Universal Share-Based Quantum Multi-Secret Sharing

• The paper introduces a universal share-based quantum multi-secret sharing scheme that reuses a common quantum share (UniShare) with individual secret shares to recover binary image secrets with perfect secrecy.
• It employs simple quantum operations like Hadamard, X, and CNOT gates to encode binary images without pixel expansion, achieving lossless reconstruction with metrics such as PSNR → ∞ and SSIM = 1.00.
• The protocol is designed to counteract quantum eavesdropping by ensuring that any unauthorized share, even when combined with others (excluding the UniShare), reveals no information about the secret images.

Searching arXiv for the cited work and closely related quantum multi-secret sharing papers. Universal share-based quantum multi-secret sharing denotes a class of quantum secret-sharing constructions in which a common share is reused across multiple secrets, so that recovery of a designated secret requires combining that secret’s individual share with the common component rather than assembling all shares simultaneously. In the image-oriented formulation introduced in “Universal share based quantum multi secret image sharing scheme” (Rabari et al., 16 Sep 2025), the setting consists of a dealer, $n$ authorized players, and a special principal authority who alone holds the Universal-share (UniShare); the secret is a set of $n$ binary images $G_1,\dots,G_n$ of size $M\times N$ pixels; and the protocol is an $(n,n+1)$ Universal-share-based Quantum Visual Multi-Secret Sharing (QVMSS) scheme. The stated goals are perfect secrecy, lossless recovery, and resistance to quantum eavesdropping, with reconstruction of any one secret image $G_k$ requiring exactly two shares—$S_k$ plus $U$—and no pixel expansion (Rabari et al., 16 Sep 2025). Related work situates this construction within a broader landscape of universal or share-based quantum multi-secret sharing based on cluster states, monotone span programs, GHZ states, and general quantum access structures (Ma et al., 14 May 2025, Rathi et al., 2023, Luo et al., 2023, Bassirian et al., 2018).

1. Concept and system model

In the formulation of (Rabari et al., 16 Sep 2025), the participants are the dealer, $n$ authorized players, and a special principal authority who alone holds the Universal-share. The secret is not a single image but a set of $n$ binary images $n$0, each with pixels taking value $n$1 or $n$2. The channel model assumes an authenticated quantum channel between dealer and each participant, no pre-shared classical keys, and standard quantum-no-cloning and uncertainty assumptions.

The security goals are explicitly specified. Perfect secrecy means that any collection of $n$3 shares without the UniShare reveals no information about any $n$4. Lossless recovery means that any single share $n$5 in combination with the UniShare $n$6 reconstructs the secret image $n$7 exactly, with zero error. The scheme is also stated to resist quantum eavesdropping threats including intercept–resend and entangle–measure attacks (Rabari et al., 16 Sep 2025).

The role of the universal share is structurally central. Because $n$8 is common to all secrets, the access structure is simplified: recovery of each $n$9 requires pairing $G_1,\dots,G_n$0 with $G_1,\dots,G_n$1 alone. The paper states that no other subset, such as $G_1,\dots,G_n$2 and $G_1,\dots,G_n$3 together, yields any information. This distinguishes the construction from schemes in which all or many shares must be recombined for each reconstruction step (Rabari et al., 16 Sep 2025).

Within the broader literature, “universality” is used in several related senses. In the cluster-state protocol of (Ma et al., 14 May 2025), universality means that a single set of shares $G_1,\dots,G_n$4 supports $G_1,\dots,G_n$5 different secrets simply by choosing new public weights $G_1,\dots,G_n$6. In monotone-span-program-based schemes, universality refers to support for arbitrary access structures rather than only threshold structures (Rathi et al., 2023, Luo et al., 2023). In the present image-sharing scheme, the universal feature is specifically the use of one common share across multiple binary image secrets (Rabari et al., 16 Sep 2025).

2. Share generation and quantum-state representation

The protocol of (Rabari et al., 16 Sep 2025) maps each pixel of each image to a qubit. For each pixel $G_1,\dots,G_n$7, the dealer prepares $G_1,\dots,G_n$8 qubits: one universal qubit $G_1,\dots,G_n$9 and $M\times N$0 secret-share qubits $M\times N$1. The paper describes three stages: initialization, universal-share generation, and secret-share generation.

During initialization, for each pixel $M\times N$2, the dealer starts with qubits in state $M\times N$3. The classical pixel of $M\times N$4 is encoded by applying an $M\times N$5 gate if and only if $M\times N$6, according to

$M\times N$7

Accordingly, $M\times N$8 if the pixel is $M\times N$9, and $(n,n+1)$0 if it is $(n,n+1)$1 (Rabari et al., 16 Sep 2025).

