Secure Key Leasing: Quantum Revocable Keys

• Secure Key Leasing is a cryptographic framework where a secret key is leased as a quantum state that prevents copying and supports verifiable deletion.
• SKL integrates techniques from lattice-based cryptography, trusted execution environments, and functional encryption to ensure collusion resistance and error tolerance.
• Applications include time-limited access, DRM, and cloud-based key management, while addressing challenges in multi-lessee security and real-world implementation.

Secure Key Leasing (SKL) is a cryptographic framework in which a lessor grants a lessee the ability to use a secret key through a quantum state rather than a copyable classical string. In the public-key setting, SKL “allows a secret key holder to generate a quantum decryption key and securely lease it to a user,” and once the user “returns the quantum decryption key (or provides a classical certificate confirming its deletion), they lose their decryption capability” (Kitagawa et al., 18 Feb 2025). Recent work places this idea within revocable cryptography, extends it from public-key encryption to functional and attribute-based settings, and studies both cryptographic and systems realizations, including classical lessors, collusion resistance, error tolerance, and hardware-enforced key handles (Chardouvelis et al., 2023).

1. Conceptual basis

SKL is motivated by a limitation of classical key distribution: a classical secret key can always be copied, so revocation cannot force a lessee to “unlearn” it. The quantum setting changes this asymmetry. A leased key is a quantum state that enables evaluation of a designated functionality, but the same state can also be subjected to a return or deletion procedure whose successful verification implies loss of the leased capability. In the formulation for public-key encryption with a classical lessor, the lessee receives a reusable quantum secret key state, later runs a deletion algorithm that outputs a classical certificate, and the lessor verifies that certificate classically; security requires that no computationally bounded quantum adversary can “simultaneously provide a valid classical deletion certificate and yet distinguish ciphertexts” (Chardouvelis et al., 2023).

The notion is closely related to secure software leasing, but the intended adversary is stronger. Secure software leasing was introduced as an alternative to quantum copy-protection, and it guarantees that once software is returned in a valid form, the user can no longer use it; however, some earlier leasing notions captured only pirate software that runs on an honest evaluation algorithm (Ananth et al., 2020). In functional encryption with secure key leasing, the security notion “captures arbitrary attack strategies and does not have such a limitation” (Kitagawa et al., 2022). This places SKL between ordinary revocation mechanisms and full quantum copy-protection: it is weaker than copy-protection, but it is substantially stronger than classical revocation or software-only license checks.

A further conceptual distinction is between leasing a general secret key and leasing a restricted capability. Secure software leasing gives a positive construction for a subclass of evasive circuits, including point functions, conjunctions with wild cards, and affine testers, but also proves an impossibility result for a class of quantum unlearnable functions for which secure software leasing does not exist (Ananth et al., 2020). This suggests that the feasibility of SKL depends strongly on the structure of the leased functionality.

2. Security models and formal notions

The first generation of public-key SKL focused on a single leased quantum decryption key. “Public Key Encryption with Secure Key Leasing” formalized PKE-SKL through algorithms $$(\mathsf{KG}, \mathsf{Enc}, \mathsf{Dec}, \mathsf{Vrfy})$$, where $\mathsf{KG}$ outputs a classical encryption key, a quantum decryption key, and a verification key; the security notions include IND-KLA, OW-KLA, and OMUR, with the core guarantee that if a returned quantum key passes verification, the adversary has lost the ability to decrypt future ciphertexts (Agrawal et al., 2023). In the same line of work, the paper also generalized SKL to identity-based encryption, attribute-based encryption, and functional encryption (Agrawal et al., 2023).

The single-key model was later identified as too weak for realistic deployments. “PKE and ABE with Collusion-Resistant Secure Key Leasing” states that previous PKE-SKL work “only considered the single-key security model, where the adversary receives at most one quantum decryption key,” and introduces collusion-resistant security for PKE-SKL, denoted PKE-CR-SKL (Kitagawa et al., 18 Feb 2025). In this model, “the adversary can adaptively obtain multiple quantum decryption keys and access a verification oracle which validates the correctness of queried quantum decryption keys,” while “the size of the public key and ciphertexts must remain independent of the total number of generated quantum decryption keys” (Kitagawa et al., 18 Feb 2025). The same paper gives an attribute-based extension, ABE-CR-SKL, and a version with classical certificates (Kitagawa et al., 18 Feb 2025).

Another line of formalization emphasizes deletion-first attack games. In the error-tolerant PKE-SKL framework, OW-VRA and IND-VRA require that after the adversary outputs a certificate and passes deletion verification, a future challenge ciphertext remains hard to recover or distinguish (Xu et al., 3 Jul 2026). In functional encryption with secure key leasing, the corresponding lessor-security experiment allows a quantum adversary to request leased keys for many functions, but challenge ciphertexts are only released if every distinguishing key has already been returned and verified (Kitagawa et al., 2022). Across these formulations, the recurring structure is the same: a successful return or deletion test is treated as a precondition for the post-return security game.

