Securing the Quantum Horizon: Encryption for the Cloud

Author: Denis Avetisyan

As quantum computing power grows, protecting data in the cloud demands new cryptographic approaches, and this review explores how homomorphic encryption can bridge the gap.

A quantum cloud architecture facilitates homomorphic addition through the implementation of the Chen algorithm, enabling computations on encrypted data without decryption.

This paper details methods and tools for building secure quantum clouds, with a case study focused on integrating Chen, GSW, and QOTP homomorphic encryption schemes within the Eclipse Qrisp framework.

The increasing capabilities of quantum computation pose a fundamental threat to currently deployed cryptographic protocols, necessitating proactive security measures for emerging cloud infrastructures. This research, ‘Methods and Tools for Secure Quantum Clouds with a specific Case Study on Homomorphic Encryption’, investigates methods for securing quantum cloud platforms through the integration of post-quantum cryptography, with a particular focus on homomorphic encryption schemes. Implementation and evaluation within the Eclipse Qrisp framework demonstrate the feasibility of leveraging algorithms like Chen, GSW, and QOTP to protect data privacy while maintaining computational functionality. How can these findings inform the development of robust and scalable quantum cloud architectures prepared for a post-quantum future?

The Looming Quantum Threat: A Foundation of Vulnerability

The bedrock of much modern digital security, algorithms like RSA, hinges on a surprisingly simple mathematical principle: the difficulty of factoring extremely large numbers into their prime components. While multiplying two large primes is computationally trivial, reversing this process – discovering those original primes given only their product – becomes exponentially harder as the number of digits increases. This asymmetry forms the basis of RSA’s security; the public key, derived from the product, is easily shared, but factoring it to reveal the private key – essential for decryption – demands immense computational resources. Currently, the largest known numbers factored are on the order of hundreds of digits, and existing algorithms would require millennia to break commonly used $2048$-bit RSA keys. However, this security isn’t inherent to the mathematics itself, but rather to the limitations of classical computing power, a vulnerability poised to be overcome with the advent of more powerful computational paradigms.

The security underpinning much of modern digital communication relies on the difficulty of certain mathematical problems, notably the factorization of large numbers into their prime components. However, Shor’s algorithm presents a significant threat to these systems. Developed by Peter Shor in 1994, this quantum algorithm can factor integers exponentially faster than the best-known classical algorithms. While classical computers require time that grows proportionally to the cube root of the number of digits in the number being factored, Shor’s algorithm reduces this to a polynomial time complexity. This means that a sufficiently powerful quantum computer – one with enough stable qubits and low error rates – could break widely used public-key encryption schemes like RSA, which are based on this computational hardness. The implications are substantial, potentially compromising secure online transactions, digital signatures, and the confidentiality of sensitive data, thus driving the urgent need for post-quantum cryptography.

The foreseeable development of scalable quantum computers presents a critical imperative for a proactive overhaul of current encryption methodologies. Existing public-key cryptosystems, such as RSA and elliptic-curve cryptography, which underpin much of modern digital security – from online banking to secure communications – are predicated on mathematical problems considered intractable for classical computers. However, these systems become vulnerable when confronted with the capabilities of quantum algorithms like Shor’s algorithm, which efficiently solves the factoring and discrete logarithm problems upon which these cryptosystems rely. Consequently, a swift and coordinated transition to quantum-resistant, or post-quantum, cryptographic solutions is no longer a matter of future preparedness, but an urgent necessity to safeguard sensitive data and maintain the integrity of digital infrastructure against a potentially disruptive technological shift. The development and standardization of algorithms like lattice-based cryptography, multivariate cryptography, and code-based cryptography are therefore vital steps in mitigating this emerging threat and ensuring continued cybersecurity in the quantum era.

This architecture demonstrates how a quantum cloud can facilitate homomorphic addition using the GSW algorithm.

Beyond Classical Boundaries: Architecting Post-Quantum Solutions

Post-Quantum Cryptography (PQC) is a field dedicated to creating cryptographic systems that can withstand attacks from both classical and future quantum computers. Current public-key cryptography, such as RSA and ECC, relies on the computational hardness of problems like integer factorization and the discrete logarithm problem, which are efficiently solvable by Shor’s algorithm on a quantum computer. PQC algorithms, conversely, are based on mathematical problems believed to be intractable for both types of computers. These include lattice-based cryptography, code-based cryptography, multivariate cryptography, hash-based signatures, and isogeny-based cryptography. The security of these approaches relies on the presumed difficulty of problems such as the Shortest Vector Problem (SVP) on lattices, decoding general linear codes, or solving systems of multivariate polynomial equations over finite fields. The National Institute of Standards and Technology (NIST) is currently leading an effort to standardize a new generation of PQC algorithms to replace vulnerable classical schemes.

