Quantum Encryption’s Limits: Why Perfect Security Remains Elusive

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Author: Denis Avetisyan

New research demonstrates fundamental limitations in achieving simulation-based security for quantum functional encryption, extending known impossibilities to the quantum realm.

This paper proves that simulation security for quantum functional encryption is unattainable under various conditions, highlighting inherent information-theoretic constraints.

Despite the promise of quantum cryptography, fundamental limitations persist in achieving idealized security notions for advanced primitives. This work, ‘On the Impossibility of Simulation Security for Quantum Functional Encryption’, rigorously demonstrates that simulation-based security-a cornerstone of functional encryption-remains unattainable even within the quantum realm, extending classical impossibility results to the quantum setting. Specifically, we prove unconditional and assumption-based barriers under various adversary models, leveraging connections to pseudorandom quantum states and public-key encryption. These findings highlight inherent limitations in designing secure quantum functional encryption and prompt further investigation into alternative security definitions and cryptographic constructions.

The Inevitable Expansion: A Foundation of Cryptographic Constraint

Many contemporary encryption methods, while robust in security, introduce a significant practical hurdle: ciphertext expansion. This phenomenon occurs when the encrypted message, or ciphertext, is substantially larger than the original plaintext. While seemingly minor, this expansion can dramatically impact storage requirements, bandwidth consumption during transmission, and computational overhead for processing. Consider applications like secure cloud storage or encrypted messaging; excessive ciphertext size translates directly into increased costs and performance bottlenecks. The issue is particularly acute with advanced cryptographic techniques designed for complex computations within the encrypted domain, where each operation further inflates the ciphertext size, potentially rendering the scheme impractical despite its theoretical security advantages. Consequently, research is increasingly focused on developing schemes that minimize, or even eliminate, this expansion to facilitate wider adoption and enable truly scalable secure computing.

The practical deployment of cryptographic schemes is often significantly hampered when encryption isn’t simply about concealing data, but about performing computations on encrypted data-a field known as homomorphic encryption or secure multi-party computation. Each operation within these computations-addition, multiplication, or more complex functions-necessarily expands the ciphertext. This expansion isn’t linear; even a relatively small number of operations can balloon the ciphertext size to impractical levels, rendering the scheme unusable for large datasets or real-time applications. Consider, for example, a privacy-preserving machine learning model; each layer of computation applied to encrypted training data or inference requests adds to the ciphertext overhead. Without addressing this ciphertext growth, the computational cost of decryption can quickly outweigh the benefits of secure computation, effectively negating the privacy gains and creating a significant bottleneck for advanced cryptographic applications.

The pursuit of cryptographic succinctness represents a pivotal challenge in modern information security. Current encryption methods frequently generate ciphertexts substantially larger than the plaintext they conceal, a phenomenon exacerbated when complex computations are performed on encrypted data. Ideally, a secure scheme would maintain a ciphertext size independent of the complexity of these computations, enabling practical applications like secure cloud computing and privacy-preserving machine learning. However, recent theoretical work demonstrates inherent limitations, proving that achieving this ideal – constant-size ciphertexts regardless of computational load – is fundamentally impossible under certain widely accepted cryptographic assumptions. This doesn’t negate the pursuit of more succinct schemes, but highlights the need for innovative approaches that carefully balance security, efficiency, and the unavoidable trade-offs between ciphertext size and computational overhead. Researchers are now focused on minimizing expansion rates and exploring alternative cryptographic paradigms to mitigate the practical limitations imposed by these impossibility results.

Compression as a Structural Necessity: Shaping the Ciphertext

A Compression Circuit is a fundamental component in the construction of succinct cryptographic schemes, serving as a mechanism to reduce the size of inputs to computations before they are processed. These circuits operate by encoding input data into a more compact representation, effectively minimizing the amount of data that needs to be handled by subsequent cryptographic operations. The primary function isn’t simply data reduction, but rather the efficient encoding of the computation itself; a well-designed Compression Circuit allows for verification of the computation on the compressed data without requiring access to the original, uncompressed input. This is critical for schemes where ciphertext size must be minimized, and computational efficiency is paramount, although recent research indicates inherent limitations in achieving simulation security in Quantum Functional Encryption, even when utilizing compression techniques.

Compression circuits minimize ciphertext size by reducing the amount of data that needs to be encrypted while maintaining the ability to verify the correctness of the computation. This is achieved through efficient encoding of input data, allowing for a more compact representation without losing information essential for verification processes. The resulting ciphertext, though smaller, still allows a verifier to confirm that the computation was performed correctly on the original input, preserving the integrity and reliability of the cryptographic scheme. This reduction in ciphertext size is critical for applications with bandwidth limitations or where storage efficiency is paramount, without compromising security or verifiability.

Compression within succinct cryptographic schemes focuses on encoding the computation itself in a space-efficient manner, rather than simply reducing the size of input data. This approach minimizes ciphertext expansion by representing the underlying operations with fewer bits. However, recent research indicates that even with these compression techniques, achieving simulation-secure Quantum Functional Encryption (QFE) remains challenging. Specifically, limitations have been demonstrated in constructing QFE schemes that can simultaneously provide strong security guarantees and maintain succinctness through compression, suggesting fundamental trade-offs exist between these properties.

Security Models as Definitive Boundaries: Defining Acceptable Trade-offs

Two primary notions of simulation security, designated ‘1-M-NA SIM-Security’ and ‘M-1-AD SIM-Security’, define contrasting requirements for functional key query allowances. ‘1-M-NA SIM-Security’ permits multiple non-adaptive queries – meaning each query is independent of any prior results – and is suitable for applications where all key requests are known in advance. Conversely, ‘M-1-AD SIM-Security’ allows only a single adaptive functional key query, where the query itself can be dynamically adjusted based on the responses to previous queries, providing increased flexibility in key request strategies. These distinct models are crucial for analyzing the security of functional encryption schemes under different threat models and query limitations.

