Letter 003: The secret of Prime Numbers
Prime numbers in cryptography
Hi everyone,
Before talking about prime numbers, I want to share one of my personal experiences with you.
Finding the truth in modern life is almost impossible for most people. It’s not just because of misinformation or disinformation, but also because of information overload. Fortunately, this kind of external noise can be filtered out relatively easily. However, we have an even more formidable enemy inside us: the ego.
Our egos do not like being proven wrong. They can trick us into believing almost anything we want to believe, even when it is completely detached from reality. So how do we sift through all the internal and external noise to find “the truth, and nothing but the truth”?
Over the years, I have developed a few mental models to help me stay on track in my search for the truth. Today, I’d like to share one of them.
When you hear a statement, ask yourself these questions:
Is there a way to prove it?
Is there a way to disprove it?
Am I prepared to accept the truth and let go of beliefs that turn out to be false?
If you cannot answer “yes” to all three questions, then you may not be in a position to make a sound judgment.
Prime Numbers and Cryptography
You may have heard that prime numbers play a key role in encryption. I’ll explain the basic idea without getting too deep into the mathematics.
Multiplying two prime numbers together is easy. However, working backward is much harder.
For example, you can quickly calculate that 13 × 19 = 247. But if I give you the number 247 and ask for its prime factors, you will probably need to spend some time figuring them out. Now imagine that instead of 247, I give you a number with hundreds of digits.
There is no algorithm to find the prime factors of a given number. We have to try all possible prime numbers starting from 1 to produce that result number. For sufficiently large numbers, even powerful computers would need an impractical amount of time to find the prime factors.
This creates what mathematicians call a “one-way function.” If you know the prime factors, calculating their product is easy. But if you only know the product, finding the original prime factors can be extraordinarily difficult.
This idea forms the foundation of public-key cryptography.
In simple terms, two large prime numbers are used to create a public key and a private key. The public key can be shared with anyone. The private key remains secret.
Anyone can use the public key to encrypt a message and send it to me. However, only I can decrypt that message because only I possess the private key.
This simple idea allows people all over the world to communicate securely, exchange sensitive information, and conduct online transactions without ever having to share their private keys.
Pretty amazing for something that starts with prime numbers.
Have a great week!