Geo-Enabled Cryptographic Key Oracle (GECKO)

• GECKO is a cryptographic framework that binds digital assets and credentials to precise physical regions, enabling secure location-based authorization.
• It integrates public-key infrastructures, symmetric-key oracles, and UWB timing protocols to support scalable, efficient spatial queries and verifiable mappings.
• Its design mitigates fraud and spoofing by enforcing spatially-bounded key distribution, making it ideal for applications like IoT, UAVs, and smart cities.

The Geo-Enabled Cryptographic Key Oracle (GECKO) is a class of cryptographic architectures and services that cryptographically bind digital assets, authorization credentials, or decryption capabilities to specific physical spatial regions. GECKO achieves location-dependent access enforcement, bidirectional mapping between physical space and digital identity, and spatially-bounded key distribution under varying operational, adversarial, and resource-constrained conditions. GECKO systems span high-assurance public-key infrastructures integrating with the global Web PKI, time/space-limited symmetric-key oracles for asset authorization in disconnected settings, and precise location-dependent keying mechanisms using ultra-wideband (UWB) radio time-of-flight quantization. The GECKO design unifies spatial cryptography, verifiable mapping of digital credentials to real-world locations, and secure, efficient, and scalable enforcement of trust relationships with rigorous cryptographic guarantees (Krähenbühl et al., 27 Nov 2025, Téglásy et al., 2022, Mukherjee, 18 Nov 2025).

1. Security Objectives and Bidirectional Trust Translation

GECKO’s principal security objective is to bind digital assets (e.g., TLS certificates, document signatures, payment credentials) to explicit physical spaces in a cryptographically verifiable and transparent manner (Krähenbühl et al., 27 Nov 2025). This mapping enables two critical modalities:

• Physical→Digital translation: A party at physical location $L$ can retrieve and verify all digital identities (e.g., certificates, URIs) asserting legitimate claims to the space enclosing $L$.
• Digital→Physical translation: Given a digital identity (domain, asset identifier), any party can unambiguously enumerate and verify the physical spaces claimed by that identifier.

This cryptographic coupling enables detection and prevention of fraud tied to location (e.g., counterfeit points of sale, fake Wi-Fi access points, real estate imposter attacks). The GECKO architecture upholds backward compatibility with established PKI mechanisms, offers scalable, low-latency spatial queries, and supports a threat model in which adversaries can compromise CA/log/map servers but cannot defeat the correctness of the location-verification oracle or the cryptographic soundness of GECKO’s spatial-credential bindings (Krähenbühl et al., 27 Nov 2025).

2. System Architectures and Implementation Variants

GECKO’s architecture is domain-specific and modular, supporting deployments ranging from global, public CA-backed PKIs to resource-constrained, symmetric-key-based oracles for maritime or IoT assets.

2.1 Geo-PKI for Digital Assets

• GeoCerts: Certificates binding a digital identifier (URI/domain) to a spatial frustum—a 3D geometric volume defined by a WGS84 polygon extruded over an altitude interval (Krähenbühl et al., 27 Nov 2025).
• Actors: Space owners, Geo CAs (certificate authorities), Geo Log servers (append-only transparency), Map servers (spatial/domain index), and relying clients.
• Workflows: Owners initiate signing requests specifying spatial claims. CAs vet claims and issue GeoCerts, which are logged with transparency using Merkle tree log structures and indexed by Map servers for high-performance lookups.
• Deployment Models: GECKO supplements the Web PKI as X.509 extensions, or operates as a standalone GeoPKI with independent trust roots.

