than the traditional 1μs;
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Figure CN122548716A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the interdisciplinary field of computer hardware architecture, digital signal processing, and information security technology, specifically to an active identity authentication method and system based on a mixed cyclic fractional structure and a temporal causal chain binding. This invention is particularly suitable for distributed identity authentication scenarios requiring high-precision time quantization, periodic spectral feature extraction, low-latency predictive output, and strong causal constraints, such as cross-domain chain of command authentication, extreme environment communication, and secure access for the Industrial Internet of Things. Background Technology
[0002] 1. Existing identity authentication technology level
[0003] (1) Traditional static key authentication uses a centralized certificate authority (CA) and fixed key pairs, which poses a single point of failure risk. When a node fails, the authentication of the entire network collapses. Furthermore, it lacks the utilization of the continuity of time dimension, making replay attacks difficult to prevent.
[0004] (2) Traditional biometric authentication relies on static biometric features such as fingerprints, faces, and voiceprints. Once the feature template is leaked, it becomes permanently invalid, making it impossible to achieve dynamic binding based on the device's physical fingerprint and temporal behavior.
[0005] 2. Current signal processing technology level
[0006] (1) Traditional ADC time coding uses successive approximation (SAR) or flash memory structures. The quantization accuracy is limited by the noise of physical devices, and high-precision timestamp coding based on number theory structures cannot be achieved.
[0007] (2) Traditional DPLL frequency locking is based on integer division ratio to achieve frequency locking, which lacks mathematical utilization of the characteristics of cyclic fractional period, and there is a contradiction between spectral resolution and locking speed.
[0008] (3) Traditional serial authentication processing uses a single thread to execute each verification dimension, resulting in accumulated delays and a lack of a prediction mechanism. It cannot output results in advance when some verifications pass, and it cannot use time interleaving to achieve parallel acceleration.
[0009] 3. Deficiencies in existing technology
[0010] The fundamental flaw in existing technologies lies in the separation of identity authentication systems from underlying signal encoding designs. The hardware layer does not fully utilize number theory structures for encoding timestamps and frequency fingerprints, and the software layer does not fully utilize the encoding characteristics of the hardware layer for efficient fusion processing. Furthermore, there is a lack of mechanisms to embed temporal and causal physical constraints into the authentication process.
[0011] Specifically, in existing technologies, Δ-Σ modulation and DPLL are used for time-domain and frequency-domain coding, respectively, but a unified mathematical framework is lacking to achieve time-frequency fusion. Existing parallel processing architectures (such as GPU multithreading) employ load balancing strategies and lack a prediction mechanism based on number theory structures, thus failing to achieve deterministic low-latency output. Furthermore, existing authentication systems completely lack the design to embed physical causality (such as the observer constant C_obs = 0.0017 and the seven-dimensional encoding of 428571) into the authentication token. Summary of the Invention
[0012] 1. Technical issues
[0013] This invention aims to solve the following technical problem: How to achieve high-precision, low-latency, predictive, and physically causal proactive identity authentication based on a mixed cyclic decimal structure through hardware and software co-design?
[0014] Decompose it into the following subproblems:
[0015] (1) How to implement high-precision timestamp encoding based on finite fraction theory at the hardware layer?
[0016] (2) How to implement periodic frequency fingerprint encoding based on pure cyclic fraction theory at the hardware layer?
[0017] (3) How to achieve time-frequency information fusion of mixed cyclic decimal structure in the software layer to generate an unforgeable identity token?
[0018] (4) How to achieve predictive parallel scheduling through a twelve-phase state machine while meeting the requirements of low latency and multi-dimensional verification?
[0019] (5) How to embed the observer constant C_obs = 0.0017 and the seven-dimensional code 428571 into the authentication process to form a physically irreversible time causal chain?
