ODKE+: Multi-Field Technical Protocols

• ODKE+ is a designation for distinct technical systems, including ontology-guided LLM knowledge extraction, optical key exchange using IM/DD, and onion-routed quantum-resilient key establishment.
• It employs layered modular designs with hybrid methods—combining pattern rules with LLM prompts and rigorous cryptographic parameterization—to optimize precision and security.
• ODKE+ systems have demonstrated practical success by refreshing large-scale knowledge graphs, ensuring physical layer security in optical channels, and securing sessions through distributed, anonymized key fragments.

ODKE+ designates several unrelated but highly technical protocols and systems across distinct fields. The ODKE+ designation has appeared in: (1) ontology-guided LLM-based knowledge extraction pipelines for knowledge graphs, (2) optical direct key exchange protocols using binary intensity modulation and direct detection under eavesdropping, and (3) onion-routed, multi-circuit key establishment protocols for quantum-resilient session security. Each instantiation is detailed independently below, anchored in the published literature and experimental deployments.

1. Ontology-Guided Open-Domain Knowledge Extraction with LLMs

ODKE+ as presented in "Ontology-Guided Open-Domain Knowledge Extraction with LLMs" (Khorshidi et al., 4 Sep 2025) specifies a modular production-scale system for the high-precision extraction and ingestion of open-domain facts from web sources—primarily Wikipedia—into large-scale knowledge graphs (KGs). The primary objective is to maintain KG completeness and temporal freshness through automated workflows, minimizing human curation costs and ensuring schema consistency across a broad predicate space.

Pipeline Architecture

ODKE+ integrates five sequential modules:

1. Extraction Initiator: Continuously monitors for entity page creations or updates and compares KG state ($KG_t$) versus newly surfaced facts ($Web_{t'}$) to detect both "missing" ($$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$) and stale facts (where $\langle e,p,o_{\text{old}} \rangle$ is superseded by $o_{\text{new}}$).
2. Evidence Retriever: Fetches full text or structured snippets for flagged entities from a web crawl index; canonicalizes entity-to-URL mapping.
3. Hybrid Knowledge Extractors:
   • Pattern-based: Deploys high-precision, field-aligned extraction rules against semi-structured tables (e.g., infoboxes), comprising a Predicate Mapper, Value Extractor (regex/unit handling), and Aggregator.
   • LLM-based with Ontology-Guided Prompting: Constructs contextually pruned "ontology snippets" per entity type $t$, listing top-K predicates (ranked by $$S(p,t) = \text{freq}_{kg}(p|t) / \max_{p'} \text{freq}_{kg}(p'|t)$$), canonical descriptions, qualifiers ($Q_p$), normalization requirements, and allowable units ($U_p$). The snippet, combined with page context, forms a constrained JSON extraction prompt for the LLM.
4. Grounder: Validates candidate triples by querying a lightweight LLM in a factual-checking regime: for each assertion generated, it outputs "Yes" only if the supporting evidence is explicit in the source context.
5. Corroborator: Normalizes extracted values, aggregates candidates per $\langle e,p \rangle$, deduplicates, and applies a linear or AutoML-derived ranking function based on a feature vector $Web_{t'}$0 (extractor type, model/rule confidence, document frequency, qualifier richness).

Prompt Construction and Schema Guidance

Ontology-guided snippets are computed offline from KG schema and metadata, producing token-limited JSON fragments (predicate, description, qualifiers, normalization rules) tailored per type. LLM extraction prompts explicitly list allowed schema fields and instruct for exact-match, non-inferential, and non-hallucinatory extraction. The grounder employs minimalistic natural language assertions for efficient, low-latency support verification.

Metrics and Results

• Production metrics: 19M high-confidence facts extracted, 195 predicates supported, 4M entity pages processed.
• Precision: 98.8% (weekly human QA), with raw LLM output at 91% pre-corroboration.
• Coverage gain: +10% answerable facts versus legacy, 48% predicate overlap with third-party KGs.
• Update lag: Average KG update latency reduced by 50 days.
• Operational modes: Batch (full re-crawl), and streaming (real-time entity edits, 150–250K new facts/day, <2h latency).
• Empirical findings: Post-grounding, hallucinations reduced by 35%. LLM-based methods are essential for full predicate coverage (>195), whereas pattern rules suffice for a small infobox subset.

