As the horizon of technology broadens, quantum computing emerges as a paradigm-shifting force, boasting the potential to revolutionize various fields including quantum cryptography. However, its ascent poses considerable encryption challenges, with implications that could be felt across the vast expanse of data security. The raw power of quantum algorithms threatens to unravel the fabric of current encryption standards, thereby rendering traditional cryptographic paradigms vulnerable. Data center managers, along with their security cohorts, are rapidly being propelled to the center stage, tasked with the urgent need to navigate this tempestuous sea of uncertainty by adopting quantum-resistant measures to ensure the continued safeguarding of sensitive information.
Key Takeaways
- Quantum computing is rapidly advancing, with significant implications for encryption and data security.
- The power of quantum algorithms poses a threat to conventional cryptographic methods used to protect sensitive data.
- Anticipating the need for quantum-resistant cryptography is central to maintaining data integrity and privacy.
- Security professionals must collaborate and prepare for potential future quantum threats to encryption.
- Understanding the impact and preparing for changes in cryptographic standards are crucial for industry resilience.
The Transformation of Encryption in the Quantum Era
The inception of quantum computing transformation marks a pivotal juncture in data encryption, heralding what many have termed the quantum era. This emerging technology promises to expedite computational processes at a pace currently unfathomable, presenting both boundless opportunities and unprecedented challenges, particularly within the realm of modern cryptography.
At the heart of the brewing storm is the stark reality that existing encryption methods—those that form the bedrock of our digital security infrastructure—stand on precarious ground. Quantum computers, with their sophisticated algorithms, are anticipated to crack complex encryptions that are considered secure against the brute-force attacks of today’s classical computers.
As we delve deeper into the quantum era, the vulnerability of traditional encryption techniques becomes increasingly discernible, necessitating the exploration and implementation of quantum-resistant algorithms.
- Asymmetric encryption: Used in securing digital communications, relies on complex mathematical problems.
- Symmetric encryption: Foundational for protecting data at rest, dependent on the obscurity of massive key spaces.
The potential for quantum algorithms to unravel these cryptographic underpinnings calls for immediate attention and action. The table below contrasts the key differences between current cryptographic methods and the promising alternatives in the context of a quantum-dominated landscape.
| Cryptographic Method | Current Reliability | Quantum Computing Impact | Quantum-Resistant Alternatives |
|---|---|---|---|
| RSA Encryption | Highly Reliable | Vulnerable to Shor’s Algorithm | Lattice-Based Cryptography |
| ECC (Elliptic Curve Cryptography) | Widely Used | At Risk of Being Broken | Isogeny-Based Cryptography |
| AES (Advanced Encryption Standard) | Robust Against Brute-Force | Efficacy Potentially Halved | Larger Key Sizes & Post-Quantum Algorithms |
| Secure Hash Algorithms (e.g., SHA-256) | Integral to Data Integrity | Quantum Attacks Theoretical but Looming | Quantum Secure Hash Functions |
In summary, the quantum era necessitates a transformative approach to data encryption, where the adoption of quantum-resistant schemes and a proactive stance in modern cryptography will be quintessential for safeguarding the digital world. As the veil of theoretical quantum supremacy recedes, the urgency to evolve and adapt our cryptographic defenses becomes imperative.
Quantum Computing and Cryptography: A Pending Revolution
At the dawn of the quantum computing revolution, the very foundation of data security is being challenged. Research in quantum computing is progressing rapidly, positioning it to transform the way we understand and use cryptographic algorithms. This imminent evolution has profound data protection concerns, as current encryption methods that secure critical infrastructure could soon be vulnerable to quantum-powered cyber attacks. Encouraging exploration into new, quantum-resistant encryption techniques becomes imperatively requisite for sustaining the security integrity of our data centers.
- The risk of quantum attacks on traditional encryption techniques necessitates a new era of cryptographic innovation.
- Research into quantum-resistant cryptographic algorithms is imperative for the protection of sensitive data.
- Collaboration between security experts, technology developers, and policymakers is crucial to prepare for impending quantum advancements.
Given the stakes, it’s imperative that security professionals and technology developers expedite the quest for resilient encryption methods. By creating cryptography that withstands quantum computing’s advanced capabilities, we not only shield data centers but we also lay down a safeguard for the future of data privacy and security.