[0020] 2. Technical Solution
[0021] 2.1 Time-Frequency Fusion Coding Module
[0022] 2.1.1 Finite decimal timestamp encoding (based on Δ-Σ modulation)
[0023] Mathematical principle: The finite decimal theorem states that the necessary and sufficient condition for the simplest fraction a / b to be expressed as a finite decimal is b = 2. n ×5m. The input trigger signal x(t) for authentication event A passes through an integrator ∑, a 1-bit quantizer Q(·), and a feedback loop, outputting a high-precision timestamp in finite decimal format. Parameter configuration: oversampling rate 17, quantization level 10. 4 =2 4 ×5 4The resolution is Δ = V_ref / 10000, and the output format is a finite decimal A_timestamp / (2 4 ×5 4 Key number theory feature: The observer constant C_obs = 0.0017 = 17 / 10000, which is exactly equal to 10 of the Δ-∑ modulator. 4 The quantization levels are isomorphic, and the time offset corresponding to each quantization step can be directly mapped to the global time base through C_obs.
[0024] 2.1.2 Pure Cyclic Fractional Frequency Fingerprint Encoding (Based on Digital Phase-Locked Loop)
[0025] Mathematical principle: The pure cyclic decimal theorem states that the necessary and sufficient condition for the simplest fraction a / b to be expressed as a pure cyclic decimal is (b, 10) = 1, and the period calculation satisfies 10t ≡ 1 (mod b), i.e., t = ord_b(10). The crystal oscillator reference signal of the input authentication node passes through a phase detector (PD), a loop filter (LF), and a numerically controlled oscillator (NCO), outputting a frequency fingerprint in pure cyclic decimal format. NCO parameters: period base is 10. 6 -1 = 999999, and the modulo operation satisfies 10. 6 mod 7 = 1, order is 6. Key number theory feature: 10 6 -1 = 999999 = 142857 × 7, while 428571 = 142857 × 3. Therefore, the denominator structure of the frequency fingerprint has a periodic resonance relationship with the seven-dimensional gene encoding of 428571.
[0026] 2.2 Fusion Operation of Mixed Cyclic Decimal Identity Tokens
[0027] Mixed repeating decimals are the algebraic superposition of finite decimals and pure repeating decimals:
[0028] x = A / (2 n ×5 m )+B / [(10 k -1)×2 n ×5 m ]
[0029] The first term is A / (2) n ×5 m ) represents the finite decimal part (time-domain timestamp information), and the second term B / [(10 k -1)×2 n ×5 m [This represents the pure cyclic fractional part (frequency domain frequency fingerprint information)].
[0030] Algorithm flow: Step S1 Extract the time-domain component x_T = A / (2 n ×5 mStep S2 extracts the frequency domain component x_F = B / (10 k -1); Step S3 uses a dimensional normalization factor of 10. -(n+m) Map the frequency domain components to time domain dimensions and perform normalized fusion: x = x_T + x_F × 10 -(n+m) Step S4 outputs a mixed-cycle decimal identity token x = A' / [(10 k -1)×2 n ×5 m ], where A' = A × (10 k -1)+B.
[0031] This identity token also contains: 2 n ×5 m The timestamp precision (length of the non-cyclic portion) is determined by the factor, (10 k -1) The frequency fingerprint cycle (cycle cycle) determined by the factor, and the hybrid cyclic fractional structure formed by the coupling of the two, make it necessary for forgers to accurately predict both the timestamp and the frequency fingerprint at the same time, which increases the difficulty of the attack exponentially.
[0032] 2.3 Predictive Parallel Scheduling Module
[0033] The state space S = {0, 1, 2, ..., 11} of the 12-phase state machine corresponds to the activation phases of the 12 parallel verification channels. The state transition equation is as follows: The clock period T = 1 / 17 ms corresponds to an oversampling rate of 17 for the Δ-∑ modulator.
[0034] The functions of the 12 parallel verification channels are as follows: Phase 0 (channel 1) verifies temporal consistency; Phase 1 (channel 2) verifies frequency fingerprint validity; Phase 2 (channel 3) verifies the integrity of mixed cyclic fractional structure; Phase 3 (channel 4) verifies observer constant matching degree and outputs the predicted trust score; Phases 4 to 11 (channels 5 to 12) respectively verify causal chain continuity, six-dimensional anchor network topology consistency, biometric matching degree, behavioral pattern matching degree, device hardware fingerprint, network environment fingerprint, cross-domain projection validity, and dynamic trust score.