Summary Table: ODKE+ Knowledge Extraction Pipeline

Module	Primary Function	Key Feature
Extraction Initiator	Detects missing/stale facts	KG-page diffing
Evidence Retriever	Collects canonicalized source documents	Deterministic URLs
Knowledge Extractors	Extracts candidate facts; hybridized LLM/pattern	Schema-constrained prompts
Grounder	Validates factual support with secondary LLM	Hallucination filtering
Corroborator	Ranks, normalizes, and exports triples	Linear/AutoML scoring

2. Optical Direct Key Exchange Plus Protocol

In the cryptographic context, ODKE+ denotes "Optical Direct Key Exchange Plus," an intensity-modulation/direct-detection (IM/DD) protocol operating over optical channels, specifically optimized under passive eavesdropping models (Banaszek et al., 2021). This protocol is a variant of classical key distribution using binary optical intensities and statistical security against an eavesdropper limited only by shot noise and device parameters.

Protocol Model

• Transmitter (Alice): Encodes bits as optical pulses with mean photon numbers $Web_{t'}$1, uniform random bit selection.
• Channel splitting: Bob receives fraction $Web_{t'}$2; eavesdropper (Eve) intercepts $Web_{t'}$3 (beam-splitter model), $Web_{t'}$4.
• Detection: Both legitimate and adversarial receivers implement direct detection with additive Gaussian noise ($Web_{t'}$5, $Web_{t'}$6).

Secret-Key Rate Analysis

The key rate per slot is

$Web_{t'}$7

where:

• $Web_{t'}$8: non-erasure probability,
• $Web_{t'}$9: Bob’s bit error rate,
• $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$0: binary entropy,
• $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$1: Eve's mutual information on Bob’s bit,
• $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$2: reconciliation efficiency.

Eve's information is computed via

$$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$3

with $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$4 the normalized Gaussian density, and normalized modulation depths $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$5, $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$6.

In the strong-splitting limit ($$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$7), the rate simplifies to

$$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$8

where $$M = \{ \langle e,p,o \rangle \in Web_{t'} \setminus KG_t \}$$9.

Design Guidance

• Modulation depth: $\langle e,p,o_{\text{old}} \rangle$0
• Hard-decision thresholds: $\langle e,p,o_{\text{old}} \rangle$1, $\langle e,p,o_{\text{old}} \rangle$2

System parameters are calibrated in real-time based on measured channel conditions ($\langle e,p,o_{\text{old}} \rangle$3, $\langle e,p,o_{\text{old}} \rangle$4) and pre-tabulated optimal $\langle e,p,o_{\text{old}} \rangle$5 pairs for given reconciliation efficiencies. This approach guarantees key rate maximization against passive, quantum-unbounded adversaries attuned only by physical noise constraints.

3. Onion-Routed Multi-Circuit Key Establishment for Quantum-Resilient Sessions

A third protocol labeled ODKE+ is specified in "Onion-Routed Multi-Circuit Key Establishment for Quantum-Resilient Sessions" (Mallick et al., 20 May 2026). Here, ODKE+ targets the "harvest-now, decrypt-later" (HNDL) threat from future cryptographically relevant quantum computers. It achieves session key confidentiality and unlinkability by partitioning a session key into $\langle e,p,o_{\text{old}} \rangle$6 cryptographically protected fragments, which are then independently transmitted over $\langle e,p,o_{\text{old}} \rangle$7 Tor circuits, each established using the NEWNYM Tor control signal.