Quantum Threats to Asymmetric Encryption
As we delve deeper into the quantum computing era, the robust structure of asymmetric encryption — a cornerstone of public key cryptosystems — stands at a precipice, facing unprecedented challenges. Shor’s algorithm has emerged as a harbinger of quantum cryptographic attacks, fundamentally questioning the durability of current encryption frameworks against the ingenious might of quantum processors.
Understanding Shor’s Algorithm
The innovative work of Peter Shor has ushered in an algorithm capable of integer factorization and computing discrete logarithms at speeds unattainable by classical computers. It is the efficiency of Shor’s algorithm in breaking down the otherwise tough cryptographic problems that position asymmetric encryption threats at the top of security agendas for organizations and governments alike.
RSA and ECC at Risk
Two of the most relied upon encryption schemes, RSA and ECC, which have provided the backbone for secure communications, now confront the bleak outlook of RSA encryption vulnerability and ECC risk. The practical implementation of Shor’s algorithm within quantum computing could negate the necessity of private keys, rendering confidential information bare and susceptible to interception.
| Encryption Method | Risk Factor | Quantum Resistance | Potential Threats |
|---|---|---|---|
| RSA | High | Low (Pre-Quantum) | Factoring large primes |
| ECC | High | Low (Pre-Quantum) | Computing discrete logarithms |
| Post-Quantum Algorithms | To Be Determined | High (Theoretical) | Yet to be tested against quantum capabilities |
With quantum technologies accelerating at a breakneck pace, the quest for quantum-resistant algorithms grows more pressing. Public key cryptosystems require urgent reinforcement to stave off the potent threats of quantum decryption. As we bear witness to the potential unravelling of contemporary cryptography at the quantum level, a new chapter of encryption resilience must swiftly emerge.
Challenges for Symmetric Encryption in Quantum Computing
As quantum computing continues its ascent, the principles of symmetric encryption face unprecedented trials. The secure digital vaults of today, guarded by the robustness of symmetric algorithms, are confronting the real possibility of being flung open by quantum advancements. Symmetric encryption challenges encapsulate this complex interplay between established security measures and the disruptive force of quantum decryption.
Grover’s Algorithm: Doubling Down on Symmetry
The cornerstone of symmetric encryption’s reliability has been the formidable task of key discovery. Traditional brute-force attacks on algorithms such as AES are infeasible due to the immense computational resources they’d require. Enter Grover’s algorithm, a quantum tool that magnifies the risks associated with symmetric encryption by slashing the key search time in half. This raises practical concerns over the capacity of symmetric algorithms to withstand quantum-enhanced threats.
Implications for AES and Other Symmetric Algorithms
AES encryption security stands as a bulwark in contemporary data safeguarding practices. Its widespread application across myriad platforms is testament to its efficacy—under current conditions. However, with the potential to dramatically reduce the buffer of security provided by an algorithm’s resistance to a brute-force approach, symmetric algorithm implications in the quantum era must not be taken lightly. Here lies the critical need to evaluate and evolve our encryption frameworks to preempt quantum vulnerabilities.
| Factor | Current Symmetric Encryption | Post-Quantum Projections |
|---|---|---|
| Key Size | Extensive (e.g., 256-bit for AES) | May require doubling to maintain security |
| Key Search Method | Brute-force impractical | Quantum key search potentially feasible |
| Security Lifespan | Long-term under classical computation | Halved effectiveness against quantum decryption |
| Algorithm Resilience | High against classical attacks | Uncertain, reassessment needed |
In the light of these impending transformations, the encryption community must vigorously pursue the development of quantum-resistant algorithms. Vigilance against Grover’s algorithm risks will act as a guiding principle in molding the next generation of encryption technology, striving to keep pace with quantum advancements. As unyielding defenders of information privacy and security, we must tackle symmetric encryption challenges head-on, forging a future where quantum decryption does not spell the end of data confidentiality.
Post-Quantum Cryptography: The Next Frontier
As the digital landscape braces itself for the quantum computing era, post-quantum cryptography stands at the forefront of a movement essential to safeguarding future communications. This new domain of cryptographic research is dedicated to developing encryption algorithms that are secure against the formidable decryptive capabilities of quantum computers.