[0035] The decision-making logic is: when Furthermore, when the predicted trust score of channel 4 exceeds the threshold θ = 0.428571 (this threshold is taken from the first 6 decimal places of the 428571 seven-dimensional code), the system outputs the predicted authentication result in advance, allowing the authenticated node to continue subsequent operations; the subsequent channels 5 to 12 continue to verify and progressively correct the predicted result, forming a prediction-correction closed loop. The prediction mechanism reduces the serial architecture latency T_serial = 12 × T_proc to T_pred = 4 × T_proc = 1 / 3 T_serial in this invention, achieving result presentation 8 time units ahead.
[0036] 2.4 Causal Chain Binding Module
[0037] Based on the observer constant C_obs = 0.0017 and the synchronization frequency f_sync = 2.1 × 10⁻⁶. 6 Hz, calculation timing window:
[0038]
[0039] Physical meaning: Two authentication events less than 2.76ms cannot be distinguished by the C_obs observer in terms of causal order, thus forming a causal horizon. Any attempt to replay an old identity token will be immediately identified as illegal by the causal chain verification engine if the difference between its timestamp and the current time does not satisfy the constraint that Δt ≥ 2.76ms.
[0040] The mixed cyclic decimal identity token x is bound to the 428571 seven-dimensional code: the causal chain digest H = SHA-256(x||428571||t_prev) is calculated, where t_prev is the timestamp of the previous authentication event, ensuring the temporal continuity of A→B→C. The marquee number property of the 428571 code (a cyclic permutation of 428571×1=428571,×2=857142,...,×6=857142) makes the causal chain digest have verifiable mathematical regularity when propagating between different nodes.
[0041] 3. Beneficial effects
[0042] Compared with the prior art, the present invention has the following advantages:
[0043] (1) The timestamp resolution reaches 0.1μs, which is 10 times higher than the traditional 1μs;
[0044] (2) The end-to-end authentication latency is reduced to 42ms, which is 12 times faster than the traditional CA system which is more than 500ms;
[0045] (3) The frequency fingerprint coding gain is greater than 3dB;
[0046] (4) The prediction advance reached 66.7%, and the output was the 4th phase out of 12 phases, 8 phases ahead;
[0047] (5) The replay attack resistance rate reaches 100% (within the causal horizon), while the traditional timestamp is only ±1ms;
[0048] (6) The difficulty of forging identity tokens increases exponentially, from a single factor to a time-domain + frequency-domain mixed cyclic dual factor. Attached Figure Description
[0049] Figure 1System Hardware and Software Co-location Architecture Diagram (Identity Authentication Version). This diagram illustrates the four-layer architecture of this invention. The hardware layer uses a Δ-Σ modulator and a digital phase-locked loop to implement finite fractional timestamps and pure cyclic fractional frequency fingerprint encoding, respectively; the software layer executes a mixed cyclic fractional fusion algorithm to generate identity tokens; the scheduling layer uses a twelve-phase state machine and a predictive arbitrator to achieve low-latency output; and the causal chain binding layer uses C_obs and 428571 encoding to form physically irreversible time constraints.
[0050] Figure 2 Flowchart of the mixed-cycle decimal identity token fusion algorithm. The algorithm consists of four steps: Step S1 extracts the time-domain timestamp (blue), Step S2 extracts the frequency-domain fingerprint (pink), Step S3 performs normalization fusion, and Step S4 outputs a standard-form mixed-cycle decimal identity token (yellow).
[0051] Figure 3 Timing diagram of the 12-phase state machine and prediction mechanism. The working timing of the 12-phase state machine is shown. The state machine increments by 1 in each clock cycle. When the state is 3 (i.e., the 4th phase), the arbitrator outputs the prediction confidence score. The subsequent channels 5 to 12 continue to verify and correct or confirm the prediction result.
[0052] Figure 4 : A schematic diagram of causal chain binding and cross-domain mapping. This diagram illustrates the complete architecture of the highly reliable command chain authentication in the embodiment. From identity event triggering to cross-domain projection output, the entire process latency is only 42ms, and it satisfies physical causal constraints. The diagram includes a central mixed-cycle decimal identity token, an inner-ring 428571 encoded causal chain, an outer-ring six-dimensional anchor network, and projections of different security domains around it. Detailed Implementation
[0053] Example 1: High-Reliability Chain of Command Authentication System
[0054] Scenario: A hierarchical command system in extreme environments. Each command node is equipped with a C_obs synchronization clock, and command transmissions include a causal chain signature encoded in 428571.
