Public-key cryptography protects your credit card information when shopping online, and explains how it maintains the confidentiality of your information through the exchange of public and private keys.

When shopping online, many people worry that someone can read the information sent between their computer and the online store’s computer and steal their credit card information. However, public key cryptography ensures that no one other than the parties sending and receiving the information can see it.
In public-key cryptography, each computer prepares a pair of keys that never overlap with any other computer. Let’s call the pair of keys that your computer has prepared public key A and secret key a. The public key A is used to communicate with other computers, and the secret key a is kept only on your computer. The information encrypted with the public key A can only be decrypted with the secret key a, and the original information cannot be decrypted with the public key A. Therefore, it is safe to give the public key A to other computers as long as only the secret key a does not leave my computer.

How public-key cryptography works

Now consider the case where you go to the online bookstore Book Village and buy a book. If the Book Village computer has a public key B and a secret key b, then as soon as my computer connects to the Book Village computer, the two computers automatically exchange their public keys, meaning that my computer knows B and the Book Village computer knows A. Now, when I enter my credit card information into my computer to order a book, my computer encrypts it with the public key B of the book village computer and sends it to it. The Book Village computer decrypts the encrypted information with its secret key B to get the original credit card information. The information sent with the public key B can only be decrypted by the Book Village computer with the secret key b, making it impossible for anyone else to decrypt my credit card information.
Since your computer’s public key A is known to other computers, this can cause problems if someone pretends to be you and orders a book from their computer with your public key A. To avoid this problem, the Book Village computer needs to verify that the information it is receiving is from your computer. To do this, the book village computer sends a random word to my computer, such as “Long live the book village,” encrypts it with my computer’s secret key A, and asks me to send the original word and the encrypted word together. In public key cryptography, the information encrypted with the secret key a can only be decrypted with the public key a. Therefore, my computer sends the original word and the encrypted word together, and the Book Village computer that receives these two pieces of information decrypts the encrypted word with the public key A and checks if it matches the original word. If they match, we know that the information must have been sent by the computer with public key A (my computer).

How secure is public-key cryptography?

Some people might worry about what happens if someone figures out the secret key a from the public key A that their computer taught them, but this is technically almost impossible. From the secret key a, the public key A can be obtained by simple computation. However, obtaining the secret key a from the public key A would take decades of computation, even on the fastest supercomputers available today. The reason for this investment of time and resources is that the mathematical foundation of public-key cryptography is very solid. It is built using mathematical problems like prime factorization, which are designed to take a very long time to solve.
Additionally, public-key cryptography continues to improve in security as computers advance. New algorithms and longer key lengths can be used to increase the strength of encryption and ensure more secure communications. Because of this, public key cryptography continues to be a reliable security technology.

Applications of public key cryptography

Public-key cryptography is used in a wide variety of fields, not just internet shopping. Examples include email security, database access control, and digital signatures. In email security, public key cryptography is used to ensure that the contents of an email are not visible to anyone other than the sender and recipient. Database access control uses public-key cryptography to ensure that users accessing a database are legitimate users and to maintain the integrity of the data. Digital signatures use public-key cryptography to verify the author of a document and prove that the document has not been altered since it was created.
Therefore, public-key cryptography is generally safe for people to use. With this technology, we can build a safer Internet environment and effectively maintain privacy and data security.
In conclusion, public key cryptography plays a very important role in online transactions such as online shopping. With this technology, we can keep our credit card information safe and secure, and we can use the Internet with confidence. In the future, public key cryptography will continue to see more advances and applications, making our digital lives safer.