3. Construction paradigms and assumption landscape

A central construction path uses lattice assumptions. “Quantum Key Leasing for PKE and FHE with a Classical Lessor” gives the first secure key leasing scheme for a decryption key of a classical public-key, homomorphic encryption scheme from standard lattice assumptions, and the protocol uses “only classical communication between a classical lessor (client) and a quantum lessee (server)” (Chardouvelis et al., 2023). The construction is based on LWE, uses NTCF-style structure, and achieves a strong notion of security in which accepted deletion certificates imply loss of decryption capability even against computationally bounded quantum adversaries (Chardouvelis et al., 2023). The same work extends the approach to levelled FHE (Chardouvelis et al., 2023).

Collusion-resistant lattice constructions broaden this paradigm. The collusion-resistant PKE and ABE paper presents “a PKE-CR-SKL scheme based on the learning with errors (LWE) assumption,” “an attribute-based encryption scheme with collusion-resistant SKL (ABE-CR-SKL), also based on the LWE assumption,” and “an ABE-CR-SKL scheme with classical certificates, relying on multi-input ABE with polynomial arity” (Kitagawa et al., 18 Feb 2025). This moves SKL from a single-lessee setting toward a multi-key setting in which verification-oracle access and collusion are part of the native model.

A different classical-lessor route uses non-local games and certified deletion. “Computational Certified Deletion Property of Magic Square Game and its Application to Classical Secure Key Leasing” presents “the first construction of a computational Certified Deletion Property (CDP) achievable with classical communication,” obtained from a compiled version of the Magic Square Game, and combines that CDP with the Kitagawa–Morimae–Yamakawa framework to realize cSKL for PKE, PRF, and digital signature (Takeuchi et al., 6 Oct 2025). The same paper emphasizes that it realizes cSKL for PRF and digital signature “for the first time” and that it weakens the assumptions needed for classical secure key leasing by using claw-state generators (Takeuchi et al., 6 Oct 2025).

Functional encryption broadens the leased functionality further. “Functional Encryption with Secure Key Leasing” defines SKFE with secure key leasing and proves a transformation from standard SKFE into SKFE-SKL “without using additional assumptions” (Kitagawa et al., 2022). From post-quantum one-way functions, it obtains bounded collusion-resistant SKFE for $\mathsf{P}/\mathsf{poly}$ with secure key leasing; it also introduces single-decryptor FE as a stronger primitive and constructs collusion-resistant single-decryptor PKFE for $\mathsf{P}/\mathsf{poly}$ from post-quantum indistinguishability obfuscation and quantum hardness of LWE (Kitagawa et al., 2022). This suggests that SKL sits naturally inside a larger hierarchy that includes functional encryption, secure software leasing, and copy-protection-like primitives.

4. Robustness, certificates, and error tolerance

A major recent development is the move from idealized quantum states to noisy ones. “Error-tolerant secure key leasing for quantum decryption keys in public-key encryption” proposes “the first error-tolerant secure key leasing (SKL) for public-key encryption” (Xu et al., 3 Jul 2026). The protocol allows the lessor to check whether the lessee has returned the key honestly even when the leased secret key is subject to noise, and the lessee can still decrypt correctly while the lessor verifies the return correctly when the amount of error is below a threshold (Xu et al., 3 Jul 2026). The paper emphasizes that the improved protocol “does not change the encoding of the secret key, and thus adds no overhead to the quantum information processing” (Xu et al., 3 Jul 2026).

The same work makes the robustness–security trade-off explicit. Its main technical contribution is “a framework to analyze the trade-off between robustness against error and security,” and it “bridge[s] the security of the error-tolerant SKL and that of the error-tolerant certified deletion with shortened codes” (Xu et al., 3 Jul 2026). In its PKE-SKL construction, the quantum encoding of the decryption key is unchanged, while classical error-correcting codes are used to tolerate errors in decryption and deletion verification (Xu et al., 3 Jul 2026). The paper gives a concrete example with concatenated Hamming $(7n,4n,3)$ codes and, for $\epsilon=0.5$, derives the condition $h(\delta)<1/7$, corresponding to approximately $2\%$ tolerated error in the Hadamard positions (Xu et al., 3 Jul 2026).

