Exploring Post-Quantum Cryptography: Review and Directions

Introduction

In the ever-changing landscape of technology, quantum computing is emerging as an incredible opportunity and major threat to digital security.  Contrary to conventional computers, quantum computers rely on the principles of quantum mechanics, including superposition and entanglement, to do complex calculations at a staggering speed. While such technology could lead to breakthroughs in fields such as materials science and pharmaceuticals, it could pose a significant risk for current cryptographic systems. The Shor algorithm is a type of algorithm that can cause damage to widely used public-key cryptography software, including Diffie-Hellman, RSA, and Elliptic Curve Cryptography (ECC), in polynomial time and render them obsolete. To combat these, post-quantum cryptography (PQC) is being developed to design quantum-resistant methods that can be able to withstand attacks from classical and quantum computers. This article explains the need for PQC and its most important algorithms, as well as the standardisation process of NIST, implementation challenges, and what the cybersecurity future holds in the quantum age, optimised for searchability using popular keywords such as “quantum security” and “quantum threat,” along with security standards for cryptography.

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The Quantum Threat to Classical Cryptography

Why Quantum Computers Are a Game-Changer

Classical computers process data with bits, which are represented by 1s or 0s.  Quantum computers make use of qubits, which are able to exist in multiple states at the same time because of superposition.  Quantum computers can solve certain issues exponentially faster than traditional systems. For cryptography, the following quantum algorithm is concerned:

• Shor’s Algorithm  Created by Peter Shor in 1994, this algorithm is able to factor large numbers of integers as well as solve discrete logarithm issues in polynomial time, dismantling the mathematical basis that underlies RSA, Diffie-Hellman, and ECC. Most asymmetric cryptography, which secures key exchange and digital signatures, relies on these algorithms.
• Grover’s algorithm: This algorithm gives an increase of quadratic speed for searching unstructured databases, which reduces security for the symmetric cryptography algorithms such as AES and 3DES by around half. As an example, AES-128’s security decreases by 64 bits, requiring bigger key sizes, such as AES-256.

A quantum menace isn’t a figment of imagination. Although large-scale quantum computers that are fault-tolerant aren’t yet in the market, experts predict that they will appear within one or two years. Google, IBM, and other tech giants are making major advancements towards this, with Google being reported to be working on improving its AI by incorporating quantum computing. The urgency is compounded by the risk of harvest-now-decrypt-later attacks, where adversaries collect encrypted data today to decrypt it once quantum computers are available.

The Need for Post-Quantum Cryptography

PQC concentrates on creating cryptographic algorithms that are safe against quantum attacks and are compatible with the existing protocols as well as networks. In contrast to quantum cryptography, which is based on quantum mechanics (e.g., quantum key distribution (QKD)), PQC uses mathematical challenges that are believed to be invulnerable against quantum-based algorithms. The purpose is to ensure the integrity and authenticity of digital data transmissions in the post-quantum era.

The significance of PQC cannot be overemphasised. Cryptography safeguards all aspects of online banking and commerce to crucial infrastructure, as well as security for the nation. An attack on these systems could lead to financial losses, privacy breaches, and threats to human safety. A breach in these systems could result in human safety threats, as well as financial losses. National Institute of Standards and Technology (NIST) has led a global effort to establish a standard for PQC algorithms This process started in 2016 and is now bringing results.

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NIST Post-Quantum Cryptography Standardization Process

A Global Effort to Secure the Future

As of 2015, NIST started the PQC Standardisation Process to seek, assess, and establish a standard for quantum-resistant algorithmic cryptography with public keys. This effort has been ongoing for several years, involving cryptographers from all over the world who have evaluated the initial submissions from 82 out of 25 nations. The process has undergone multiple rounds, with significant milestones scheduled for 2024 and 2025.

• Third round (2022): The NIST chose CRYSTALS-Kyber as the algorithm for public-key encryption along with key establishment as well as CRYSTALS-Dilithium, Falcon, and SPHINCS+ to create digital signatures. These algorithms were selected due to their security, speed, and flexibility.
• Round 4 (Ongoing): Additional algorithms, like HQC, were selected to be standardised on the 11th of March, 2025, to broaden that PQC portfolio.
• Standardisation Final (2024): On August 13, 2024, NIST released FIPS 203 and FIPS 204, along with FIPS 205, which define algorithms that are derived from CRYSTALS-Kyber, CRYSTALS, and SPHINCS+, respectively.  NIST has now established these standards for immediate use.

