CrossKEY: 3D MR–iUS Registration & Cross-Layer Systems

• CrossKEY is a design idiom featuring a patient-specific 3D keypoint descriptor that aligns MRI to intraoperative ultrasound using deep learning and RANSAC refinement.
• It extends to cross-layer key systems that enhance passwordless authentication by synchronizing short-lived enrollment tokens without duplicating private keys.
• Additionally, CrossKEY underpins a hybrid quantum-enhanced key encapsulation method that integrates classical lattice cryptography with CHSH-based entanglement verification.

CrossKEY is used in recent research in two distinct but related ways. Most directly, it is the name of a patient-specific 3D cross-modal keypoint framework for matching and rigidly registering preoperative MRI to intraoperative ultrasound in neurosurgery. In a broader interpretive sense, the term has also been used to describe cross-layer and cross-device key systems that preserve a conventional cryptographic core while adding a second coordination or certification layer: one case distributes enrollment rights rather than WebAuthn private keys, and another couples Kyber with a CHSH-based quantum nonlocality test during key exchange (Morozov et al., 24 Jul 2025, Mitra et al., 2023, Cherkaoui et al., 15 Nov 2025).

1. Terminological scope and principal referents

In the current literature, the most explicit referent of CrossKEY is the framework introduced in "A 3D Cross-modal Keypoint Descriptor for MR-US Matching and Registration" (Morozov et al., 24 Jul 2025). There, CrossKEY denotes a 3D cross-modal keypoint detection and description pipeline for MRI–iUS correspondence estimation and rigid registration. The framework is built around patient-specific matching-by-synthesis, probabilistic keypoint detection, a 3D Siamese descriptor, and RANSAC-based rigid alignment.

In adjacent discussions, CrossKEY is also used as a conceptual shorthand for systems that coordinate heterogeneous layers without collapsing them into a single substrate. One such use appears in the interpretation of TUSH-Key, where a cross-device passwordless architecture keeps FIDO2/WebAuthn authentication unchanged while synchronizing short-lived enrollment capabilities instead of authenticator private keys (Mitra et al., 2023). Another appears in the interpretation of CHSH-enhanced Kyber, where a standard Module-LWE KEM is augmented by a CHSH nonlocality test on shared EPR pairs, yielding a hybrid, cross-layer key encapsulation framework with both computational and quantum-complexity-theoretic security anchors (Cherkaoui et al., 15 Nov 2025).

Context	CrossKEY meaning	Source
3D medical image computing	3D cross-modal keypoint descriptor for MR–iUS matching and rigid registration	(Morozov et al., 24 Jul 2025)
Passwordless authentication	Cross-device architecture that distributes enrollment rights, not WebAuthn private keys	(Mitra et al., 2023)
Hybrid post-quantum cryptography	Cross-layer KEM combining Kyber with CHSH-certified quantum verification	(Cherkaoui et al., 15 Nov 2025)

2. CrossKEY in MR–iUS matching and rigid registration

CrossKEY in its primary, named sense addresses intraoperative registration of real-time ultrasound to preoperative MRI in neurosurgery, where modality-specific appearance, resolution, and field-of-view differ sharply. The framework takes as input a preoperative 3D MR volume $I_{\text{MR}} \in \mathbb{R}^{\Omega}$ and an intraoperative 3D ultrasound volume $I_{\text{US}} \in \mathbb{R}^{\Omega}$, and outputs sparse but reliable cross-modal correspondences together with a rigid transformation aligning MRI to iUS. Its niche is explicitly a patient-specific, fully 3D, cross-modal keypoint descriptor tailored for MR–iUS, rather than a dense deformable registration model or a 2D matcher lifted to volumetric data (Morozov et al., 24 Jul 2025).

The pipeline has four components. First, synthetic iUS volumes are generated from the patient’s MR sequences using MMHVAE. For each non-empty subset of the available MR sequences and for each $\gamma \in \{0.3,0.5,0.7,1\}$, MMHVAE synthesizes a 3D iUS volume, producing

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$

Because these synthetic iUS volumes are co-registered with MRI, they provide exact location-wise positive pairs for supervised contrastive training.

