# Can we break an RSA algorithm

## AES and RSA encryption

### This is how we encrypt here at Boxcryptor

We encrypt files and thus ensure increased protection against espionage and data theft. We use a combination of AES-256 encryption and RSA encryption for encryption. Here we explain the two algorithms.

### AES-256 encryption

The public encryption algorithm **Advanced Encryption Standard (AES)** is one of the most widely used and most secure encryption methods. For example, it is used in the United States for government documents of the highest level of confidentiality.

Its success story began in 1997 when a successor to the aging encryption standard DES was sought. The search officially announced by the standard institute NIST lasted four years. In the end, the Rijndael algorithm - developed by Joan Daemen and Vincent Rijmen - prevailed against the large number of applicants. It was convincing in terms of security as well as performance and flexibility. In 2001 it was officially announced as the new AES standard.

Its mode of operation is based on a series of byte replacements (substitutions), scrambling (permutations) and linear transformations that are carried out on data blocks of 16 bytes - hence the name block encryption. These operations are repeated several times, with an individual round key calculated from the key being used in the calculations in each of these rounds. If only a single bit in the key or in the data block is changed, a completely different cipher block is created - an advantage over traditional stream encryption.

The designations AES-128, AES-192 and AES-256 specify the length of the key: 128, 192 or 256 bits - a drastic improvement on the DES key length of 56 bits. For comparison: cracking a 128-bit key with a modern supercomputer would take longer than the assumed age of the universe - and Boxcryptor uses a 256-bit key. To date, no practically feasible attack is known for any of the AES variants. AES is therefore the preferred encryption standard for governments, banks and high-security systems worldwide. And for Boxcryptor.

### RSA encryption

**RSA** is one of the currently most widespread asymmetric encryption systems. It was originally developed in 1973 by the English secret service GCHQ, but then placed under the highest level of secrecy. The encryption method owes its civil rediscovery to the cryptologists Ron Rivest, Adi Shamir and Leonard Adleman (hence the abbreviation RSA), who came across it in 1977 while analyzing another cryptographic problem.

In contrast to classic, symmetrical encryption methods, RSA works with two keys: a public and a private key. To decrypt a message, you then need the counterpart of the key used for encryption. As a rule, the public key is generally accessible since it is not possible to calculate the private key from it.

This property enables a wide range of applications for asymmetric cryptosystems, the most common of which is the digital signature. A fingerprint encrypted with RSA is attached to a file, with which the recipient can verify both the sender and the integrity of the document.

The security of RSA is based on the mathematical problem of breaking up large numbers into their prime factors. A message to be encrypted is viewed by the algorithm as a single, large number. When encrypting, the message is raised to the power of the key, and the remainder is divided by a specified product of two prime numbers. If you repeat this process with the opposite key, you get the plain text back. The best known way to break the encryption is to calculate the prime factors of the divisor. However, it is currently not possible to calculate these factors for numbers larger than 768 bits. Because of this, modern security systems rely on keys with a minimum length of 3072 bits.

### Encryption at Boxcryptor

Boxcryptor implements a combined encryption process based on asymmetrical RSA and symmetrical AES-256 encryption. Each file has its own unique and randomly generated file key that is generated when the file is created.

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