The 1-M-NA SIM-Security model defines a security notion where multiple, non-adaptive functional key queries are permitted. This means a challenger provides keys for several functions, but each key request is made independently of any previous responses. While suitable for scenarios with pre-determined key requests – such as batch processing or static key distribution – formal proofs demonstrate the impossibility of realizing 1-M-NA SIM-Security as a secure Quantum Functional Encryption (QFE) scheme. This limitation stems from the inherent properties of quantum computation and its interaction with functional encryption constructions, specifically concerning the ability to distinguish between encrypted data and random noise under this security model.

The ‘M-1-AD SIM-Security’ model defines a security notion permitting a single adaptive functional key query; this means the query can be formulated based on the results of prior queries, allowing for a dynamic and responsive key request process. While offering increased flexibility compared to non-adaptive models, ‘M-1-AD SIM-Security’ has been mathematically proven to be unattainable as a simulation-secure quantum functional encryption (QFE) scheme. This impossibility result indicates inherent limitations in constructing QFEs that support adaptive key queries while maintaining robust security against simulation-based attacks.

The Illusion of Adaptability: A Pursuit Constrained by Fundamental Limits

The foundation of secure functional encryption lies in distinguishing between two types of key queries: non-adaptive and adaptive. A non-adaptive functional key query operates under strict limitations; the encryption key generated is independent of any data the attacker might subsequently observe. Conversely, an adaptive query permits the key generation process to dynamically respond to previously received ciphertext, allowing for a more nuanced and potentially powerful encryption scheme. This adaptability, while enhancing robustness against evolving threats, introduces significant theoretical challenges; proving the security of systems reliant on adaptive queries is demonstrably more complex than their non-adaptive counterparts, ultimately impacting the feasibility of certain security models within the framework of functional encryption.

The pursuit of truly dynamic encryption schemes hinges on the capability of responding to prior data – known as adaptive queries – which promises heightened robustness against evolving cyber threats. This approach allows encryption to shift and change based on intercepted information, effectively frustrating attackers attempting to decrypt stored or transmitted data. However, despite its appeal, provably secure adaptive functional key queries are demonstrably impossible within the framework of simulation-secure Quantum Functional Encryption (QFE). Theoretical limitations, established through rigorous cryptographic proofs, reveal that achieving this level of adaptability fundamentally conflicts with the requirements for provable security in these systems, forcing cryptographers to explore alternative, albeit less flexible, approaches to maintaining data confidentiality.

Certain levels of functional encryption, specifically those offering adaptive query capabilities, face fundamental limitations rooted in cryptographic assumptions. Researchers have demonstrated that achieving both ‘M-1-AD SIM-Security’ – allowing multiple queries with adaptation to previous responses – and ‘Succinct 1-1-NA SIM-secure QFE’ – a streamlined, non-adaptive form – is impossible if Pseudorandom States (PRS) exist. This suggests a trade-off between functionality and provable security under these conditions. Furthermore, the possibility of constructing a ‘1-M-NA SIM-secure QFE’ – enabling a single query with multiple key usages, but without adaptation – has been ruled out, relying on the established limitations of classical Public-Key Encryption as a foundation for its impossibility. These findings collectively highlight inherent boundaries in designing functional encryption schemes and emphasize the crucial role of underlying assumptions in defining achievable security levels.

The study meticulously charts the inevitable entropy within cryptographic systems, echoing a fundamental truth about all complex constructions. Any attempt at perfect, lasting security, even leveraging the intricacies of quantum mechanics, faces the relentless march of time and the emergence of vulnerabilities. As Vinton Cerf observed, “Any benefit which appears to last forever is, by definition, an illusion.” This resonates deeply with the paper’s core finding – that simulation-based security for quantum functional encryption is fundamentally unattainable, not due to a lack of ingenuity, but because the very notion of a perpetually secure system is an illusion within the temporal landscape of computation. The limitations exposed aren’t flaws in the schemes themselves, but inherent characteristics of systems operating within time.

What Remains to Be Seen?

This work, echoing earlier limitations in classical cryptography, confirms a certain inevitability. The pursuit of simulation-based security for quantum functional encryption appears, under established conditions, to be a refinement of aspiration rather than a viable path. The system’s memory, in this case the impossibility result itself, dictates the boundaries of what can be proven secure. Any attempt to circumvent these limits will invariably introduce new forms of technical debt-simplifications enacted at the cost of future, potentially unforeseen, vulnerabilities.

The focus, then, shifts. Rather than striving for an elusive ideal of perfect simulation, attention may be more productively directed toward alternative security notions. Perhaps a nuanced understanding of what constitutes ‘secure enough’ – a pragmatic assessment of acceptable risk – will yield more fruitful avenues of research. The limitations revealed here are not necessarily a dead end, but a signpost indicating the need for a recalibration of cryptographic goals.

It remains to be seen whether the field will embrace this pragmatic shift, or continue to chase the phantom of absolute security. The history of cryptography suggests the latter is more likely. Yet, even in failure, there is value. Each constraint discovered is a lesson learned, a deepening of the understanding of the fundamental trade-offs inherent in any information system. The decay is inevitable; the manner of that decay, however, is still within the realm of influence.

Original article: https://arxiv.org/pdf/2601.17497.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-01-27 12:40