Threat Model

• Adversary $\langle e,p,o_{\text{old}} \rangle$8: Archives all ciphertext and can eventually break classical public-key encryption. Controls a fraction $\langle e,p,o_{\text{old}} \rangle$9 of the Tor relay set ($o_{\text{new}}$0 total relays) but not all.
• Anonymity property: $o_{\text{new}}$1's probability of linking all $o_{\text{new}}$2 fragments for a single session decays as $o_{\text{new}}$3, under the assumption of (quasi-)independent circuit selection.

Protocol Steps

• Session tag and key parameters are agreed out-of-band.
• The client requests a session key (256–768 bits typical), specifying number of fragments $o_{\text{new}}$4, from the Key Management Service (QKMS), via a Tor-based onion service proxy.
• QKMS splits the session key, optionally shuffles fragments, encrypts each with the client’s key (RSA-2048 or a hybrid KEM), and distributes fragments to the proxy’s channels.
• For each bundle/chunk of fragments, proxies trigger a new Tor circuit (SIGNAL NEWNYM), wait for stabilization, then POST to the client’s hidden service endpoint.
• Client reconstructs the session key after all $o_{\text{new}}$5 encrypted fragments are received and decrypted.

Pseudocode is provided for all roles (QKMS, proxy, client) in the protocol (Mallick et al., 20 May 2026).

Security Analysis

• Per onion circuit, end-to-end correlation probability is approximately $o_{\text{new}}$6.
• For $o_{\text{new}}$7 independent circuits, adversary's success probability is $o_{\text{new}}$8.
• With $o_{\text{new}}$9 and $t$0, this implies $t$1 circuit correlations, effectively ensuring unlinkability between the key and the associated session.

Parameterization and Performance

• Number of fragments ($t$2): Security rises exponentially with $t$3; latency increases linearly (Tor circuit build and stabilization dominate: per-circuit 0.5–1.5s typical).
• Encryption: RSA-2048 or hybrid KEM per fragment; AES-GCM for data after establishment.
• Measured prototype: 13–20s end-to-end latency (n=10), with ≈88% Tor-overhead; cryptographic processing ≈12%; per-fragment decryption cost 0.18–0.21s.
• Trade-off: High anonymity suitable for non-interactive, high-confidentiality session setup with multi-year security requirements.

Parameter	Security Impact	Latency Impact
$t$4 (fragments)	Anonymity $t$5 (exp.)	Linear in $t$6
$t$7 (key length)	Fragment size adjustment	Crypto cost per frag.
Fragment encryption	PQ-resilience (hybrid KEM)	Extra per-fragment ops

4. Core Insights and Lessons Learned

Across these diverse ODKE+ instantiations, the following principles underpin their effectiveness:

• Layered, modular design enhances both adaptability and production viability, whether for LLM-centric pipelines or distributed cryptographic protocols.
• Schema and context anchoring (in LLM-based extraction and PG KEM selection) delivers both precision and resilience to adversarial or unstructured input.
• Hybridization (pattern rules plus ML/LLM for extraction, PQ + classical for encryption) leverages complementary strengths, expanding coverage while containing operational costs and error rates.
• Parameter tuning—whether for key establishment anonymity (via $t$8) or optical modulation (via $t$9, $$S(p,t) = \text{freq}_{kg}(p|t) / \max_{p'} \text{freq}_{kg}(p'|t)$$0)—enables systems to dynamically optimize under real-world latency, resource, or security constraints.
• Verification and corroboration modules systematically reduce error rates (hallucinations, false positives) to practical thresholds for deployment.

5. Practical Applications and Impact

In KG construction, ODKE+ has demonstrated production-scale capacity to refresh knowledge graphs with millions of high-confidence, schema-compliant facts, substantially reducing update lag and boosting real-world task coverage (Khorshidi et al., 4 Sep 2025). In cryptography, ODKE+ protocols deliver sound, quantifiable security either rooted in physical channel statistics (optical, shot-noise-limited settings (Banaszek et al., 2021)) or in composite anonymity via network fragmentation and post-quantum cryptography (Tor-based sessions (Mallick et al., 20 May 2026)). These results indicate broad applicability where trustworthiness, interpretability, and adversarial robustness are core operational requirements.