Deletion certificates themselves have become a central axis of design. In the LWE-based classical-lessor construction, the deletion certificate is classical and is verified by a classical lessor using only classical communication (Chardouvelis et al., 2023). In the collusion-resistant ABE setting, classical certificates are obtained through multi-input ABE with polynomial arity (Kitagawa et al., 18 Feb 2025). In the Magic Square line, the certified deletion property of the compiled game is the engine that allows a classical lessor to verify deletion in cSKL for PKE, PRF, and digital signature (Takeuchi et al., 6 Oct 2025). This suggests that the problem of SKL increasingly decomposes into two layers: a capability layer that gives reusable quantum evaluation, and a certificate layer that proves deletion through a classical interface.

5. Systems realizations and hardware-backed analogues

Several systems papers describe mechanisms that are not quantum SKL in the narrow formal sense but are explicitly framed as SKL substrates or realizations. “KeyVisor -- A Lightweight ISA Extension for Protected Key Handles with CPU-enforced Usage Policies” presents a lightweight ISA extension that offloads key handling to the CPU, keeping underlying keys inaccessible to memory and enforcing policies such as de-/encryption-only use, limited lifetime, process binding, and revocation (Schwarz et al., 2024). The paper states that “KeyVisor’s ‘protected key handles with CPU-enforced usage policies’ is essentially a concrete SKL substrate integrated into the CPU ISA,” and reports 1439 cycles on average for a TLS 1.2 approximately 1500-byte record, about 6% overhead over pure AES-GCM without KeyVisor controls (Schwarz et al., 2024).

TEE-backed cloud services supply another systems interpretation. “Keys in the Clouds: Auditable Multi-device Access to Cryptographic Credentials” describes a server-side TEE-based Cloud Key Store in Intel SGX, with remote attestation, password-authenticated access, policy-based access controls, delegation for a specified time and/or a limited number of uses, and a secure audit log (Kurnikov et al., 2018). The paper reports approximately 6,000 signature operations per second on a single desktop PC and states that the latency is in the same order of magnitude as using locally-stored keys and 20x faster than smart cards (Kurnikov et al., 2018). The same paper is explicitly described as implementing SKL for centrally stored, TEE-protected personal keys (Kurnikov et al., 2018).

Temporal enforcement appears in distributed systems as trusted leasing rather than quantum deletion. “T-Lease: A Trusted Lease Primitive for Distributed Systems” defines a lease that maintains its correctness properties even in the presence of a clock-manipulating attacker and exposes generic APIs for applications (Trach et al., 2021). Its key invariant is that “the lease duration at the granter must be a superset of the lease duration at the holder,” which is directly relevant to time-bounded key use (Trach et al., 2021). This suggests that systems-side SKL can be decomposed into non-exportability, policy-constrained use, and trusted temporal enforcement.

6. Applications, misuse, and open problems

SKL has been presented as useful for subscription-based decryption, time-limited access to sensitive data, DRM-like settings, cloud-based access control with auditability, and multi-device credential access (Schwarz et al., 2024). The Cloud Key Store paper shows concrete delegation of keys to other users for a specified time and/or a limited number of uses, while KeyVisor demonstrates automotive feature licensing and a read-only network middlebox as real-world use cases (Kurnikov et al., 2018). This suggests that SKL is best understood not as a single primitive but as a family of revocable-capability mechanisms spanning quantum cryptography, TEEs, and hardware key isolation.

The same ideas also admit malicious use. “RansomClave: Ransomware Key Management using SGX” is described as “essentially a concrete instantiation of Secure Key Leasing (SKL),” in which an attacker uses an enclave to generate, hold, and conditionally release decryption keys to a victim based on blockchain-verified payments (Bhudia et al., 2021). The paper states that RansomClave “enables new trustless key release schemes” and reports encryption overhead inside the enclave of approximately 12.76% versus native, with decryption overhead of approximately 34.05% (Bhudia et al., 2021). This use case is not merely anecdotal: it shows that SKL-like mechanisms can strengthen both benign revocation systems and adversarial conditional-release systems.

Open problems remain substantial. The LWE-based classical-lessor PKE/FHE construction identifies several limitations: it relies on subexponential LWE hardness, gives only levelled FHE, and addresses a single lessee with a one-shot revocation model (Chardouvelis et al., 2023). The Magic Square cSKL line still treats parallel repetition for the compiled game as a heuristic (Takeuchi et al., 6 Oct 2025). Secure software leasing proves that there is a class of quantum unlearnable functions for which secure software leasing does not exist, and the impossibility also rules out quantum copy-protection for an arbitrary class of quantum unlearnable functions (Ananth et al., 2020). Recent work on collusion-resistant PKE and ABE (Kitagawa et al., 18 Feb 2025) and on error-tolerant PKE-SKL (Xu et al., 3 Jul 2026) directly addresses two of the most visible early gaps: multi-key collusion and physical noise. This suggests that current SKL research is converging on three frontier questions: how to obtain stronger classical-lessor interfaces, how to make deletion robust under noise and repeated use, and how far revocable quantum capabilities can be pushed before impossibility barriers reappear.