Second, CrossKEY constructs a probabilistic cross-modal saliency map. SIFT3D is run on MRI and on each synthesized iUS volume. The resulting binary masks are aggregated into modality-specific heatmaps, smoothed with a 3D Gaussian with $\sigma = 2$, normalized to $[0,1]$, and fused by

$$P_{\text{comb}} = 1 - (1 - P_{\text{MR}})(1 - P_{\text{US}}).$$

An iUS field-of-view prior $M_w$, derived from distance to the FoV center of mass, modulates the fused map,

$P_{\text{res}} = P_{\text{comb}} \cdot M_w.$

Training keypoints are then sampled stochastically from $P_{\text{res}}$ under two explicit constraints: at least $I_{\text{US}} \in \mathbb{R}^{\Omega}$0 of the $I_{\text{US}} \in \mathbb{R}^{\Omega}$1 patch must lie inside the iUS FoV, and any two selected keypoints must satisfy $I_{\text{US}} \in \mathbb{R}^{\Omega}$2.

Third, a shared-weights 3D Siamese encoder $I_{\text{US}} \in \mathbb{R}^{\Omega}$3, implemented as a 3D ResNet-18, maps MR and synthetic iUS patches of size $I_{\text{US}} \in \mathbb{R}^{\Omega}$4 to L2-normalized descriptors,

$I_{\text{US}} \in \mathbb{R}^{\Omega}$5

Descriptor similarity is measured by squared Euclidean distance. Training uses a triplet loss

$I_{\text{US}} \in \mathbb{R}^{\Omega}$6

together with curriculum-based hard negative mining. At epoch $I_{\text{US}} \in \mathbb{R}^{\Omega}$7 out of warm-up $I_{\text{US}} \in \mathbb{R}^{\Omega}$8,

$I_{\text{US}} \in \mathbb{R}^{\Omega}$9

and the negative-selection score is

$\gamma \in \{0.3,0.5,0.7,1\}$0

with $\gamma \in \{0.3,0.5,0.7,1\}$1. The framework also uses curriculum rotation augmentation, with $\gamma \in \{0.3,0.5,0.7,1\}$2 increasing linearly from $\gamma \in \{0.3,0.5,0.7,1\}$3 to $\gamma \in \{0.3,0.5,0.7,1\}$4 over the first 1000 epochs.

Fourth, inference uses the learned saliency distribution in MRI and a uniform 3D grid with 4 mm spacing inside the real iUS FoV. Descriptor matching is performed by nearest neighbor search and Lowe’s ratio test,

$\gamma \in \{0.3,0.5,0.7,1\}$5

with $\gamma \in \{0.3,0.5,0.7,1\}$6 for CrossKEY. Sparse matches are converted into a rigid transformation by a 3-iteration RANSAC-based procedure with a 5 mm inlier threshold and up to 4000 iterations per stage.

Evaluation on 3D MRI–iUS pairs from ReMIND reports an average precision of $\gamma \in \{0.3,0.5,0.7,1\}$7, a matching score of $\gamma \in \{0.3,0.5,0.7,1\}$8, and $\gamma \in \{0.3,0.5,0.7,1\}$9 correct matches per case across 11 patients. On the ReMIND2Reg benchmark, the method achieves a mean Target Registration Error of $$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$0 mm, presented as $$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$1 mm in summary form. The method is described as interpretable, requiring no manual initialization, and showing robustness to iUS field-of-view variation. The authors also state that, to their knowledge, it is the first fully 3D learned keypoint descriptor specifically tailored to MR–iUS (Morozov et al., 24 Jul 2025).

3. CrossKEY as a model for cross-device passwordless key coordination

In passwordless authentication, CrossKEY is not the formal name of the protocol in the cited work, but TUSH-Key is explicitly presented as a blueprint for a CrossKEY-style architecture. The central design choice is to leave FIDO2/WebAuthn unchanged for actual relying-party authentication while avoiding synchronization of authenticator private keys. Each device still generates its own WebAuthn key pair locally, stores the private key in TPM, TEE, or equivalent secure hardware, and registers only the public key with the relying party. Cross-device portability is obtained by transferring short-lived access tokens that authorize additional device enrollment, rather than cloning $$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$2 across devices (Mitra et al., 2023).