The McEliece cryptosystem is a public-key encryption algorithm considered a leading post-quantum cryptography (PQC) candidate due to its reliance on the established hardness of decoding general linear codes – a problem not known to be efficiently solvable by quantum computers. Specifically, the system utilizes Goppa codes, a subclass of linear codes, for encryption. The security of McEliece rests on the difficulty of distinguishing between a random linear code and a Goppa code, even with quantum algorithms. Error correction is integrated through the use of Hamming codes, enabling reliable decryption despite potential noise or transmission errors. While requiring relatively large key sizes compared to current asymmetric algorithms like RSA or ECC, the McEliece cryptosystem offers a structurally different approach to security that is believed to be resistant to attacks from both classical and quantum adversaries.

Learning With Errors (LWE) is a problem in lattice-based cryptography that forms the basis for several post-quantum cryptographic schemes. The LWE problem postulates that, given a random matrix $\mathbf{A}$ and a secret vector $\mathbf{s}$, it is computationally difficult to distinguish between the distribution of $\mathbf{A}\mathbf{s} + \mathbf{e}$ and a uniformly random vector, where $\mathbf{e}$ is a short error vector. The security of LWE relies on the hardness of solving this problem, even with quantum algorithms. Importantly, LWE allows for provable security reductions; meaning the security of a cryptographic scheme built on LWE can be directly linked to the assumed hardness of solving the LWE problem itself, providing a quantifiable level of assurance. Variations like Ring-LWE further enhance efficiency and security by operating over polynomial rings.

While Post-Quantum Cryptography (PQC) addresses the threat of quantum computers breaking current encryption, secure computation methods are also essential. PQC secures data at rest and in transit, but many applications require processing data while it remains encrypted, preventing exposure during computation. Techniques like homomorphic encryption, secure multi-party computation (SMPC), and zero-knowledge proofs allow operations on ciphertexts, yielding encrypted results that, when decrypted, match computations performed on the plaintext. These technologies, combined with PQC, create a more comprehensive security solution, enabling confidential data analysis, collaborative computing, and privacy-preserving machine learning without requiring decryption of sensitive information.

Evidence of Capability: Homomorphic Encryption in Action

Homomorphic Encryption (HE) is a form of encryption that allows computations to be performed directly on ciphertext – data that remains encrypted – without requiring decryption first. This is achieved through specific encryption schemes designed with properties that preserve mathematical relationships even after encryption. Consequently, a user can send encrypted data to a service for processing, and the service can perform calculations on the ciphertext. The result, also in ciphertext, can then be sent back to the user, who decrypts it to obtain the final result, all without the service ever accessing the plaintext data. The security of HE relies on the difficulty of reversing the homomorphic operation to reveal the underlying plaintext, ensuring data confidentiality throughout the entire computation process.

Pyfhel and Concrete are software libraries designed to lower the barrier to entry for developers utilizing Homomorphic Encryption (HE) schemes. Pyfhel, built on the BFV and CKKS schemes, is a Python library offering a high-level API and supports both integer and floating-point arithmetic. Concrete, developed by Zama, focuses on the TFHE scheme, enabling fully homomorphic encryption with faster performance for certain workloads due to its gate-level implementation. Both libraries provide tools for key management, ciphertext manipulation, and evaluation of computations on encrypted data, abstracting away much of the complex underlying cryptography and allowing developers to focus on application logic rather than cryptographic primitives. These libraries include pre-built functions and optimized routines, facilitating experimentation and deployment of HE-based solutions in various domains.

The One-Time Pad (OTP) is a theoretically unbreakable encryption technique, achieving perfect secrecy when implemented correctly; however, its practical application is severely limited. The OTP requires a key that is as long as the message itself and used only once. This necessitates secure key distribution and storage equal in size to the data being encrypted, a logistical challenge for all but the most limited communication scenarios. Furthermore, the requirement of a unique key for each message renders the OTP unscalable for applications requiring the encryption of large volumes of data or frequent communication. Consequently, research has focused on developing practical alternatives like Homomorphic Encryption (HE) which, while not achieving perfect secrecy, offers a balance between security and usability for real-world deployments.