2.2 Symmetric-Key Oracles for Disconnected or Low-Bandwidth Environments

• Key Derivation: Keys are derived as $$K_{(C,T)} = RC5.Enc_{MK}^{r,w} (\mathrm{Pad}_{2w}(M))$$ where $M$ is an encoding of geocell $C$ (via Open Location Code) and time interval $T$, and $MK$ is a 2040-bit master key (Téglásy et al., 2022).
• Authorization granularity: Keys are cryptographically bound to discrete geocells (e.g., 5.5 km OLC cells) and time intervals. Each asset stores only keys for which it is authorized and can prove this with challenge-response MACs over an acoustic or low-bandwidth physical layer.
• Operational Flow: Keys are pre-distributed (e.g., via TLS when surfaced), minimizing underwater/remote comms. The protocol resists spoofing and replay via nonces, narrow key scope, and short rekey intervals (Téglásy et al., 2022).

2.3 Location-Dependent Key Transmission via UWB Timing

• JMTK Protocol: An AES-256 key (after SHA-256 hashing) is implicitly encoded into a sequence of UWB packet transmission timing offsets. Legitimate receivers within a well-defined spatial region reconstruct the key from inter-packet arrival intervals (Mukherjee, 18 Nov 2025).
• Spatial Enforcement: Only listeners in the authorized region observe the correct timing pattern; those outside experience quantization errors, guaranteeing erroneous key recovery.
• Realization: High-resolution timing hardware (e.g., Ciholas DWETH101, <8ns error) and precise flight-time compensation yield spatial tolerance on the order of centimeters.

3. Spatial Data Structures, Indexing, and Proofs

GECKO leverages advanced spatial indexing to efficiently represent and authenticate the mapping between digital identities and physical regions.

• Sparse Merkle Trees (SMT): Map servers maintain a global 3D SMT; leaves correspond to 1 meter horizontal × 1 meter vertical resolution. Each node stores a Merkle commitment to the set of GeoCerts within its volume (Krähenbühl et al., 27 Nov 2025).
• Spatial Querying: Arbitrary query volumes $V$ are over-approximated by a minimal set of prefix nodes $(n_{xy}, n_z)$. Map servers return proofs of presence or absence (PoP/PoA), consisting of relevant GeoCerts, SMT hash paths, and server signatures.
• Verification: Clients reconstruct hash paths, verify the signed map head (SMH), check GeoCert validity, and apply complex trust preferences, e.g., ignoring GeoCerts from CAs with lower trust-levels if higher-trust certificates cover the same space.

Table: GECKO Data Structures

Component	Structure	Precision
GeoCert spatial frustum	Polygon + altitude range	Meter-level (WGS84)
SMT node (surface+alt)	(n_xy, n_z) prefixes	1m × 1m × 1m
Key oracle geocell	Open Location Code (OLC)	5.5 km cell-side

These structures enable global, efficient, and cryptographically auditable mapping between assets and volumes.

4. Cryptographic Protocols, Key Management, and Authorization

GECKO relies on robust, auditable protocols for certificate issuance, key distribution, and query authentication.

• GeoCert Protocol: Space owners submit Certificate Signing Requests (CSRs) with spatial metadata. Geo CAs issue and log certificates, which map servers ingest and Merkle-commit under the signed map head (Krähenbühl et al., 27 Nov 2025). GeoCerts are X.509 extensions or standalone, and are chained to guarantee child spatial subsets always fall under ancestor volumes.
• Symmetric Key Oracle Protocol: Keys $K_{(C,T)}$ are generated from the master key for fine-grained (cell, time) pairs. Underwater or remote assets authenticate possession through MAC-based challenge-response. Master key protection uses threshold secret sharing (e.g., (11, 6) Shamir scheme). The key oracle resists brute-force (keyspace $2^{2040}$), replay, and GPS spoofing (Téglásy et al., 2022).
• Location-Dependent Key Recovery: The JMTK protocol’s transmission times $(t_0, ..., t_{32})$ are computed by $f(H)$, incorporating per-anchor flight-time offsets. Decoding at the receiver’s location involves extracting gaps, quantizing to slots, and reconstructing the hash sequentially. Error correction (e.g., Hamming code) and CRC validation enhance robustness (Mukherjee, 18 Nov 2025).

5. Security Analysis, Threat Models, and Mitigations

The GECKO security model addresses threats across network, measurement, and key compromise dimensions.