The system consists of client devices running a TUSH-Key Daemon, standard FIDO2 authenticators, a relying-party server extended to issue access tokens, and a TUSH-Key Server that stores only device metadata, Diffie–Hellman public keys, and encrypted access tokens. Device registration binds a user identity obtained through Microsoft SSO/OAuth2, a UUIDv4 device identifier, and a DH key pair

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$3

For synchronization, a sender device authenticates normally with WebAuthn, requests an RP-issued access token, retrieves the list of sibling devices from the TUSH-Key Server, computes a shared secret for each receiver,

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$4

and encrypts the token under AES-128-CBC in a Fernet-based implementation,

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$5

Each receiver polls the server, retrieves its ciphertext and the sender’s DH public key, recomputes

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$6

decrypts the token, and then performs a standard WebAuthn registration, generating a fresh local credential

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$7

This architecture is significant for CrossKEY-style reasoning because the cryptographic identity becomes multi-device without multi-device secret cloning. The paper explicitly contrasts this with passkeys, which synchronize private keys or symmetric-wrapped equivalents through proprietary clouds and are described as conflicting with the NIST SP 800-63B requirement that multi-factor cryptographic authenticators shall not facilitate cloning of the secret key onto multiple devices. In the prototype, the TUSH-Key protocol is modeled in HLPSL and analyzed with AVISPA using the OFMC and CL-AtSe backends, both of which report the protocol as SAFE under the assumed Dolev–Yao adversary. The measured average sync time is 447 ms, average WebAuthn enrollment time is 580 ms, and combined auto-enrollment is approximately 1 second. The prototype supports Windows and Android, with future extension to iOS/iPadOS noted as planned (Mitra et al., 2023).

4. CrossKEY as a model for hybrid quantum-enhanced key encapsulation

A second conceptual use of CrossKEY appears in the interpretation of CHSH-enhanced Kyber, where the term denotes a hybrid, cross-layer key encapsulation framework. The construction preserves the algebraic structure of CRYSTALS-Kyber and compatibility with the Fujisaki–Okamoto transform, but embeds a CHSH nonlocality test into the key exchange phase. The resulting protocol combines classical lattice hardness with a physical entanglement-verification layer, so that an adversary breaking the KEM must either solve Module-LWE or solve a QMA-complete 2-local Hamiltonian instance under the paper’s stated complexity assumption $$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$8 (Cherkaoui et al., 15 Nov 2025).

The classical backbone is standard Kyber. Key generation samples

$$\mathcal{D}_{\text{synUS}} := \left\{ I^{(k)}_{\text{synUS}} \right\}_{k = 1}^{4 \times (2^K - 1)}.$$9

and computes

$\sigma = 2$0

The paper also models state evolution as a Markov chain over

$\sigma = 2$1

with

$\sigma = 2$2

The quantum layer distributes $\sigma = 2$3 EPR pairs,

$\sigma = 2$4

and measures them in CHSH settings. For round $\sigma = 2$5, Alice chooses $\sigma = 2$6, Bob chooses $\sigma = 2$7, and outcomes $\sigma = 2$8 yield

$\sigma = 2$9

The standard CHSH expression is

$[0,1]$0

The classical bound is $[0,1]$1, corresponding to $[0,1]$2, whereas the quantum Tsirelson bound is $[0,1]$3, corresponding to $[0,1]$4. The paper states that observing $[0,1]$5 constitutes irrefutable evidence of genuine quantum entanglement, and that honest quantum behavior satisfies

$[0,1]$6

with Chernoff–Hoeffding concentration giving negligible soundness error for polynomial $[0,1]$7.

The CHSH layer is coupled to Kyber in two ways. As a certification mechanism, failure of the CHSH test aborts the session. As an entropy mechanism, the modulation factor

$[0,1]$8

is used conceptually to modulate the effective LWE noise, yielding

$[0,1]$9

The paper maps the CHSH game to the 2-local Hamiltonian problem through

$$P_{\text{comb}} = 1 - (1 - P_{\text{MR}})(1 - P_{\text{US}}).$$0

with the associated decision problem stated as QMA-complete.