Lattice-Based Cryptography
Lattice-based encryption is garnering industry-wide attention due to its unique quantum resistance profile. Unlike traditional encryption reliant on number theory, lattice algorithms are built upon mathematical structures that are inherently difficult for quantum algorithms to crack, making them compelling candidates for securing sensitive data against quantum threats.
Advancements in Code-Based Cryptography
In parallel, code-based encryption methods are undergoing significant refinement. These systems, particularly ones like the McEliece algorithm, are designed to be resistant to the quantum computing onslaught. While they operate on the principle of employing error-correcting codes which burdens quantum computers with the infeasible task of decoding corrupted messages, concerns such as unwieldy key sizes do persist.
Understanding the comparative strengths of these emerging cryptographic paradigms provides valuable insights for stakeholders in the cybersecurity and encryption arenas, as illustrated by the table below:
| Encryption Method | Key Characteristics | Quantum Resistance Level | Practical Considerations |
|---|---|---|---|
| Lattice-Based Encryption | Complex geometric structures | High | Efficient at scale, still under development |
| Code-Based Encryption | Error-correction coding | Varies by algorithm | Large key sizes, proven durability |
We are witnessing a vital transition phase where post-quantum advances continue to evolve, driven by the need to anticipate quantum computing’s disruptive potential. By investing in research across lattice and code-based methodologies, the field aims to develop an arsenal of cryptographic tools that will ensure the security and privacy of information in the quantum future.
The Promising Avenue of Quantum Key Distribution
Quantum Key Distribution (QKD) is at the forefront of revolutionary communication security, leveraging the intricate principles of quantum mechanics. This advanced form of encryption is making waves in the security realm due to its ability to detect any form of interception or eavesdropping inherently. As QKD development progresses, its potential to transform secure communications is attracting global attention and research investment.
One of the standout features of QKD is its implementation of quantum mechanics, specifically the concept that a quantum system cannot be measured without disturbing it. This fundamental property ensures that any intrusion into the key transmission process can be immediately identified, as the presence of an eavesdropper will inevitably alter the system’s state and be detectable by the legitimate parties involved in the communication process.
According to the National Security Agency, while QKD represents a partial solution to emerging security challenges posed by quantum computing advancements, it heralds a dynamic shift towards more secure cryptographic protocols.
The implementation of QKD systems is an area burgeoning with potential, propelling us towards a future of uncompromisingly secure communication channels. Researchers and developers are tirelessly pushing the boundaries of quantum mechanics to devise robust QKD systems that might one day become the gold standard for secure communications worldwide.
Multivariate and Isogeny-Based Cryptography: Potential Quantum Answers
In our exploration of the frontiers of quantum-safe security, the emergence of multivariate cryptography and isogeny-based cryptography heralds new directions in the development of post-quantum encryption methods. These innovative approaches incorporate complex mathematical structures to bolster our defense against potential quantum threats, illustrating the evolution of cryptographic science into realms that defy the capabilities of quantum-powered attacks.
Complex Equations: The Multivariate Approach
Multivariate cryptography distinguishes itself by operating on complex systems of polynomial equations, a strategy that leans on the intricate relationship between variables to create intractable problems for would-be attackers. This method stands as a promising component of quantum-safe strategies, posing a significant challenge to the advanced computational power of quantum computers due to the difficulty of solving such equations without access to the private key.
Elliptic Curve Isogenies: A Fresh Perspective
Elliptic curve encryption, long established in cryptographic implementations, is gaining an innovative ally with isogeny-based cryptography. Shifting away from the vulnerabilities of logarithmic problems attacked by quantum algorithms, isogeny-based schemes focus on the mapping between elliptic curves—known as isogenies. These maps present a daunting task for quantum decryption, as there is no known quantum algorithm that can efficiently compute the related isogeny problem. This positions isogeny-based cryptography as a concrete step towards creating cryptographic frameworks resilient in a future where quantum computing reigns.
As our computational landscapes continually evolve, the need for quantum-safe strategies has never been more critical. By exploring multivariate and isogeny-based cryptography, we reinforce the very fabric of data security, preparing for a world where quantum computing’s immense power must be met with equally formidable cryptographic defenses.
Preparing for the Quantum Leap in Cryptographic Practices
As the digital landscape braces for the seismic shifts introduced by quantum computing, the urgency for evolving cryptographic standards is palpable. With quantum supremacy on the horizon, data protection strategies are under scrutiny to ensure cryptographic readiness in the face of emerging quantum threats. The forethought and preparation today will pave the way for secure systems tomorrow, adapting cryptographic systems to thwart quantum risks.
