Quantum Cryptography vs. Bitcoin

Dr. Shaista Hussain

November 24, 2025

Quantum computing is the next frontier in technological opportunities and threats. Bitcoin’s cryptographic security is expected to become most vulnerable by around the year 2030, where it is possible that we will see compromised wallets and stolen assets unless robust standards are adopted by corporate structures promptly.​ This means that a large percentage of Bitcoin addresses will be vulnerable, especially if their public keys were ever previously exposed.

How Quantum Computers Threaten Bitcoin

Quantum computers (QC) leverage quantum bits (qubits) that represent both 0 and 1 simultaneously, making it possible to perform calculations exponentially faster than those done by classical computers. Algorithms like Shor’s can break the cryptographic foundations of Bitcoin, making it possible to deduce private keys from public keys rapidly. This would allow attackers to forge transactions and drain wallets, especially for addresses where public keys have already been exposed on the blockchain.​

Public-key cryptographic systems like RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography) rely on the mathematical difficulty of integer factorization and discrete logarithms, respectively. These problems are computationally infeasible for classical computers to solve within a reasonable timeframe, which is what makes it a safe bet at the moment for securing encrypted data. Bitcoin relies on ECC, which turns private keys into public ones through equations that are easy to compute, but practically impossible to reverse.

Symmetric and Asymetric Encryption Visualization

Shor’s v. RSA and ECC Vulnerabilities

RSA encryption involves factoring large semi-prime numbers (products of two large prime numbers); while, ECC security uses the complexity of the elliptic curve discrete logarithm problem. Standard algorithms, like the general number field sieve, require significantly exponential time to factor in large numbers, making decryption impractical without the private key.

However, Shor’s Algorithm leverages quantum computing’s ability to perform quantum Fourier transforms, enabling it to factor large numbers exponentially faster than classical methods. Thus, once quantum computers reach a sufficient scale, they could render RSA and ECC encryption obsolete.

Limitations of Classical Computing

Classical computers rely on brute-force or highly optimized number field sieve methods for integer factorization, which scale poorly as key sizes increase. A 2048-bit RSA key, for example, is currently considered secure because even the most powerful supercomputers would take thousands of years to factor it.

On the other hand, an advanced QC employing Shor’s Algorithm could break a 2048-bit RSA key in hours or days.

While current quantum computers are not yet powerful enough to execute Shor’s Algorithm on meaningful key sizes, rapid advancements in quantum hardware suggest that cryptographically relevant quantum computers could emerge within the next two decades.

Post quantum cryptography (PQC) is the domain addressing these topics, working on developing mathematical scenarios that should be resistant to quantum attacks.

How Grover’s Algorithm Affects Symmetric Encryption

Unlike Shor’s Algorithm which directly compromises public-key cryptography, Grover’s Algorithm threatens symmetric encryption with faster brute-force attacks. Typical brute-force methods check all possible keys in sequence, making key length especially important. Grover’s Algorithm allows QCs to search through possibilities in time.

Impact on Encryption Standards

The Advanced Encryption Standard (AES), which is widely used for secure communication, is particularly affected by Grover’s Algorithm. AES-128, for instance, would be drastically reduced, making it vulnerable to quantum attacks. Also, cryptographic hash functions like SHA-256, which are used for data integrity verification and digital signatures, would see their effective security halved, making collision attacks more feasible.

One primary way to counteract Grover’s Algorithm is to double the key size of symmetric encryption schemes. For example, AES-256 would offer an equivalent quantum security level of AES-128, maintaining an acceptable level of protection. Also, increasing the output size of hash functions can help maintain resistance. These tactics do provide mitigation, but they do not eliminate the risks entirely, making developing quantum-resistant cryptographic techniques necessary for long-term security.

The U.S. National Institute of Standards and Technology (NIST) is leading a worldwide initiative to standardize post-quantum cryptographic algorithms. Several promising approaches to PQC include:

• Lattice-based cryptography: Relies on the hardness of mathematical problems like the Shortest Vector Problem (SVP) and Learning With Errors (LWE), which remain resistant to classical and quantum attacks.
• Hash-based cryptography: Uses secure hash functions to create digital signatures, providing a quantum-resistant alternative to RSA and ECC-based signatures.
• Multivariate polynomial cryptography: Based on solving systems of multivariate polynomial equations, an approach that has proven difficult for both classical and quantum computers to crack.

Cybersecurity in the Quantum Era

QC evolution is making it necessary for businesses and governments to be proactive about cybersecurity posture assessments and proactive mitigations. Organizations should adopt cryptographic agility (switching between cryptographic algorithms without significant disruptions). This includes implementing hybrid encryption models that combine classical and post-quantum cryptographic techniques, ensuring a smooth transition as quantum-resistant standards emerge.

Many Bitcoin developers are migrating to quantum-resistant signature schemes, eg. from ECDSA to PQC-based wallets.​

Steps for future-proofing data can include:

• Inventorying and assessing cryptographic dependencies to identify vulnerabilities to quantum threats.
• Beginning testing post-quantum cryptographic algorithms in non-critical systems using SAIF CHECK’s Quantum Cryptography risk assessment.
• Planning a phased migration strategy to replace quantum-vulnerable encryption with quantum-safe alternatives, using SAIF CHECK’s Control Reports.