The foundation of the global transition towards PQC is the NIST process, which thoroughly vets standard algorithms to ensure security and efficiency.

Key PQC Algorithm Families

PQC methods are based on mathematical calculations thought to be resistant to quantum attacks. The most popular families are:

1. Lattice-Based Cryptography:
   • Overview  It is based on problems such as that of the Shortest Vector Problem (SVP) and Learning with Errors (LWE), which are computationally difficult for quantum and classical computers.
   • Key Algorithms:
     • CRYSTALS-Kyber Key Encapsulation Mechanism (KEM) to secure key exchange, designed to speed and compact keys.
     • CRYSTALS-Dilithium is a digital signature scheme that has strong security and a high level of performance.
     • Falcon  The HTML0 Falcon is a simple signature scheme, perfect for devices with limited space.
   • Advantages  The advantages include high efficiency, smaller keys, and a wide range of applications. across various applications.
   • Problems require careful implementation to avoid side-channel attacks.
2. Code-Based Cryptography:
   • Overview  Based on error-correcting codes, especially those of the McEliece Cryptosystem, which has been studied for over 40 years.
   • Key Algorithms: HQC (standardised in 2025) and Classic McEliece.
   • Benefits The benefits include a long-standing security track record and the ability to withstand quantum attacks.
   • Issues  Large key sizes render it less suitable for devices with limited resources.
3. Hash-Based Cryptography:
   • Overview: Utilises hash functions to generate unique signatures that can be extended to multiple uses through Merkle Trees.
   • Key Algorithms: SPHINCS+ SPHINCS+ is a stateless signature scheme that works in conjunction with the XMSS.
   • Advantages  Security guarantees are strong and based on well- understood hash functions.
   • Problems  Signature sizes are huge, and the capacity to sign is limited.
4. Multivariate Quadratic Cryptography:
   • Overview is based on the solution of multivariate quadratic equations that are not NP-hard.
   • Key Algorithms: Rainbow (under study).
   • Advantages: Fast signature generation.
   • The challenges, security concerns and huge important dimensions.
5. Isogeny-Based Cryptography:
   • Overview  Based on isogenies of the elliptic curves, HTML0 offers tiny key sizes.
   • Key Algorithms: SIKE (Supersingular Isogeny Key Encapsulation).
   • Challenges 2022: An attack has compromised SIKE, which highlighted the need to further analyse the analysis of cryptanalysis.

The families are various methods of PQC, which balances security as well as performance and compatibility. The use of multiple algorithms from NIST guarantees robustness since each family is not immune to any future breakthroughs in cryptanalytic technology.

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Implementation Challenges and Transition Strategies

Technical Challenges

The transition to PQC is among the most difficult tasks in the time of Internet. The main challenges are:

• performance: PQC algorithms often require greater computational resources, bigger key sizes, as well as increased bandwidth in comparison to conventional algorithms. For instance, code-based systems such as Classic McEliece have key sizes in the megabyte range. This poses problems for IoT devices.
• Interoperability: PQC algorithms must be compatible with protocols that are already in use, such as TLS and OpenVPN, as well as OpenSSH. This means that updates are required to hardware, software and firmware on billions of devices.
• Side Channel Attacks  Lattice-based algorithms, like Kyber, are susceptible to bugs in the implementation that can leak information via the power or timing.
• backward compatibility To prevent disruption to legacy systems, the organisations must be able to support both traditional and PQC algorithms.