NIST’s Role in Shaping Post-Quantum Standards
The National Institute of Standards and Technology (NIST) assumes a pivotal role in this transition period—crafting the blueprint for cryptographic systems resilient in the age of quantum computing. With a proactive stance toward quantum computing standards, NIST post-quantum cryptography efforts are setting the stage for a secure future. The institute’s endorsement of quantum-resistant algorithms marks a critical step in shaping the cryptographic landscape, acknowledging the pressing need to fortify encryption against quantum decryption capabilities.
Strategies for Today’s Data Protection
To safeguard sensitive information against the backdrop of quantum computing advancements, organizations must develop comprehensive data protection strategies. The nature of data, its requisite protection lifespan, and the cryptographic methodologies currently securing it should be thoroughly evaluated. Proactive adaptation and the incorporation of NIST-reviewed quantum-resistant algorithms will ensure that both current and future data remain secure amid the myriad of quantum threats.
| Strategy | Benefits | Considerations |
|---|---|---|
| Inventory of Cryptographic Systems | Reveals potential vulnerabilities and allows for targeted improvements. | Requires thorough knowledge of current encryption systems and data usage. |
| Review of NIST-Endorsed Algorithms | Ensures alignment with federal guidance and industry best practices. | May necessitate revamping existing systems for compatibility. |
| Collaboration for Cryptographic Readiness | Promotes a unified approach to enhancing security protocols. | Success relies on participation across all organizational levels. |
| Lifetime Analysis of Data Protection | Helps determine the urgency for transition to quantum-resistant algorithms. | Involves predicting future threats and technology’s evolution. |
Knowing that cryptographic wisdom lies not only in creating unbreakable codes but in anticipating the keys that might one day unlock them, the race to outpace quantum computing threats is well underway. The leadership from NIST and a well-orchestrated blend of readiness and resilience initiatives are the quintessential elements in navigating the upcoming quantum era in cryptography.
Economic and Industrial Implications of Quantum Progress
The burgeoning quantum computing industry is poised to cause a seismic shift in the global economy. With its profound decryption capabilities, quantum computing stands to redefine the fields of cybersecurity, finance, and beyond. These technological strides signal substantial economic implications as industries gear up for a transformative horizon, propelled by quantum innovations.
Key sectors are set to revolutionize their current methodologies, driven by quantum computing’s promise in sophisticated problem-solving areas such as drug discovery, logistical optimization, and climate modeling. The ripple effect on job creation and market dynamics adds another layer to the quantum narrative, setting the stage for a new epoch in technology-driven economic expansion.
Government entities, keenly aware of the stakes, have initiated the groundwork for incorporating post-quantum cryptographic standards. The mutual goal across nations is to establish a secure digital infrastructure capable of withstanding the powerful decryption prowess that quantum computers may soon wield.
While the horizon is rife with optimism, the trajectory of quantum computing is equally laden with challenges and competition. Here is a snapshot of the current state of the industry:
| Aspect | Detail | Impact |
|---|---|---|
| Funding | Large-scale investment across public and private sectors | Accelerates research and development; fosters innovation |
| Workforce Development | Increased demand for skilled professionals in quantum sciences | Catalyzes education and specialized job markets |
| International Collaboration | Combined efforts to set post-quantum standards | Promotes global security and interoperability |
| Competitive Landscape | High-stakes race to quantum supremacy | Drives industrial espionage and proprietary advancements |
Moreover, as the deadline for transitioning to quantum-resistant protocols approaches, there is a surge in both strategic interest and resource allocation to mitigate quantum risks, with 2035 often cited as a pivotal year.
As the timeline for quantum readiness contracts and expansion continues, the overarching narrative remains clear: quantum computing is not merely an incremental step forward; it’s a transformational leap that warrants comprehensive strategic planning and foresight from all economic players.
Quantum Computing: From Theoretical Possibility to Tactical Capability
Quantum computing has long been confined to theoretical discussions, but recent advances have shifted the dialogue to its tangible applications and the strategies needed for harnessing its power. The transition from speculation to practicality is evident in Google’s landmark achievement and the subsequent considerations surrounding the protection of quantum research.