The integration of Homomorphic Encryption (HE) with Post-Quantum Cryptography (PQC) addresses critical security vulnerabilities in modern computation, particularly within cloud environments. While HE allows computation on encrypted data, current HE schemes rely on mathematical problems susceptible to attacks from quantum computers. PQC algorithms, designed to resist quantum attacks, provide a foundational layer of security for the encryption keys and parameters used in HE schemes. This combined approach mitigates both classical and quantum threats, ensuring confidentiality and integrity even if a quantum computer becomes available. This paper demonstrates a functional integration of HE and PQC, showcasing a pathway to build truly secure cloud computing architectures where data remains private and computations are verifiable, even against advanced adversarial models.

This architecture demonstrates how a quantum cloud can facilitate homomorphic addition using a Quantum One Time Pad.

Impact and Realization: Secure Cloud Services in a Quantum Age

The advent of quantum cloud services, while promising unprecedented computational power accessible over networks, simultaneously introduces a complex landscape of security vulnerabilities. These services, by their very nature, expose quantum resources to external networks, creating avenues for both data breaches and sophisticated malware attacks. Traditional encryption methods, reliant on the computational difficulty of certain mathematical problems, are increasingly threatened by the potential of quantum computers to efficiently solve these problems. This heightened risk stems from the remote access inherent in cloud computing, where data is not physically secured on local machines, but rather transmitted and stored on distributed servers. Consequently, safeguarding quantum cloud services requires proactive development of novel security protocols and architectures designed to withstand attacks from both classical and quantum adversaries, ensuring the confidentiality and integrity of sensitive data processed within this emerging paradigm.

Quantum Key Distribution (QKD) offers a fundamentally new approach to securing communication by leveraging the laws of quantum physics. Unlike traditional cryptographic methods that rely on mathematical complexity, QKD’s security is rooted in the No-Cloning Theorem, which states that an unknown quantum state cannot be perfectly copied. This principle allows for the secure distribution of encryption keys; any attempt to intercept and copy the key during transmission inevitably introduces detectable disturbances, alerting the legitimate parties to the intrusion. Consequently, QKD provides a theoretically unbreakable method for key exchange, guaranteeing confidentiality even against adversaries with unlimited computational power-a critical advantage as quantum computers capable of breaking current encryption standards emerge. Its application to cloud services ensures that data transmitted to and from the cloud, and data stored within it, remains confidential, offering a crucial layer of protection in an increasingly vulnerable digital landscape.

A robust defense against emerging quantum threats necessitates a multi-faceted security strategy, and the convergence of Post-Quantum Cryptography (PQC), Homomorphic Encryption (HE), and Quantum Key Distribution (QKD) provides precisely that. PQC algorithms aim to replace currently used public-key cryptography that is vulnerable to attacks from quantum computers, safeguarding data in transit. Simultaneously, HE allows computations to be performed on encrypted data without decryption, ensuring confidentiality even during processing. Crucially, QKD offers an unparalleled level of security for key exchange, leveraging the laws of physics – specifically the No-Cloning Theorem – to detect any eavesdropping attempts. By layering these technologies, sensitive information remains protected both while being transmitted and while stored, creating a resilient shield against both classical and future quantum-powered attacks and establishing a new standard for data security in the cloud.

This research details a significant advancement in securing cloud computing by integrating homomorphic encryption (HE) with the Eclipse Qrisp framework. Qrisp, an open-source platform designed for quantum information science, now benefits from HE’s unique capability: performing computations on encrypted data without decryption. This integration allows for confidential data processing within the cloud, safeguarding sensitive information from unauthorized access even during computation. The work demonstrates a functional implementation, outlining the challenges overcome in bridging these two technologies and providing a pathway for developers to build genuinely secure quantum cloud services. By combining the strengths of both HE and Qrisp, this study represents a crucial step toward a future where cloud-based quantum computing resources can be accessed with enhanced data privacy and confidentiality, mitigating risks posed by increasingly powerful computational threats.

A quantum cloud system defines distinct authorization boundaries to manage access permissions for administrators, internal users, and external customers.

The Quantum Computing Ecosystem: Building a Secure Future

Eclipse Qrisp functions as a comprehensive software development kit, simplifying the complex process of building and deploying applications for quantum computers. This high-level framework abstracts away many of the intricacies of quantum hardware and programming languages, allowing developers to focus on algorithm design rather than low-level implementation details. By providing a standardized interface and a suite of tools, Qrisp facilitates the creation of portable quantum applications that can run across various quantum computing platforms. The framework supports the entire application lifecycle, from initial development and testing to deployment and monitoring, fostering a more accessible and efficient quantum computing ecosystem for both researchers and industry professionals. It enables rapid prototyping and experimentation, accelerating the pace of innovation in this emerging field.

