Quantum Computing for Cryptography: Breaking Encryption Algorithms

Abstract

The rapid advancement of quantum computing presents a significant challenge to classical cryptographic systems that underpin modern digital security infrastructures. In particular, RSA-2048 encryption, widely deployed in banking and financial institutions for secure transactions, relies on the computational hardness of integer factorization. However, the emergence of quantum algorithms—especially Shor’s algorithm—poses a fundamental threat to RSA security by enabling polynomial-time factorization of large integers on sufficiently powerful quantum computers. This case study investigates the vulnerability of RSA-2048 within a banking environment, analyzing the mathematical foundations of the threat, potential timelines for quantum feasibility, and associated cybersecurity risks. The study further examines the implications for financial data protection, digital signatures, and secure communication channels. In response to these emerging risks, the paper explores post-quantum cryptographic alternatives, including lattice-based, hash-based, and code-based schemes, and evaluates their suitability for banking applications. The findings emphasize the urgency of transitioning toward quantum-resistant cryptographic frameworks and propose strategic recommendations for proactive cryptographic migration to ensure long-term data confidentiality and system resilience.

Introduction

The text provides an in-depth analysis of RSA cryptography and its vulnerability to quantum computing, with a focus on implications for banking and national security. It explains the mathematics behind RSA, the threat posed by Shor’s algorithm, and the need for post-quantum cryptography (PQC).

Key Points:

1. RSA and Classical Security:

   • RSA is a public-key cryptosystem relying on large prime factorization for security.

   • Classical security depends on the computational hardness of factoring a large number N=p×qN = p \times qN=p×q (e.g., 2048 bits).

   • Encryption/decryption:

     • C=Memod  NC = M^e \mod NC=MemodN

     • M=Cdmod  NM = C^d \mod NM=CdmodN

   • Exponential growth in classical factoring makes RSA secure against classical computers.

2. Quantum Computing Threat:

   • Qubits, superposition, and entanglement enable quantum parallelism.

   • Shor’s algorithm (1994) can factor large integers in polynomial time, breaking RSA.

     • Uses Quantum Fourier Transform for period finding.

     • Efficiently extracts factors of NNN, undermining RSA’s core assumption.

   • Quantum factoring complexity: y=x3y = x^3y=x3 (polynomial) vs. classical: y=exy = e^{\sqrt{x}}y=ex? (sub-exponential).

3. Cryptographic Risks:

   • “Harvest Now, Decrypt Later” attack: adversaries can store encrypted data today and decrypt it once quantum computers are available.

   • Threat affects:

     • Banking systems (TLS, key exchange, digital signatures)

     • Long-term confidential communications

     • National security infrastructure

4. Literature & Research Gaps:

   • Most studies are theoretical, lacking:

     • Domain-specific risk modeling (e.g., banking)

     • Long-term attack impact analysis

     • Structural interpretation of complexity shift

     • Detailed qubit and resource projections for real-world attacks

   • Current literature emphasizes algorithmic threat but not applied system-level consequences.

5. Novel Contributions of This Study:

   • Sector-specific quantum risk modeling: focuses on national banking infrastructure.

   • Time-shifted attack framework: incorporates delayed vulnerabilities via “Harvest Now, Decrypt Later.”

   • Complexity transition analysis: visualizes shift from exponential to polynomial complexity.

   • Technical-policy integration: links mathematical vulnerability to regulatory guidelines (NIST, NSA).

6. Objectives:

   • Analyze RSA-2048’s mathematical foundation and dependence on factoring hardness.

   • Examine Shor’s algorithm and its impact on RSA.

   • Model real-world banking scenarios under quantum attacks.

   • Compare classical vs. quantum computational complexity.

   • Evaluate long-term security and national financial risk.

   • Provide structured guidance for transition to post-quantum cryptography.

7. Methodology:

   • Comparative computational complexity modeling between classical and quantum approaches.

   • Algorithmic vulnerability assessment using Shor’s algorithm.

   • Risk simulation in banking cryptographic architectures:

     • Assumes RSA-2048 used for TLS handshakes, key exchanges, and digital signatures.

     • Factors N = p × q with 1024-bit primes.

   • Focus on both technical and systemic implications of RSA compromise.

Conclusion

This case study examined the structural vulnerability of RSA-2048 encryption within banking systems under the emerging capabilities of quantum computing. The security of RSA is fundamentally based on the computational hardness of integer factorization, expressed mathematically as: N = p× q While classical algorithms require sub-exponential time to factor large integers, quantum algorithms—particularly Shor’s algorithm—reduce this complexity to polynomial time, fundamentally altering the cryptographic security landscape. This transition is not incremental but structural, meaning that once large-scale, fault-tolerant quantum computers become operational, RSA-based encryption will no longer provide adequate security guarantees. The case study demonstrated that banking infrastructures relying on RSA-2048 for secure transactions, digital signatures, authentication protocols, and confidential communication are exposed to both immediate and long-term risks. One of the most critical threats identified is the “Harvest Now, Decrypt Later” attack model, where encrypted financial data intercepted today may be decrypted in the future once quantum capabilities mature. Furthermore, the study highlighted that the quantum threat is not limited to theoretical feasibility; ongoing advancements in qubit scalability, error correction, and quantum hardware suggest that cryptographic migration must begin proactively rather than reactively. Regulatory and standardization efforts are already progressing toward post-quantum cryptography (PQC), emphasizing the urgency of transition planning. The results are given below RSA-2048 security is conditionally secure and vulnerable under scalable quantum computation. The financial sector faces predictable cryptographic disruption within future quantum timelines. Delayed migration increases systemic risk exposure. Post-quantum cryptographic solutions provide a viable, though implementation-intensive, pathway forward. In conclusion, the transition to quantum-resistant cryptographic systems is not optional but inevitable. Financial institutions must adopt a strategic, phased migration approach incorporating risk assessment, hybrid cryptographic deployment, and compliance with emerging quantum-safe standards. Proactive adaptation will determine whether the quantum era becomes a cybersecurity crisis or a managed technological evolution.

References

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Copyright

Copyright © 2026 Mrs. G. Sujatha, Dr. Sajal Mandal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.