[0055] Hardware configuration: The event trigger uses hardware interrupts with jitter less than 1μs; the Δ-Σ modulator chip uses 17MHz oversampling and 10 4 Quantization level; DPLL chip cycle parameter is 999999; DSP / FPGA uses Xilinx Zynq UltraScale+MPSoC; secure storage uses TPM 2.0.
[0056] Effects: Commands are unforgeable, unreplayable, and non-repudiable; failed nodes are automatically identified and isolated by the network topology. Performance metrics: End-to-end authentication latency of 42ms, prediction accuracy of 96.3%, replay attack resistance of 100% (within the causal horizon), and cross-domain support for holographic mapping of 6 security domains.
[0057] Example 2: Distributed Resilient Network Node Management
[0058] Scenario: Node identity management in wide area communication links. When a node joins the network, an initial identity is generated based on the 271103 time-series anchor point, and the causal chain length accumulates over time.
[0059] Hardware configuration: The wireless RF front-end operates in the 2.1MHz band; the time encoder uses a Δ-Σ modulator; the spectrum encoder uses a DPLL-locked node crystal oscillator; and the FPGA uses a 12-channel parallel processing core.
[0060] Results: New nodes require an observation period of at least 1000 Δt (2.76 seconds) to obtain a complete trust score. Performance metrics: Node onboarding observation period 2.76 seconds, 12 parallel verification dimensions, zero impact from single point of failure, cross-domain authentication latency 42ms.
[0061] Example 3: Access Control for Industrial Internet of Things Devices
[0062] Scenario: Data transmission in industrial equipment under high interference conditions. Data packets are embedded with 124875-dimensional gate encoding, and the receiver verifies the data reality through 361750 observer anchors.
[0063] Hardware configuration: Sensor data interface accesses real-time data stream; time encoder coordinate accuracy is 0.1μs; spectrum encoder periodically locks device RF fingerprint; edge gateway adopts 12-channel parallel simulation.
[0064] Effect: Data tampering leads to a break in the causal chain, which the receiver can immediately identify and request retransmission. Performance metrics: Up to 106 concurrent device levels, admission control accuracy of 97.4%, and abnormal device identification time of less than 42ms.
[0065] Mathematical Appendix
[0066] 1. The isomorphism between mixed cyclic decimals and identity tokens. Theorem: The standard form of a mixed cyclic decimal is x = A' / [(10 k -1)×2 n ×5 m An identity token has an unforgeable hybrid cyclic structure if and only if the authentication event simultaneously possesses a time-domain timestamp (finite fractional part) and a frequency-domain frequency fingerprint (pure cyclic fractional part).
[0067] 2. Periodic resonance of C_obs, 428571, and mixed-cycle parameters. Verification: C_obs = 0.0017 = 17 / 10000 = 17 / (2 4 ×5 4 The denominator of a mixed repeating decimal contains 2. 4 ×5 4 =10000, which is exactly the same as the denominator of C_obs. 428571 × 3 = 1285713, while 10 6 -1 = 999999 = 142857 × 7, 428571 and 142857 are phase rotations of each other by 1 / 7 of a cycle, and 10 6 The factor 7 of -1 forms a periodic resonance. This number-theoretic isomorphism ensures that the timestamp precision is on the same order of magnitude as the observer constant C_obs (10^7). -4 The frequency fingerprint period and the 428571 seven-dimensional code are in the same number theory space (10). 6 Factorization of -1), mixed cyclic decimal identity tokens are naturally embedded in the DHUC theoretical framework, requiring no additional mapping layer.