At the heart of quantum computation lies the qubit, a fundamentally different unit of information than the classical bit. While a bit represents either a 0 or a 1, a qubit utilizes the principles of superposition, allowing it to represent 0, 1, or a combination of both simultaneously. This is not merely probabilistic; it’s a core quantum property that dramatically expands computational possibilities. Furthermore, qubits can become entangled, creating a correlation where the state of one instantly influences the state of another, regardless of the distance separating them. This interconnectedness, combined with superposition, enables quantum computers to explore a vast number of possibilities concurrently, offering the potential for exponential speedups in solving certain complex problems – such as drug discovery, materials science, and cryptography – that are intractable for even the most powerful classical computers. The power isn’t simply about faster processing, but about accessing a different computational space enabled by these uniquely quantum phenomena.

The promise of quantum cloud services hinges not only on harnessing the power of quantum computation, but also on ensuring the confidentiality and integrity of data processed within these systems. This work demonstrates the critical importance of integrating quantum frameworks with established secure computation techniques like Homomorphic Encryption (HE) and Post-Quantum Cryptography (PQC). By combining these approaches, sensitive data can be processed on quantum computers without ever being decrypted – or exposed – to the underlying infrastructure. This integration addresses a key vulnerability: the potential for data breaches as quantum computers become more powerful and accessible. The research showcases a practical implementation of this hybrid approach, paving the way for secure quantum cloud services that can handle sensitive workloads with confidence and unlock the full potential of this emerging technology.

The advancement of quantum computing isn’t solely a technical endeavor; it demands a unified approach involving researchers, developers, and industry leaders. Progress requires a continuous exchange of knowledge, with academic institutions pioneering foundational algorithms and hardware, developers translating these innovations into practical applications, and industry leaders providing the resources and real-world testing grounds for scaling these technologies. This synergistic relationship is particularly vital for addressing the complex security challenges inherent in quantum computation. Establishing standardized protocols, open-source tools, and shared datasets fosters interoperability and accelerates the development of a robust and reliable quantum ecosystem. Ultimately, a collaborative spirit ensures that the transformative potential of quantum computing benefits society as a whole, paving the way for secure communication, optimized resource allocation, and groundbreaking scientific discoveries.

A typical Quantum Key Distribution (QKD) system enables secure communication through the exchange of quantum states.

The exploration of integrating homomorphic encryption with quantum computing frameworks, as detailed in the study, underscores a fundamental tenet of system design: structure dictates behavior. The paper meticulously demonstrates how the chosen encryption schemes-Chen, GSW, and QOTP-interface with Eclipse Qrisp, influencing the overall security architecture. This careful consideration of interconnectedness echoes a sentiment articulated by John McCarthy: “The best way to predict the future is to invent it.” The research doesn’t merely anticipate the threats of quantum computing but actively constructs a solution, highlighting how a thoughtfully designed system can proactively shape its own security landscape. The study emphasizes that modifying one part of a system-in this case, cryptographic methods-triggers a domino effect, necessitating a holistic understanding of the entire architecture.

What Lies Ahead?

The integration of homomorphic encryption with quantum computing frameworks, as demonstrated with Eclipse Qrisp, represents a necessary, though not sufficient, step toward securing data in a post-quantum world. Current explorations, focused on schemes like Chen, GSW, and QOTP, largely address the symptoms of the threat – the vulnerability of existing cryptographic protocols. A more holistic understanding requires acknowledging that security isn’t merely about swapping algorithms, but about fundamentally re-evaluating data handling practices within the cloud paradigm.

The practical implementation of these schemes remains constrained by computational overhead. The promise of performing computations on encrypted data is alluring, but the cost of doing so currently dwarfs the benefits for many applications. Future work must prioritize optimization – not simply of the encryption schemes themselves, but of the entire system architecture. Exploring hybrid approaches, combining lattice-based cryptography with quantum key distribution, may offer a more balanced pathway, though the inherent complexity introduces new challenges in verification and standardization.

Ultimately, the true measure of success will not be the elegance of the cryptographic solutions, but the resilience of the system as a whole. Good architecture is invisible until it breaks, and only then is the true cost of decisions visible.

Original article: https://arxiv.org/pdf/2512.17748.pdf

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