What is asynchronous RSA encryption?

Asynchronous RSA encryption is a cryptographic method based on the RSA algorithm used to transfer information securely over insecure networks (such as the internet). The term ‘asynchronous’ in this context means that the encryption and decryption are done with different keys. This is different from symmetric encryption methods, where the same key is used to both encrypt and decrypt the data.

RSA Encryption Basics

RSA is an acronym for the names of the three inventors: Rivest, Shamir and Adleman, who developed the method in 1977. It is one of the best-known asymmetric encryption methods and uses two mathematically related keys:

1. public key
2. Private key (Private Key)

The public key is used to encrypt data and the private key is used to decrypt that encrypted data.

Asymmetric encryption (also known as public-key encryption)

In asymmetric encryption (such as RSA), there are two keys:

• The public key is publicly distributed and can be used by anyone to encrypt data. It is not secret.
• The private key remains secret and is used only by the person or system that created it to decrypt data encrypted with the public key.

Asynchronous RSA encryption means that when sending a message, the sender uses the recipient’s public key to encrypt the message. Only the recipient, who has the matching private key, can decrypt this message.

How RSA encryption works

1. Key generation:
   First, two large prime numbers ( p ) and ( q ) are randomly selected to generate the private and public keys. These prime numbers are combined to calculate the modulus ( n = p × q ), which is part of the public key.
2. Public key (Public Key):
   The public key consists of the modulus ( n ) and an exponent ( e ). The exponent ( e ) is a number that is related to the encryption and is publicly known.
3. Private key (Private Key):
   The private key also consists of the modulus ( n ), but also of a different exponent ( d ), which remains secret and is only known to the owner of the private key. The private key is calculated using a mathematical formula from ( p ), ( q ) and ( e ).
4. Encryption:
   To encrypt a message ( M ), it is processed with the recipient’s public key and the formula
   [
   C = M^e \mod n
   ],
   where ( C ) is the cipher text (i.e. the encrypted message).
5. Decryption:
   The recipient decrypts the message ( C ) with his private key and the formula
   [
   M = C^d \mod n
   ]
   where ( M ) is the original, unencrypted message (plaintext).

Since the private key is only known to the recipient, no one else can decrypt the message, even if they know the public key.

RSA applications

RSA is widely used in the following areas:

1. Secure communication: RSA is frequently used in SSL/TLS protocols, which are used for secure connections on the internet. Here, RSA is used for the secure exchange of keys to establish an encrypted connection between a web server and a browser.
2. Digital signatures: RSA can also be used to create digital signatures. This involves using the sender’s private key to sign a message, and the recipient can use the sender’s public key to verify that the signature is valid and that the message has not been altered.
3. Key exchange: In many protocols, RSA is used to securely exchange keys that are then used for symmetric encryption of data (e.g. when establishing a secure connection).
4. Cryptocurrency: Many cryptocurrencies use RSA or similar methods to verify digital signatures and guarantee the authenticity of transactions.

Advantages of RSA encryption

1. High security: RSA’s security is based on the mathematically difficult task of factoring large numbers. An attacking third party would have to calculate the private key by factoring a very large modulus ( n ), which is virtually impossible even with modern computers when sufficiently large numbers are used.
2. Key exchange without security gaps: Since the private key is never transmitted over the network, it remains secret and safe from attackers.
3. Use for digital signatures: RSA is also used to create digital signatures that guarantee the authenticity and integrity of messages or transactions.

Conclusion

Asynchronous RSA encryption provides a secure method for exchanging data over insecure networks. It is based on the principle of using two different keys – a public and a private key. This technique is very secure and is used in a wide variety of applications, particularly for secure communication, authentication and digital signatures. However, RSA is computationally expensive, which is why it is often combined with symmetric methods in practice.