The universal share is generated by applying a Hadamard gate to the universal qubit: $(n,n+1)$2 After measurement in the computational basis, $(n,n+1)$3 is taken as the universal share bit. The scheme characterizes this as a true quantum-random bit (Rabari et al., 16 Sep 2025).

Secret-share generation is then carried out in a random-grid style. For each $(n,n+1)$4, the universal qubit $(n,n+1)$5 is used as the control of a CNOT onto $(n,n+1)$6. The post-CNOT target qubit is denoted $(n,n+1)$7, and the effect at the bit level is

$(n,n+1)$8

In Dirac notation, the CNOT action is

$(n,n+1)$9

The dealer distributes the share-qubit sequences $G_k$0 to the $G_k$1 participants and keeps or transmits $G_k$2 to the principal authority (Rabari et al., 16 Sep 2025).

This design differs from other quantum multi-secret sharing architectures in the cited literature. The image-sharing protocol explicitly states that, unlike many quantum-secret-sharing protocols based on GHZ or Bell states, it uses only single-qubit superpositions and two-qubit CNOT gates (Rabari et al., 16 Sep 2025). By contrast, (Ma et al., 14 May 2025) employs cluster states and rotated-basis measurements; (Luo et al., 2023) uses $G_k$3-qudit GHZ states and generalized Pauli embeddings; and (Rathi et al., 2023) reconstructs secrets with qudits, the $G_k$4-dimensional quantum Fourier transform, and controlled-SUM gates.

3. Reconstruction and threshold behavior

Reconstruction in (Rabari et al., 16 Sep 2025) is local to the target secret. Any authorized party who holds one share $G_k$5 and the universal share $G_k$6 can perfectly recover $G_k$7. For each pixel $G_k$8, the reconstructor prepares qubits $G_k$9 and $S_k$0 from $S_k$1 and $S_k$2, and applies CNOT with $S_k$3 as control and $S_k$4 as target. Since $S_k$5, the target becomes

$S_k$6

Measurement of the target in the computational basis yields $S_k$7, exactly the original pixel (Rabari et al., 16 Sep 2025).

The reconstruction algorithm therefore requires only one CNOT and one measurement per pixel. The paper states that this reconstruction is lossless. It further reports that, because the protocol is purely XOR-based on fully reversible quantum gates, the recovered images $S_k$8 coincide pixel-by-pixel with the originals; in simulation, $S_k$9, $U$0, and correlation $U$1 (Rabari et al., 16 Sep 2025).

The threshold parameters are described as $U$2: all $U$3 secrets are shared in parallel, and for each pixel the dealer deploys $U$4 qubits. Reconstruction of any one secret $U$5 requires exactly two shares—$U$6 plus $U$7. The paper emphasizes that no other subset yields information. It also states that the dealer may share arbitrarily many binary images subject only to quantum-channel bandwidth (Rabari et al., 16 Sep 2025).

This threshold behavior differs from that of the cluster-state protocol of (Ma et al., 14 May 2025), which is formulated as a quantum $U$8 threshold multi-secret sharing protocol based on Lagrangian interpolation and cluster states, where only $U$9 instead of $n$0 participants are required to reconstruct multiple quantum secrets. In that setting, a dealer chooses a random polynomial $n$1 of degree $n$2, distributes classical shares $n$3, and encodes secret-specific rotation angles $n$4. Reconstruction proceeds via teleportation-style cluster-state links, local private angles $n$5, and cumulative $n$6-rotations that cancel because $n$7 (Ma et al., 14 May 2025). The image-sharing scheme thus realizes universality through a common share, whereas the cluster-state construction realizes it through reusable classical share structure and public weights.

4. Security properties and adversarial model

The security analysis in (Rabari et al., 16 Sep 2025) focuses on intercept–resend and entangle–measure attacks. Against intercept–resend, an eavesdropper who measures the transmitted qubits of $n$8 without knowing $n$9 learns random bits, because each $n$0 and $n$1 is uniform. Any measurement by Eve in the computational basis yields $n$2 or $n$3 with probability $n$4, independent of $n$5. This is the basis for the claim that any single share alone is statistically independent of the secrets (Rabari et al., 16 Sep 2025).

