This is 天風. Today I will be talking about prime factorization of extremely difficult mathematical puzzles that I am researching.
As I have mentioned before, I am an amateur researcher. In other words, I do research as a hobby. my research interests include cryptography and economics . But economics is on vacation for a while. On the other hand, cryptography is very active. I am not the person who creates the codes, but the person who solves them . Of course, eventually I would like to use that knowledge to create a code that no one can break. Basically, any kind of encryption is possible. In particular, I am currently passionate about prime factorization.
Prime factorization divides the product of prime numbers, which are either the number itself or a natural number that is divisible by 1, and derives which prime number is multiplied by which prime number. Specifically, 7 is a prime number. This is only divisible by 1 and 7 . Also, 13 is a prime number. This is also only divisible by 1 and 13. This means that 7 multiplied by 13, 7 x 13, can only be divided by 1, 7, or 13. When you look at this, it seems surprisingly easy, but when it comes to large digits, it becomes difficult to do anything.
Here's the question. Which prime number is 5017219 multiplied by?
You may need a computer to solve this. Taking advantage of this difficulty in factoring, it is also used as a code . This encryption is called RSA encryption . Currently, our lives are protected by encrypting Internet communications and financial institution PIN numbers. How long are the codes used in practice? It is also said to be 2 to the 2048th power, or approximately 10 to the 700th power. Our bank account pin numbers are protected by numbers like 10 followed by 700 zeros. This is completely impossible even with modern computers.
However, it is said that it may be possible to crack this strong code using quantum computers, which have recently become a hot topic. I'll talk about that another time.
That's why prime factorization is very difficult. This difficulty is also related to the pnp problem, which is the most difficult problem in mathematics (a short story: there is also a story that prime factorization is not NP-complete). Is there a way to efficiently perform prime factorization using modern computers? That is the author's research theme. Of course, it's not about knowing your bank PIN number. I don't have that kind of hacking ability. Just in case.
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