Transition Strategies

To tackle these issues, experts suggest these strategies:

• Hybrid Cryptography  Hybrid Cryptography combines classical and PQC algorithms to ensure protection against emerging and new threats. For instance, using Kyber in conjunction with ECC is a way to fall back in case PQC algorithms fail.
• Early adoption: NIST, NSA, and CISA encourage organisations to start moving forward because it could be many years. Cloudflare and Google have already implemented PQC for servers and browsers.
• Inventory and planning  Organisations should be aware of systems that rely on vulnerable cryptography and prioritise updates to critical infrastructure.
• Industry Collaboration  Projects such as those of the Open Quantum Safety initiative, which is backed by Microsoft, are working on libraries similar to the liboqs library to ease PQC integration.
• education and training The process of preparing IT professionals to be ready for PQC adoption is crucial, as demonstrated by industry surveys that demonstrate increasing awareness among cybersecurity experts.

This is especially important for vital infrastructure such as the energy grids and healthcare systems in which cyber-attacks can have devastating effects. A 2024 research paper highlighted the necessity of custom PQC options for control systems in industrial environments, which balance security and low-latency requirements.

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Industry and Government Initiatives

Industry Adoption

Tech companies are rapidly adopting PQC:

• Google has been able to implement PQC within Chrome, as well as its risk modelling, which focuses on the importance of early integration.
• Cloudflare regularly posts updates on PQC use, including its usage in browsers and servers.
• Microsoft contributes to the NIST process as well as the Open Quantum Safe project, which integrates PQC into protocols such as OpenVPN as well as OpenSSL.
• SEALSQ and WISeKey: PQC companies are making waves in tackling immediate quantum threats and could end up surpassing quantum computing companies in their growth.

The DigiCert study of IT professionals from Europe, the USA, Germany, and Japan revealed a strong understanding of PQC and its significance, as many predict that quantum computers will destroy traditional cryptography within 10 years.

Government and Standardization Efforts

The government is placing a high priority on PQC:

• United States: NIST’s standards are likely to be widely used throughout the world, and NSA and CISA are issuing guidelines for early adoption.
• International Standards: The ISO/IEC JTC1/SC 27 committee has created PQC standards since the year 2015, including a document that is in a state (SD8) that outlines the quantum-resistant cryptography.
• European Union: The PQCRYPTO project, which is funded through Horizon 2020, has published reports on PQC embedded systems, focusing on the long-term security.

These initiatives are part of the worldwide consensus on the necessity for PQC to ensure the security of the digital infrastructure.

The Role of AI in Post-Quantum Cryptography

Artificial Intelligence (AI) is playing two roles in the PQC world. On the one hand, AI can help improve security systems through optimising protocols and identifying vulnerabilities. On the other hand, quantum computers can boost AI-driven cryptanalysis, which will increase the need for PQC. A 2024 study emphasised AI’s ability to improve the distribution of quantum keys and develop hybrid cryptographic systems; however, it stressed the necessity of scalable, low-latency solutions.

Future Directions and Research Opportunities

The research field of PQC is still in its infancy, and various different research avenues are coming up.

• Cryptanalysis  Analysing and analysing PQC algorithms is vital to find flaws, as evidenced by the attack of 2022 on SIKE.
• Optimization  The goal is to reduce important sizes and computational costs for devices that are constrained, including IoT and mobile devices.
• Quantum Cryptography: While PQC is a viable option, QKD and other quantum-based methods can be utilised in high-security situations even with distance limitations.
• Policies and Standardisation: Working on global standards and guidelines to ensure smooth transition, as highlighted by NIST and ISO.

The rapid growth of PQC publications—more than 50% of the past 25 years of research since the year 2019— suggests its increasing importance.

Conclusion

Post-quantum cryptography is a crucial response to the imminent threat of quantum and will ensure that systems in digital form are secure in a quantum-based era. The NIST’s standardisation program has led to the creation of strong algorithms like CRYSTALS-Kyber and CRYSTALS-Dilithium, along with SPHINCS+ and NCS+, which are helping these technologies gain broad acceptance. However, the shift to PQC is an enormous undertaking that requires technical development, industry collaboration with industry and an active plan. Starting from the lattice-based method of encryption and mixed cryptography  The PQC ecosystem provides various solutions to ensure security and efficiency. As quantum computing develops, businesses must now take action to secure sensitive data from the possibility of future attacks. By adopting PQC, businesses can secure the privacy, integrity, and authenticity in our online environment, thereby safeguarding the future of businesses, nations, and individuals alike.