Against entangle–measure attacks, the paper states that if Eve attempts to entangle her ancilla $n$6 with $n$7 via a controlled-unitary, the subsequent dealer–receiver CNOT and measurement will induce a detectable error rate. By standard BB84-style arguments, any non-trivial probe on a random-grid share qubit will with nonzero probability flip the correlation and reveal Eve’s presence (Rabari et al., 16 Sep 2025).

The paper gives an explicit error-detection bound: if Eve interacts with fraction $n$8 of the qubits, the disturbance on those qubits leads to a detection probability at least

$n$9

By sampling a small subset of pixels and comparing parity checks of $n$00, the honest parties can bound Eve’s information. It is further stated that, if Eve’s operation is modeled by a unitary $n$01 on the share qubit plus ancilla, trace-distance arguments show her maximum information satisfies $n$02, where $n$03 is the induced bit-error rate (Rabari et al., 16 Sep 2025).

Related protocols exhibit different security mechanisms. In (Ma et al., 14 May 2025), all qubits travel with BB84-style decoys, and intercept–resend on the secret qubits or cluster links is detected with exponentially small undetected probability $n$04. Internal security is also analyzed: a malicious reconstructor cannot extract useful information about others’ $n$05 without the privately chosen $n$06, and any subset of $n$07 players cannot cancel the dealer’s encryption (Ma et al., 14 May 2025). In (Rathi et al., 2023), cheat detection is delegated to a Black box that stores a matrix $n$08 and participant eigenvalues $n$09; participants submit shadow pairs $n$10, and the Black box checks linear independence and eigenvalue consistency before releasing true shares. That protocol also claims robustness against eavesdroppers and participants (Rathi et al., 2023).

A common misconception is that all quantum multi-secret sharing requires large-scale entanglement. The image-sharing scheme explicitly rejects this for its own construction: it uses only $n$11, $n$12, CNOT, and measurement, and requires no large-scale entangled states (Rabari et al., 16 Sep 2025). Another potential misconception is that “universal” always means arbitrary access structures. In the cited literature, it can instead denote one common share serving multiple secrets (Rabari et al., 16 Sep 2025), one set of classical shares supporting multiple quantum secrets (Ma et al., 14 May 2025), or support for arbitrary monotone access structures via MSPs (Rathi et al., 2023, Luo et al., 2023).

5. Resource profile and comparison with related constructions

The resource profile of (Rabari et al., 16 Sep 2025) is specified per image collection of size $n$13. Each share $n$14 is one qubit per pixel, plus the dealer or authority keeps one qubit $n$15 per pixel. No pixel expansion occurs: all shares and the secret have dimension $n$16. The total quantum resources are stated as $n$17 qubits, $n$18 Hadamard gates to create $n$19, $n$20 NOT gates to encode $n$21, $n$22 CNOTs to produce $n$23, and $n$24 measurements (Rabari et al., 16 Sep 2025).

The paper compares the scheme to classical random-grid MSS, to $n$25 quantum schemes based on GHZ clusters, and to Luo et al.’s $n$26 MSS. The stated comparison is that the image-sharing protocol adds quantum-randomness and eavesdropping detection at no pixel-expansion cost relative to classical random-grid MSS; uses simpler gates and no large-scale entanglement relative to GHZ-cluster-based schemes; and recovers each secret with only two shares instead of $n$27 relative to Luo et al.’s scheme (Rabari et al., 16 Sep 2025).

The cited literature provides complementary baselines for these comparisons.

Scheme	Core primitives	Access/recovery property
Universal share-based QVMSS (Rabari et al., 16 Sep 2025)	$n$28, $n$29, CNOT, measurement	$n$30; recover $n$31 from $n$32
Cluster-state QMSS (Ma et al., 14 May 2025)	cluster states, $n$33, $n$34, rotated measurements	$n$35; any $n$36 reconstruct multiple quantum secrets
MSP-GHZ multi-secret sharing (Luo et al., 2023)	GHZ states, generalized Pauli operators, GHZ-basis measurement	arbitrary monotone $n$37 via MSP
MSP with cheat identification (Rathi et al., 2023)	$n$38-dimensional QFT, SUM gates, Black box checks	multi-access structures with cheat detection

The monotone-span-program line of work generalizes the access structure beyond threshold models. In (Luo et al., 2023), a monotone span program $n$39 encodes the access structure $n$40, and because any monotone access structure can be realized by an MSP, the quantum-share embedding works for arbitrary $n$41, not just threshold. The scheme embeds shares into an $n$42-qudit GHZ state via generalized Pauli operators and recovers multiple secrets by one GHZ-basis measurement (Luo et al., 2023). In (Rathi et al., 2023), the dealer creates multiple secrets $n$43, embeds them into an MSP vector $n$44, derives shares $n$45, and distributes shadow shares derived from a randomly invertible matrix $n$46; only participants authenticated by the Black box acquire their secret shares to recover the multiple secrets (Rathi et al., 2023).