The Story of Google’s Quantum Supremacy
Reaching what is hailed as a quantum leap, Google achieved what is known as ‘quantum supremacy,’ setting a quantum computing milestone. Their quantum processor, Sycamore, completed a calculation in mere minutes—a task that traditional supercomputers could take thousands of years to solve. This significant event underscores the rapid pace at which quantum technology is advancing, predicting a future where problems once considered intractable are within reach.
Secrecy and Openness in Quantum Advancements
The delicate balance between secrecy and openness in the realm of quantum computing is crucial, both for fostering innovation and protecting sensitive information. While academic exchange promotes progress, the inadvertent leak of Google’s quantum supremacy draft highlights the perils of maintaining quantum computing secrecy. Such events serve as a reminder of the challenges faced in guarding the confidentiality of advancements with profound implications on global cybersecurity.
As we edge closer to realizing the CRQC threat, the dialogue shifts towards the urgency to bolster our cryptographic defenses, ensuring future readiness against quantum disruptions.
The juxtaposition of the need for openness in research, fostering collaboration and growth, against the imperative to shield against the CRQC threat frames the narrative of quantum computing’s ascendancy. The repercussions are profound, as the deployment of resilient cryptography becomes not just an objective but a necessity for secure communication in the impending quantum era.
Here’s an overview of the critical discourse surrounding this dual-edged aspect of quantum research:
| Aspect | Openness | Secrecy |
|---|---|---|
| Objective | Promote collective innovation and knowledge-sharing | Protect against premature exposure of sensitive data and strategic advantages |
| Risks | Accelerated proliferation of quantum capabilities may outpace security measures | Lack of collaborative research could stagnate progress and lead to isolated growth |
| Strategic Significance | Encourages a global effort in advancing the frontiers of quantum research | Prevents potential adversaries from acquiring strategic quantum capabilities |
| Policy Implications | May require international treaties on knowledge exchange and use of quantum tech | Demands rigorous protocols to ensure tight-knit containment of quantum breakthroughs |
The discourse on quantum computing does not stop at mere theoretical debates but extends to practical and strategic domains where policy, research fidelity, and cultural shifts in cryptography are in constant flux. Considering such dynamics, the onus is upon us to strike the right balance that will sustain the burgeoning power of quantum computing while keeping a vigilant eye on security imperatives.
The Role of Government in Steering Quantum Cryptanalysis
The ascendancy of quantum computing threatens to overturn current norms of cybersecurity initiatives, making the government role in facilitating a swift and secure transition to post-quantum cryptography paramount. The White House, understanding the gravity of the situation, has outlined critical directives to shepherd the nation through the challenges posed by quantum cryptanalysis.
President Biden’s administration has committed to a comprehensive roadmap with the objective of transitioning national cybersecurity initiatives to be quantum-resilient. By drawing on both internal and external sectors of expertise, and with robust funding mechanisms in place, the government is not only a regulator but an active participant in forging the future state of encryption.
| Cybersecurity Initiative | Goals | Completion Timeline |
|---|---|---|
| Advancing Post-Quantum Cryptography | Implement quantum-resistant cryptographic systems in critical infrastructures | By 2035 |
| Public-Private Collaboration | Strengthen partnerships between the government, industry, and academia | Ongoing |
| Quantum Computing R&D Funding | Provide substantial resources for research in quantum-resistant technologies | Ongoing with iterative assessments |
In the face of these impending changes, maintaining the secrecy of advancements that could compromise national security is more than a matter of protocol—it’s imperative. Continued assessment of the state of quantum cryptanalysis will ensure that the nation is not left vulnerable to the decryption prowess of future quantum technologies.
“To secure the future, we must lead the present. Adopting and innovating security in the face of quantum computing is not optional—it’s necessary for our national defense.”
With every new horizon in technology, there comes an array of challenges and opportunities. The government’s proactive engagement in charting the course for quantum cryptanalysis endeavors will be the bulwark against the potential upheavals in national and global encryption-based security systems.
International Collaboration and Competition in Quantum Research
The international quantum race is intensifying as nations and companies vie for dominance in quantum computing and cryptography. This intricate ballet of global competition and cooperation is pivotal to unleashing quantum innovation while ensuring that strategic assets remain protected. With the promise of reshaping everything from cybersecurity to material sciences, the quantum race is not just a scientific pursuit, it’s at the heart of future economic and national security.