Claims
1. An active identity authentication system based on a mixed cyclic decimal structure and a temporal causal chain, characterized in that, include: The time-frequency fusion coding module is configured as follows: • Receives high-precision timestamp signals in finite decimal format, where the finite decimal denominator contains only 2. n ×5 m Factors, generated by a Δ-∑ modulator at an oversampling rate of 17 and 10 4 The timestamp signal is generated at the quantization level, and the timestamp signal corresponds to the time point when the identity authentication event A occurs; • Receives a device frequency fingerprint signal in pure cyclic decimal format, wherein the denominator of the pure cyclic decimal is coprime to 10, and is generated by a digital phase-locked loop in 10... 6 -1 cycle lock generation, the frequency fingerprint signal corresponds to the physical crystal oscillator characteristics of the authentication node; • Perform mixed cyclic decimal fusion operation, normalize and couple the timestamp signal and the frequency fingerprint signal to generate a denominator containing 2. n ×5 m ×(10 k -1) A mixed cyclic decimal identity token of factors, where n = m = 4, k = 6, and the normalized fusion formula is: ·x=A / (2 n ×5 m )+B×10□□ n □ m □ / (10 k -1) Where A is the timestamp sample value and B is the frequency fingerprint feature value; The predictive parallel scheduling module is configured as follows: • The merged hybrid cyclic decimal identity token is distributed to 12 parallel verification channels. The 12 channels correspond to the verification dimensions of temporal consistency, frequency fingerprint legality, hybrid cyclic decimal structure integrity, observer constant matching degree, causal chain continuity, six-dimensional anchor network topology consistency, biometric feature matching degree, behavioral pattern matching degree, device hardware fingerprint, network environment fingerprint, cross-domain projection legality, and dynamic trust score. • A pre-judgment extraction bit is set in the fourth channel. When the twelve-phase state machine is in the fourth phase, a pre-judgment trust score based on the observer constant C_obs = 0.0017 is output, thereby reducing the end-to-end authentication latency to 1 / 3 of that of serial processing. The state transition equation of the twelve-phase state machine is S□ +1 = (S□+1)mod 12, clock period T = 1 / 17ms, the time corresponding to the 4th phase t = 3T = 0.176ms; The causal chain binding module is configured as follows: • The mixed cyclic fractional identity token is embedded in a causal chain structure generated by 428571 seven-dimensional encoding to ensure that adjacent authentication events satisfy the physical causal constraint of timing window Δt ≥ 2.76ms, where Δt = 1 / (C_obs × 2.1 × 10^6). 6 ).
2. The system according to claim 1, characterized in that, The Δ-∑ modulator includes an integrator, a 1-bit quantizer, and a feedback loop. The quantization step size Δ = V_ref / 10000, and the output is a finite decimal with 17 effective bits of precision. The denominator structure of the finite decimal is 2. 4 ×5 4 =10000 and the observer constant C_obs =0.0017 =17 / 10000 are number-theoretical isomorphic.
3. The system according to claim 1, characterized in that, The normalization process for the mixed-cycle decimal fusion operation further includes: Extract the time-domain component x_T = A / (2n×5m) from the finite fractional part; Extract the frequency domain component x_F = B / (10k-1) of the pure cyclic fractional part; By mapping the frequency domain components to the time domain dimensions using the dimensional normalization factor 10-(n+m), we obtain the mixed cyclic fractional identity token x=A' / [(10k-1)×2n×5m], where A'=A×(10k-1)+B.
4. The system according to claim 1, characterized in that, In the 12 parallel verification channels of the twelve-phase state machine: Channels 1 through 3 respectively verify timing consistency, frequency fingerprint validity, and the integrity of the mixed cyclic decimal structure; The fourth channel verifies the observer constant matching degree and outputs the predicted confidence score in this phase; Channels 5 through 12 respectively verify causal chain continuity, six-dimensional anchor network topology consistency, biometric matching degree, behavioral pattern matching degree, device hardware fingerprint, network environment fingerprint, cross-domain projection legitimacy, and dynamic trust score. When the predicted trust score of the 4th channel exceeds the threshold θ = 0.428571, the system outputs the predicted authentication result in advance, and corrects or confirms the result through the causal chain binding module after the verification of the subsequent 5th to 12th channels is completed.
5. The system according to claim 1, characterized in that, The generation process of the 428571 seven-dimensional code includes: Calculate the pure repeating decimal 0.142857142857… of 1 / 7, and extract the repeating block 142857; Perform a left-hand 4-bit phase rotation operation on the cycle block to obtain 428571; Using 428571 as the gene code for the causal chain identifier, and combining it with the denominator factor (10) of the mixed cyclic decimal identity token... 6 -1) A periodic resonance is formed, where 428571×3=142857×9=1285713, and 428571×0.0017=728.5707…, the integer part 728=2 3 ×7×13.
6. The system according to claim 1, characterized in that, It can be applied to high-reliability cross-domain proactive identity authentication, extreme environment command chain authentication, distributed resilient network node management, or industrial IoT device access control.