6. Relation to general quantum access structures and universal computation

Universal share-based quantum multi-secret sharing belongs to a wider program of distributing quantum information over structured share spaces. One branch studies arbitrary quantum access structures and in-place computation on shared states. “Computing on Quantum Shared Secrets for General Quantum Access Structures” (Bassirian et al., 2018) constructs a $n$47 threshold scheme using the $n$48 CSS code, then builds $n$49 schemes and arbitrary access structures by induction. The encoding uses the 7-qubit CSS code, with logical operators $n$50 and $n$51, and distributes the physical qubits among players so that no single party has information about the secret, whereas any two parties can recover by local CNOTs (Bassirian et al., 2018).

That work extends from sharing to universal in-place computation. Clifford operations are carried out transversally on the encoded shares, and universality is completed by gate teleportation using pre-shared logical magic states

$n$52

Authorized subsets can therefore perform universal quantum computation on the shared state without recovering it in one location (Bassirian et al., 2018).

This broader perspective suggests that universal share-based quantum multi-secret sharing is not a single protocol family but a design pattern spanning several layers of abstraction. At one level, the image-sharing scheme of (Rabari et al., 16 Sep 2025) is a concrete $n$53 QVMSS for binary images with a common universal share. At another level, cluster-state, MSP, and GHZ-based constructions show how reusable shares, arbitrary access structures, or multi-secret recovery can be engineered by different combinations of algebraic secret sharing and quantum-state processing (Ma et al., 14 May 2025, Rathi et al., 2023, Luo et al., 2023). A plausible implication is that “universal share-based” methods can be understood as schemes in which a reusable structural component—whether a common quantum share, a classical share vector, or an access-structure encoding—amortizes the cost of distributing multiple secrets.

7. Applications, limits, and research directions

The image-sharing protocol identifies secure image communication as its primary application domain, with confidential image sharing across enterprise data access and military communications cited as examples (Rabari et al., 16 Sep 2025). The absence of pixel expansion, lossless recovery, and the use of only $n$54, $n$55, CNOT, and measurement make the scheme technically distinct within quantum visual cryptography. The paper explicitly presents it as combining the strengths of quantum computing and visual cryptography (Rabari et al., 16 Sep 2025).

The cluster-state protocol of (Ma et al., 14 May 2025) emphasizes practical deployment features of a different kind. It states that the dealer can be offline after sending secrets, that required quantum operations are all common quantum operations, and that experiments on IBM Q prove correctness and feasibility. The reported implementation tested the $n$56 secret example on IBM’s 5-qubit device using a linear chain $n$57, with circuit depth per secret approximately $n$58 layers and observed state fidelity $n$59 for $n$60 and $n$61 for $n$62 after error mitigation (Ma et al., 14 May 2025).

The MSP-based cheat-identification scheme extends applicability in another direction: multi-access structures, participant authentication, and robustness under dit-flip noise, $n$63-phase-flip noise, and amplitude-damping noise. Its fidelities are given as

$n$64

$n$65

and

$n$66

for the three noise models considered (Rathi et al., 2023).

The literature also delineates present limits. The image-sharing scheme is confined to binary images and an $n$67 access pattern (Rabari et al., 16 Sep 2025). The cluster-state construction requires coordination of private rotation angles and cluster links (Ma et al., 14 May 2025). The Black-box-based scheme presumes a trusted cheat-detection mechanism and hidden matrix $n$68 (Rathi et al., 2023). The general-access-structure framework based on concatenated 7-qubit encodings keeps all shares as qubits but may require exponentially many of them in the worst case of a very complicated access structure (Bassirian et al., 2018).

Several extensions are explicitly identified in the cited works. For the cluster-state protocol, potential extensions include verifiability via trap qubits or hash tags on rotation angles, dynamic join/leave by re-running only small local re-keying for classical shares, and general access structures via weighted Lagrange interpolation or graph-state adjustments (Ma et al., 14 May 2025). In the context of universal share-based image sharing, these directions suggest routes by which common-share constructions might be generalized beyond binary image secrets and threshold-like recovery patterns.