aCAPTCHA: Verifying That an Entity Is a Capable Agent via Asymmetric Hardness
Organizations: Nankai University · Tsinghua University
Abstract
As autonomous AI agents increasingly populate the Internet, a novel security challenge arises: "Is this entity an AI agent?" It is a new entity-type verification problem with no established solution. We formalize the problem through a three-class entity taxonomy (Human, Script, Agent) based on a verifiable agentic capability vector <x, r, s> (action, reasoning, and memory). A timing threshold t exploits the asymmetric hardness between human cognition and AI processing to separate the three classes. We define the Agentic Capability Verification Problem (ACVP) through three necessity primitives, each testing one capability dimension. Building on this foundation, we introduce aCAPTCHA (Agent CAPTCHA), a time-constrained security game for agent admission whose security rests on ACVP hardness under t. We instantiate aCAPTCHA through time-bounded natural-language understanding as a multi-round HTTP verification protocol, and evaluate it with preliminary agent trials that validate the protocol's soundness and completeness. aCAPTCHA provides a composable, infrastructure-free admission gate for any service where entity-type verification is required.
Figures & tables
| Mechanism | What it verifies |
| OAuth / mTLS / API Key | Credential possession |
| WebAuthn | Channel + credential binding |
| DID / VC | Decentralized credential possession |
| CAPTCHA | Requester is human (cognitive challenge) |
| reCAPTCHA v3 | Behavioral risk score (anomaly detection) |
| MAS / IoA 1 | Controlled-environment participation |
| Dimension | Human | LLM Agent |
| Text ingestion | 238 wpm 1 silent reading ( Brysbaert, 2019 ) ( 5 tps 3 ) | Entire context window in one prefill pass ( 1 s) |
| Comprehension ceiling | 300 wpm with full comprehension ( Carver, 1992 ) | Quality independent of speed |
| Working memory | 3–5 chunks 2 ( Cowan, 2001 ) | Full context window (128 k–1 M tokens) |
| Choice reaction time | 350–384 ms per decision ( Pashler, 1994 ) | Single forward pass ( 500 ms) |
| Decision scaling | +150 ms/bit (Hick’s law) ( Hick, 1952 ) | Constant (parallel attention) ( Vaswani et al., 2017 ) |
| Text output | 40 wpm typing ( Dhakal et al., 2018 ) | 50–200 tps ( 2 k–9 k wpm) |
| Parameter | Description | Controls |
| Per-round timing budget | Human exclusion | |
| Safety margin ( ) | Threshold strictness | |
| Session timeout | Max session duration | |
| Narrative length (tokens) | Separation gap | |
| Number of domains | Domain diversity | |
| Narrative sets per domain | Corpus size |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| ID | Domain | FORD | Description | Entity Examples | Reasoning Patterns |
| biochemistry | Biochemistry | 1. Natural Sci. | Enzyme kinetics, assay results, inhibitor profiles, metabolic pathways | Enzymes, compounds, metabolic intermediates, receptor subtypes | Kinetic anomaly persistence, inhibition mechanism attribution, replicate confirmation |
| cybersecurity | Cybersecurity | 2. Eng. & Tech. | Threat intelligence, vulnerability analysis, incident response, network forensics | CVEs, IP addresses, malware families, attack vectors, threat actors | Attack attribution, false positive elimination, lateral movement tracing |
| clinical_trials | Clinical Trials | 3. Medical | Drug efficacy, adverse events, patient cohorts, endpoint analysis | Drug candidates, adverse events, patient subgroups, biomarkers | Efficacy signal vs. confounding, adverse event attribution, subgroup analysis |
| food_safety | Food Safety | 4. Agricultural | Contaminant screening, microbiological testing, batch traceability, regulatory compliance | Pathogens, chemical residues, food batches, testing methods, tolerance limits | Contamination source tracing, threshold exceedance attribution, cross-batch comparison |
| financial_markets | Financial Markets | 5. Social Sci. | Macroeconomic indicators, equity indices, yield curves, credit spreads | Economic indicators, funds, currency pairs, sector indices | Sustained deviation vs. noise, trend reversal attribution, cross-market correlation |
LLM Agent Verification
LLM agent verification checks whether agents’ actions, evidence, policies, and completion claims satisfy explicit requirements.
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