Why Quantum Computers Can Break Traditional Hash and Signature Algorithms – and What Alternatives Exist

By Eckhart Mehler, Cybersecurity Strategist and AI-Security Expert

As quantum computing advances, it becomes increasingly clear that many of today's cryptographic systems are not future-proof. The main threat comes from powerful quantum algorithms, particularly Shor's Algorithm, which can efficiently break asymmetric cryptographic schemes. However, even classical hash functions are not immune to quantum attacks. How exactly does this work – and what alternatives exist?

?? How Quantum Computers Threaten Hash and Signature Schemes

Unlike classical computing, which relies on binary states (0 and 1), quantum computers utilize qubits that can exist in superposition and leverage entanglement to perform parallel computations. This enables algorithms that can exponentially accelerate certain cryptographic problems.

1. Shor's Algorithm: The Demise of Classical Digital Signatures

Shor's Algorithm (1994) uses quantum Fourier transforms to solve integer factorization and the discrete logarithm problem exponentially faster than classical methods. This affects widely used cryptographic schemes, such as:

• RSA: The security of RSA relies on the hardness of integer factorization. A sufficiently powerful quantum computer could break an RSA-2048 key within hours.
• Elliptic Curve Cryptography (ECC): ECC relies on the difficulty of solving the discrete logarithm problem over elliptic curves, which is also broken by Shor's Algorithm.
• DSA and ECDSA: Digital Signature Algorithms based on discrete logarithms are rendered insecure in a post-quantum world.

?? Example: A 2048-bit RSA key, which would take classical computers billions of years to break, could be factorized within minutes using a large-scale quantum computer.

2. Grover's Algorithm: Weakening Hash Functions

Grover's Algorithm provides a quadratic speedup for unstructured search problems, which can be applied to collision finding in cryptographic hash functions.

• Classical hash functions like SHA-256 or SHA-3 normally provide collision resistance at . Grover reduces this complexity to , meaning a 256-bit hash function effectively has only 128-bit security against quantum attacks.

?? Example: Bitcoin's proof-of-work uses SHA-256. If a quantum computer could efficiently apply Grover's Algorithm, mining difficulty would need to increase exponentially to maintain network security.

?? Post-Quantum Cryptography: The Future of Secure Signatures and Hashing

To counteract these threats, researchers are developing Post-Quantum Cryptography (PQC). The most promising candidates come from mathematical problems believed to be resistant to quantum attacks:

1. Lattice-Based Cryptography

Lattice problems such as Learning with Errors (LWE) and Shortest Vector Problem (SVP) have no known quantum solutions. This makes them strong contenders for post-quantum security.

?? Examples:

• CRYSTALS-DILITHIUM and FALCON (digital signatures, NIST PQC finalists)
• Kyber (encryption, also a NIST PQC finalist)

?? More on NIST PQC Standardization

2. Hash-Based Signatures

Hash-based digital signatures, such as SPHINCS+, provide strong security by relying only on cryptographic hash functions rather than number-theoretic problems.

• Pros: High security and well-understood foundations
• Cons: Larger signature sizes and verification times

?? Example: SPHINCS+ is stateless, making it suitable for blockchain applications, unlike stateful schemes like XMSS.

3. Code-Based Cryptography

McEliece cryptosystem (1978) is based on error-correcting codes and has withstood decades of cryptanalysis.

• Drawback: Large public keys (hundreds of kilobytes)
• Strength: Very high security margins

4. Multivariate Polynomial Cryptography

Schemes like Rainbow rely on solving systems of nonlinear multivariate equations, which are believed to be quantum-resistant.

• Rainbow was recently broken by classical means, illustrating the need for careful security analysis before widespread adoption.

?? More details on Multivariate Cryptography

??? What Should Organizations Do Now?

• Evaluate PQC alternatives: Follow NIST's post-quantum cryptography standardization efforts and start testing hybrid cryptographic solutions.
• Adopt hybrid cryptography: Use a combination of classical and PQC schemes to transition securely.
• Conduct security audits: Review cryptographic dependencies in IT infrastructure and plan migrations.

?? Example: Google Chrome has already experimented with hybrid post-quantum TLS key exchanges using Kyber.

?? Google's Post-Quantum TLS Experiment

?? Conclusion: The Future is Post-Quantum Secure!

Quantum computers pose a real threat to existing cryptographic protocols. Organizations must proactively transition to Post-Quantum Cryptography (PQC) to ensure long-term security. The shift is not just an update but a strategic transformation that requires planning and execution now.

How do you see the transition to post-quantum cryptography? Which PQC solutions do you think will dominate? ??

Stay informed, stay resilient

This article is part of my series “Cybersecurity in the Age of AI and Quantum Computing: Threats, Opportunities, and Solutions”, exploring how cutting-edge technologies like AI and quantum computing are reshaping the cybersecurity landscape. Discover actionable strategies to counter quantum-based attacks, AI-driven vulnerabilities, and navigate global regulations while preparing for a secure digital future.

About the Author: Eckhart Mehler is a leading Cybersecurity Strategist and AI-Security expert. Connect on LinkedIn to discover how orchestrating AI agents can future-proof your business and drive exponential growth.

#Cybersecurity #QuantumComputing #PostQuantumCryptography

This content is based on personal experiences and expertise. It was processed, structured with GPT-o1 but personally curated!