The Race for Quantum Advancement
The drive for supremacy in quantum computing endeavors is accelerating, with countries investing heavily to capitalize on the promise of quantum technology. As the global talent pool grows, so does the importance of collaboration across borders. However, these partnerships are delicately balanced against the competitive spirit that propels the quest for quantum breakthroughs.
While distinct entities lay unique claims to aspects of the quantum realm, the overarching mission to advance humankind’s computing capabilities remains a common goal. Thus, the challenge lies in nurturing an ecosystem that promotes sharing and innovation among members of the quantum community, while strategically protecting intellectual property and maintaining a competitive edge within the international arena.
Ideas and Talent: The Global Quantum Community
The dynamic quantum community is the nucleus of progress in this field, featuring a blend of established experts and rising stars from academia and industry. Fostering this community involves a delicate interplay between securing critical expertise and endorsing open scientific collaboration to propel the field forward. In this ever-evolving landscape, the cultivation and retention of top talent remain essential strategies for maintaining a frontline position amidst the frenetic pace of quantum research.
The phenomenon of brain circulation, where talent and ideas migrate globally, bolsters the synergistic development of quantum technologies. However, each entity engaged in the international quantum race must also contend with the protective necessity of securing proprietary information—a nuanced challenge that continues to shape the global posture toward quantum innovation and discovery.
Understanding Quantum Computing’s Impact on Data Security
The introduction of quantum computing into the realm of data security signals a transformative shift, necessitating a comprehensive quantum state understanding to anticipate the evolution of cryptography. At the crux of this shift are qubits, the fundamental units of quantum information, which operate under the enigmatic laws of quantum mechanics.
Deciphering Qubits and Quantum States
Conceptualizing the qubits interpretation involves grappling with their probabilistic existence in multiple states simultaneously, known as superposition. This capacity to occupy various states enables quantum computers to conduct numerous computations at once, dramatically accelerating data processing and cryptanalysis—potentially making existing encryption protocols vulnerable.
The data security impact is profound as we inch closer to a world where quantum computers can break through the robust encryption that currently protects our most confidential information. This anticipated cryptographic disruption has set the stage for an urgent need to revolutionize our approach to information security, with the development of quantum world precautions and mitigation strategies.
The Future of Information Safety in a Quantum World
The information safety future depends on the successful creation and implementation of quantum-resistant cryptographic methods. These advanced methods must be resilient against the formidable processing power of quantum computers to preserve data integrity and maintain privacy in an increasingly uncertain digital landscape.
As we delve deeper into the intricacies of the quantum world, the cryptography evolution becomes not just an academic exercise, but a critical safeguarding measure. Key to this endeavor is coding new algorithms with the foresight of quantum capabilities, ensuring that our collective digital future is secured against even the most advanced cryptanalytic assaults.
Conclusion
The rise of quantum computing stands at the confluence of opportunity and threat, heralding a quantum computing conclusion that resonates across the expanse of data security. It is a wake-up call to the guardians of cryptography, urging an acceleration in the pursuit of encryption resilience. As the very foundations of cryptographic principles face unresolved questions against the might of quantum capabilities, organizations are compelled to re-evaluate their encryption strategies with foresight and vigor.
The cryptography outlook requires a resilient mindset, one that embraces the inevitability of quantum advancements and the concurrent risks they pose. Ensuring encryption remains a step ahead demands collaboration; a synergy of minds across the frontiers of industry, academia, and government. As we stand on the brink of quantum computing’s broadening horizon, it becomes crucial that all players in the field of data protection engage collectively to devise, refine, and implement quantum-resistant algorithms.
The path forward is marked by shared efforts to future-proof cryptographic practices against the formidable decryption power emerging from quantum progress. Staying informed and agile, while investing in research and development of cutting-edge encryption methods, will serve not only as a shield safeguarding our digital assets but also as a guiding beacon illuminating the way for a secure transition into the post-quantum era.
Source Links
- https://www.rand.org/pubs/commentary/2023/09/when-a-quantum-computer-is-able-to-break-our-encryption.html
- https://www.techtarget.com/searchdatacenter/feature/Explore-the-impact-of-quantum-computing-on-cryptography
- https://courses.csail.mit.edu/6.857/2022/projects/Su-Zhang-Zhu.pdf