Within the FO-based CCA framework, the advantage bound is

$$P_{\text{comb}} = 1 - (1 - P_{\text{MR}})(1 - P_{\text{US}}).$$1

The paper presents parameter examples for Kyber-512, Kyber-768, and Kyber-1024, with corresponding “+CHSH” effective security bits of 162.7, 241.1, and 325.3, and a reported session latency of 1.05–3.2 ms, described as less than 5% overhead relative to the classical baseline. In this interpretation, CrossKEY denotes a single protocol spanning classical lattice cryptography, quantum nonlocality, and complexity-theoretic reductions (Cherkaoui et al., 15 Nov 2025).

5. Structural commonalities across the different uses

Taken together, these usages suggest a common structural pattern. CrossKEY, in this broader sense, refers to systems that preserve a standard core mechanism while adding a second layer that crosses a boundary otherwise left unaddressed by the baseline. In the medical-imaging case, the conventional component is sparse rigid registration, while the crossing mechanism is patient-specific synthesis and cross-modal descriptor learning. In TUSH-Key, the conventional component is ordinary WebAuthn authentication, while the crossing mechanism is end-to-end encrypted synchronization of enrollment rights. In CHSH-enhanced Kyber, the conventional component is the Module-LWE KEM with FO transform, while the crossing mechanism is entanglement verification via CHSH.

This suggests that CrossKEY is best understood not as a single algorithmic family but as a design idiom. The idiom is conservative at the core and heterogeneity-embracing at the boundary. The core is left “as-is” or “essentially intact,” while the added layer addresses a missing form of portability, certification, or correspondence: MRI to iUS in one case, device to device in another, and computational hardness to physical nonlocality in a third (Morozov et al., 24 Jul 2025, Mitra et al., 2023, Cherkaoui et al., 15 Nov 2025).

A plausible implication is that the term is most useful where a system must bridge incompatible representations without replacing the trusted substrate already deployed. The imaging framework does not abandon rigid registration; it makes sparse correspondences more reliable. TUSH-Key does not replace FIDO2; it changes onboarding semantics. CHSH-enhanced Kyber does not replace Kyber or FO; it overlays a quantum witness and a second hardness axis. That commonality is interpretive rather than canonical, but it is strongly supported by the way the cited works are framed.

6. Limitations, caveats, and open directions

The named CrossKEY framework in MR–iUS registration is explicitly patient-specific and currently rigid. Training is performed separately for each patient, with about 5 hours of preoperative offline training, and the reported registration stage uses only rigid transformations despite the presence of brain shift and post-resection deformation. The paper suggests combining its sparse correspondences with biomechanical models or deformable B-spline frameworks for fuller compensation of non-rigid effects, and also notes dependence on the quality and diversity of synthetic iUS generation (Morozov et al., 24 Jul 2025).

The TUSH-Key blueprint for CrossKEY-style passwordless systems has a different limitation profile. The prototype supports Windows and Android, with iOS/iPadOS left as future work. Automatic sync depends on TUSH-Key Server availability, requires a daemon on each device, and stores the device DH keys on disk rather than in the WebAuthn authenticator boundary. The paper also states that backup and recovery semantics are not fully specified, particularly for the case where all devices are lost and for future cryptographic agility beyond classical Diffie–Hellman (Mitra et al., 2023).

The CHSH-enhanced Kyber interpretation carries the strongest theoretical claims but also the heaviest infrastructural assumptions. It requires entanglement distribution, CHSH measurement hardware, and a quantum link between endpoints. The security proofs are game-based rather than UC-style, the paper itself notes that no full UC composition is given, and the integration of CHSH-derived outcomes into effective LWE noise is argued conceptually through variance broadening rather than through a separate information-theoretic secrecy reduction. The headline reduction is also phrased under the unusual assumption $$P_{\text{comb}} = 1 - (1 - P_{\text{MR}})(1 - P_{\text{US}}).$$2, which is part of the paper’s positioning and not a standard cryptographic assumption (Cherkaoui et al., 15 Nov 2025).

Across all three usages, the open problem is not merely improving the underlying primitive but specifying how a boundary-crossing layer should compose with established systems. In imaging, that means composition with deformable models and broader modality pairs. In passwordless authentication, it means standardization of token issuance, device registration, and recovery. In hybrid post-quantum cryptography, it means sharper composition theorems and realistic deployment models for quantum-assisted endpoints.