• Transparency and Auditability: All GeoCerts are logged transparently using Merkle append-only logs (STH/SMH) and are subject to third-party SCT gossip to detect equivocation or omission (Krähenbühl et al., 27 Nov 2025).
• Split-view Attacks: Map servers must produce consistent SMHs; signed states and proof-gossip ensure attack detection.
• Authorization Verification: Clients discard lower-trust GeoCerts in favor of higher-trust conflicting certificates, as defined by explicit trust-preference policies. Each GeoCert includes an explicit location-validation attribute (e.g., “in-person-EV”, “mail-PUK”) supporting fine-grained client validation and downgrade-prevention.
• Spatial Key Oracles: Eavesdroppers on the physical layer cannot derive the keys without possession of correct keying material or spatial presence; distinct keys per cell and time interval quash misuse in adjacent regions or times (Téglásy et al., 2022).
• UWB Timing Approach: Without secret per-region anchor distances, passive adversaries cannot recover the key from packet captures; legitimate recovery works only inside a spatial ball of radius $R$, outside which timing errors exceed $T_{\text{slot}}/2$ per-byte (Mukherjee, 18 Nov 2025).

6. Performance Evaluation and Scalability

GECKO demonstrates high scalability, low computational overhead, and practical feasibility across its different architectural instantiations.

• Spatial Indexing: The 3D SMT supports sub-meter global resolution. With ≈1.7 million GeoCerts, map servers service >19,000 spatial queries per second (median response ≤11 ms), and scale via geographic/domain sharding (Krähenbühl et al., 27 Nov 2025). Maximum global coverage is estimated at ≈330 million GeoCerts.
• Client Verification: Proof sizes are modest (few kB), SMT verification median ~1 ms, and bandwidth costs negligible even for mobile clients.
• Symmetric Key Oracle: Storage for complete global coverage (≈26 million keys) is <500 MB; typical real-world assets store only a few MB for authorized regions. Key challenge/response underwater achieves round-trip of milliseconds on microcontrollers, with acoustic link dominating latency/energy costs (Téglásy et al., 2022).
• UWB Key Oracle: Full key-oracle transmission is completed in ≈100 ms. End-to-end latency for first decrypted byte <150 ms, and throughput for encrypted data transmission reaches ≈320 kB/s. Hardware is compact and commodity-priced ($\sim$US$2,000$, <1U) (Mukherjee, 18 Nov 2025).

7. Extensions, Generalizations, and Integration

GECKO generalizes location-bound authorization and asset identity across environments:

• Terrestrial IoT, UAVs, and Smart Cities: Substitution of OLC/cell-grid encodings enables fine-grained key-bound authorization for distributed IoT and aerial assets (Téglásy et al., 2022).
• Web PKI and Standardization: GECKO’s approach is backward-compatible; GeoCert fields can be ignored by legacy clients, while advanced agents enforce geo-authority policies. PKI integration spans extension of X.509 to stand-alone GeoPKI models (Krähenbühl et al., 27 Nov 2025).
• Multi-party/Threshold Authorization: Future variants propose secret-sharing keys across multiple region centers, enforcing collaborative spatial presence (e.g., threshold decryption).
• Rolling Keys and Continuous Attestation: Dynamic challenge–response interleaving, with region-stable rolling keys, can maintain persistent session-level attestation without re-key negotiation (Mukherjee, 18 Nov 2025).
• General Attribute-based Encryption: The pattern of "encode attributes, encrypt under master key, derive per-attribute keys" applies broadly to attribute-based and policy-driven cryptography in cyber-physical systems (Téglásy et al., 2022).

GECKO, as formalized in (Krähenbühl et al., 27 Nov 2025, Téglásy et al., 2022), and (Mukherjee, 18 Nov 2025), presents a set of cryptographic tools and rigorously specified mechanisms for binding, distributing, and verifying digital trust on the basis of geographic space, with robust performance, resilience to a broad class of attacks, and extensibility to diverse real-world settings.