Summary of the Core Content
This article uses a concept familiar even to elementary school students—finding factors—to explain the underlying logic of the Shor algorithm, a core technique in quantum computing. It clearly outlines the inherent limitations of traditional computers when it comes to breaking down very large numbers and explains why this algorithm, developed in 1994, has become the “number one threat” to the global digital encryption system. The entire explanation avoids complex mathematical formulas, making the otherwise advanced concepts in cryptography and quantum computing accessible to a general audience.
---
Detailed Explanation of Each Point
1. Why the money in your phone is safe… thanks to “incomprehensibly large numbers”
All aspects of our digital lives—everything from WeChat payments and online banking transfers to accessing private cloud storage and transmitting confidential financial reports from listed companies, even the verification of ownership for encrypted assets like Bitcoin—rely on a technique called RSA (Rapid Secure Encryption). The basis of this technology is that it’s easy to multiply two large prime numbers together, but extremely difficult to reverse the process and determine the original prime numbers from the product. For example, multiplying two three-digit prime numbers takes just a second, but trying to reverse this process would take a long time. If the prime numbers are each over 300 digits long, the resulting number can be as large as 617 digits. Even if all the world’s supercomputers were used to try, it would take hundreds of millions of years to factorize such a number. In other words, the security of our digital economy over the past few decades has been safeguarded by this natural mathematical barrier.
2. The Shor algorithm doesn’t just rely on “billions of times faster computing power”; it changes the entire problem
A common misconception about quantum computers is that they are simply more powerful and calculate faster than traditional computers. However, that’s not the case. Traditional computers trying to factorize large numbers is like trying to open a locked door with a million keys; no matter how much computing power is combined, it would still take hundreds of millions of years to find the right key. The genius of the Shor algorithm lies in its ability to transform the problem completely. Instead of trying to factorize the number, it converts it into a completely different problem: finding the repeating pattern in a sequence of numbers. For instance, in the sequence 2, 4, 8, 2, 4, 8, 2, 4, 8, the pattern is 3. While traditional computers would have to check each number individually, the superposition principle in quantum mechanics allows them to consider all possible states simultaneously. With a quantum Fourier transform, they can instantly determine the pattern, eliminating the need for a brute-force search.
3. Why the financial world is urgently preparing for the Shor algorithm, even though it’s been around for 30 years?
Many people wonder why there was no panic when the algorithm was first proposed. The reason is that until recently, there was no hardware capable of executing the Shor algorithm effectively. To factorize a 617-digit RSA number, quantum computers would need to have tens of thousands or even hundreds of thousands of stable quantum bits. In recent years, however, quantum hardware has advanced faster than expected. Companies like Google, IBM, and domestic quantum computing firms have successfully demonstrated the Shor algorithm in laboratories, proving that such “quantum decoders” are no longer just theoretical concepts. Central banks, internet giants, and cryptography standardization organizations are working around the clock to develop new encryption standards that are resistant to quantum attacks. If we wait until practical quantum computers become available, all current encrypted data would be vulnerable. Hackers could store encrypted information for decades before the Shor algorithm can decrypt it, exposing sensitive financial records and business secrets.
4. The Shor algorithm represents the most valuable strategy in business: “changing the game to overtake competitors”
This algorithm’s approach is highly applicable to business competition. For decades, computer manufacturers have been competing by increasing computing power, but they’ve hit a ceiling in breaking down large numbers. The Shor algorithm shows that it’s possible to solve the same problem using a completely different approach. Many disruptive business innovations have followed this pattern: instead of competing in traditional ways (e.g., opening restaurants or owning taxis), companies have redefined their strategies to overcome existing barriers. For example, ride-hailing services have eliminated the need for individual taxis by integrating existing resources. The Shor algorithm’s approach demonstrates how a new, more efficient solution can emerge without relying on increased computing power. It’s a classic example of how technology can transform problems by changing the perspective and adopting a different approach.