An RSA cryp­tosys­tem is an asym­met­ric en­cryp­tion that is used in online data transfers due to its ease of use. It consists of a public and a private RSA key. The public key is used for en­cryp­tion and its private coun­ter­part for de­cryp­tion. Since there is no algorithm that can determine the private key from the public key, the method is con­sid­ered secure. In addition to en­cryp­tion, the RSA cryp­tosys­tem is also suitable for gen­er­at­ing digital sig­na­tures.

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What is RSA en­cryp­tion?

The most important feature of asym­met­ric en­cryp­tion is that there is not a single key to re-decrypt a file, for example, but two. In RSA en­cryp­tion, there is a public key, which is freely ac­ces­si­ble, and a private key, which should prefer­ably only be known to a single person. The original en­cryp­tion is done with the public RSA key. However, the private RSA key is required for de­cryp­tion. If the key is lost, the en­cryp­tion can almost certainly not be broken.

The basis of the RSA cryp­tosys­tem is the trapdoor function known from math­e­mat­ics. This states that a function can only be reversed if ad­di­tion­al in­for­ma­tion is in­tro­duced. If this in­for­ma­tion isn’t provided, there are too many variables, meaning a solution cannot be cal­cu­lat­ed in a realistic time frame. In the case of the RSA cryp­tosys­tem, the private RSA key contains this ad­di­tion­al in­for­ma­tion.

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How are RSA keys used?

An RSA cryp­tosys­tem can be used to convert data, text, or even an image into an algorithm and made un­rec­og­niz­able. Without the private RSA key, the cor­re­spond­ing file remains un­read­able and can neither be de­ci­phered with the naked eye nor decoded by a program. The un­der­ly­ing data is first converted into natural numbers and then encrypted using the public RSA key. Both the public and the private RSA key consist of a pair of numbers, with one of the two numbers being identical in each case. This number is called the RSA module.

The two remaining numbers are called the en­cryp­tion exponent and de­cryp­tion exponent. They are formed from randomly selected prime numbers that have ap­prox­i­mate­ly the same scale but should not be too close to each other. Then, the numbers are cal­cu­lat­ed using math­e­mat­i­cal formulas. The en­cryp­tion process is publicly available and can therefore be easily re­pro­duced. However, to make the encrypted text readable again, the private RSA key is needed in addition to the public key. Until now, there has been no algorithm that reliably breaks down a number into its prime factors.

Image: Example of RSA encryption
Without the private RSA key, the en­cryp­tion cannot be unlocked. / Source: https://trav­is­tid­well.com/jsencrypt/demo/

What are RSA cryp­tosys­tems used for?

RSA en­cryp­tion is used in many areas of everyday digital life. For example, the com­mu­ni­ca­tion protocol HTTPS (Hypertext Transfer Protocol Secure) or SSL cer­tifi­cates are in most cases secured with an RSA en­cryp­tion. An RSA cryp­tosys­tem is also suitable for en­crypt­ing emails, digital mes­sen­gers, image data, or a hard disk. Since de­cryp­tion would take too much time even at the highest computing power without the necessary RSA key, the method is con­sid­ered com­par­a­tive­ly secure.

In many cases, an RSA cryp­tosys­tem is combined with other methods of en­cryp­tion to ensure that content or data cannot be opened or read without au­tho­riza­tion. Even if you convert your website to SSL, in most cases a com­bi­na­tion of different en­cryp­tions is used.

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Digital sig­na­tures using RSA en­cryp­tion

In addition to RSA en­cryp­tion, which is used, for example, in SSL or TLS protocols the technique is also suitable for creating a digital signature. To confirm the au­then­tic­i­ty of a message or file, and to also ensure that the file has not been sub­se­quent­ly edited, the signature is created using the private RSA key. The public key can then be used to check whether the signature and the cor­re­spond­ing file still match.

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