How Long Would It Take for Quantum Computers to Break HapPhi's Encryption?

Eric Beans
October 6, 2024

We live in an era where technology moves fast, and with every leap forward comes the natural question of what risks it poses to our security systems. One of the most discussed and anticipated threats on the horizon is quantum computing. Quantum computers promise to revolutionize everything from material science to AI. However, they also pose a very real threat to cryptography—the bedrock of secure communication and data protection.

As someone working directly with lattice-based cryptography—specifically the BFV encryption scheme—the question of how long quantum computers would take to break our encryption comes up often. Let’s dive into this and break down what BFV encryption is, how quantum computers approach encryption, and what timelines we're really looking at.

What Makes BFV Encryption Strong?

The BFV encryption scheme (Brakerski/Fan-Vercauteren) is part of the Fully Homomorphic Encryption (FHE) family. It allows for encrypted data to be used in operations, like addition and multiplication, without ever needing to decrypt it. This is especially useful in fields like cloud computing and data sharing because it means sensitive information can stay private and encrypted while still being useful.

But the strength of BFV isn’t just in its ability to process encrypted data. The real strength comes from its foundation in lattice-based cryptography, which is built on the hardness of the Ring Learning With Errors (RLWE) problem. Lattice-based cryptography is known for being quantum-resistant, meaning that even future quantum computers wouldn’t easily break it.

Now, why is this? Lattice-based cryptography leverages mathematical structures (lattices) that are incredibly complex and difficult to solve. Unlike traditional encryption systems, like RSA or Elliptic Curve Cryptography (ECC), which rely on prime factorization or discrete logarithms (both of which quantum algorithms like Shor’s Algorithm can solve), RLWE-based encryption doesn’t have a known efficient quantum algorithm that can break it.

Quantum Computers: Threat or Hype?

Quantum computers are fascinating. Instead of using bits like classical computers (which are either 0 or 1), quantum computers use qubits, which can represent both 0 and 1 simultaneously due to quantum superposition. This property allows them to process vast amounts of data in parallel, providing an exponential speed-up for certain problems.

The potential quantum threat to cryptography comes from quantum algorithms. For example, Shor’s Algorithm can factor large numbers exponentially faster than any known classical algorithm, which spells disaster for encryption schemes like RSA and ECC, which are based on the difficulty of factoring large numbers or computing discrete logarithms.

However, it’s important to note that quantum computers currently have a long way to go. The largest quantum computers today operate with around 50-100 qubits, which is orders of magnitude away from the scale necessary to break the encryption we use today.

Can a Quantum Computer Break BFV Encryption?

Here’s where it gets interesting. While quantum computers are a threat to classical encryption systems like RSA, lattice-based systems like BFV are a different story.

The most well-known quantum algorithm for breaking cryptography is Shor’s Algorithm, but it doesn’t apply to lattice-based cryptography like BFV. The hardness of lattice problems remains out of reach for quantum algorithms. Even the best-known quantum algorithm for lattice-based systems, Grover’s Algorithm, can only provide a quadratic speed-up, which isn’t enough to render BFV vulnerable.

Let’s look at this in practical terms. BFV encryption operates at a level that offers security comparable to 128-bit or 256-bit AES encryption. With Grover’s Algorithm, this would reduce to an effective security level of 64 bits, which is still computationally infeasible to break.

In real-world terms, breaking a BFV-encrypted message would require a quantum computer that doesn’t just have thousands but millions of qubits—and not just any qubits, but stable, error-correcting qubits that can handle long, complex computations. As it stands, no quantum computer in existence comes remotely close to that. We’re not just decades, but multiple decades, away from quantum computers that could even begin to pose a credible threat to BFV encryption.

The Quantum Computer of Tomorrow

Even with exponential growth in quantum computing development, a quantum computer capable of breaking BFV would need several breakthroughs, including:

  1. Millions of Qubits: Today’s quantum computers have tens or hundreds of qubits, with significant error rates. A quantum computer would need to scale to millions of logical qubits to break BFV encryption.
  2. Quantum Error Correction: Quantum computers are highly prone to errors, and quantum error correction is still a developing field. Before a quantum computer can tackle cryptographic problems, it must solve the error-correction challenge to sustain long, error-free computations.
  3. Quantum Algorithms for Lattice-Based Problems: As of now, no efficient quantum algorithm exists that can solve the RLWE problem. Even with potential advances in quantum algorithms, we don’t have any reason to believe that a breakthrough is coming that will make lattice-based encryption vulnerable.

Given these hurdles, it’s unlikely that even the most advanced quantum computers in the next few decades would be able to crack BFV encryption. While quantum computing is developing rapidly, we are not yet at the point where they can threaten lattice-based encryption schemes.

What About the Future?

At Happy, we are constantly looking at both the present and future of encryption. Lattice-based cryptography, such as the BFV encryption scheme, is recognized as a leading candidate in the post-quantum cryptography race. Institutions like the National Institute of Standards and Technology (NIST) are working on standards for quantum-resistant cryptography, and lattice-based schemes are currently at the forefront.

We see this as a powerful validation that the work we’re doing with BFV encryption will hold strong, even in a future where quantum computing becomes mainstream. But we’re not standing still. At Happy, we keep a close eye on the development of quantum technologies, and as new cryptographic techniques are developed, we’ll be ready to integrate them into our solutions.

Conclusion: How Long Will It Take?

In summary, the BFV encryption scheme is built on lattice-based cryptography, which is one of the strongest candidates for post-quantum cryptography. Even with quantum computing on the rise, the RLWE problem remains unsolved by quantum algorithms, and we’re still far from the point where quantum computers pose a threat to BFV encryption.

It could take decades or longer for quantum computers to reach the level where they can even begin to crack lattice-based encryption schemes. And as that technology evolves, so will our cryptography. At Happy, we’re committed to staying ahead of the curve and ensuring that your data remains secure—today and tomorrow.

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