The most important and interesting about encryption.
A series of articles understandable even to non-specialists.
Asymmetric encryption was previously discussed in this article.
One of the most recognized asymmetric encryption algorithms is RSA, named after the initials of its creators – Rivest, Shamir, and Adleman. The algorithm was developed since the mid-1970s and was patented in the US in 1983. In 1990, the RSA algorithm began to be used by the US Department of Defense. The RSA algorithm is used in data exchange protocols and digital signature protocols. This algorithm is also used in cryptocurrency blockchains.
The mathematical basis of the RSA algorithm
Mathematically, the basis upon which the RSA algorithm operates is factorization. Recall that a Prime number is a number that can only be divided exactly by 1 and by itself. A good example of a Prime number is 17. The RSA algorithm employs random prime numbers, say p and q, of large values. They are then multiplied and the resulting number n is used in several mathematical operations. As a result, we have two values: one secret (the same back door – private key) and one public (public key).
For those who are good at math, the process looks like this:
As for the cryptographic robustness of the RSA algorithm, the main task of a potential hacker is to calculate two prime factors p and q. In 2010, this task was successfully performed by a group of scientists who were able to calculate the prime factors for the 768-bits cryptographic key of RSA. It took two years and hundreds of computers to crack the RSA-768. Scientists have concluded that the RSA algorithm can be stable only if the key size is at least 1024 bits. But processing speed of computers is increasing, and the 1024-bit key is not enough for reliable protection of information. Currently, the recommended RSA key length is 2048 bits, but will not last long. Unfortunately, if the intruders managed to get the secret key, they will be able to read not only the current encrypted message but all the previous ones. In addition, the cracking of the RSA algorithm is an easy task for a quantum computer. You can read more about it here.