# Cryptography/Brute force attack

A **brute force attack** against a cipher consists of breaking a cipher by trying all possible keys. Statistically, if the keys were originally chosen randomly, the plaintext will become available after about half of the possible keys are tried. The underlying assumption is, of course, that the cipher is known. Since A. Kerckoffs first published it, a fundamental maxim of cryptography has been that security must reside only in the key. As Claude E. Shannon said a few decades later, 'the enemy knows the system'. In practice, it has been excellent advice.

As of the year 2002, symmetric ciphers with keys 64 bits or fewer are vulnerable to brute force attacks. DES, a well respected symmetric algorithm which uses 56-bit keys, was broken by an EFF project in the late 1990s. They even wrote a book about their exploit -- Cracking DES, O'Reilly and Assoc. The EFF is a non-profit cyberspace civil rights group; many people feel that well-funded organisations like the NSA can successfully attack a symmetric key cipher with a 64-bit key using brute force. This is surely true, as it has been done publicly. Many observers suggest a minimum key length for symmetric key algorithms of 128 bits, and even then it is important to select a secure algorithm. For instance, many algorithms can be reduced in effective keylength until it is computationally feasible to launch a brute force attack. AES is recommended for use until at least 2030.

The situation with regard to asymmetric algorithms is much more complicated and depends on the individual algorithm. Thus the currently breakable key length for the RSA algorithm is at least 768 bits (broken publicly since 2009), but for most elliptic curve asymmetric algorithms, the largest currently breakable key length is believed to be rather shorter, perhaps as little as 128 bits or so. A message encrypted with a 109 bit key by an elliptic curve encryption algorithm was publicly broken by brute force key search in early 2003. As of 2015, a minimum key length of 224 bits is recommended for elliptic curve algorithms, and 2048 bits for such other asymmetric key algorithms as RSA (asymmetric key algorithms that rely on complex mathematical problems for their security always will need much larger keyspaces as there are short-cuts to cracking them, as opposed to direct brute-force).

## Contents

## Common Brute Force Attacks[edit]

The term "brute force attacks" is really an umbrella term for all attacks that exhaustively search through all possible (or likely) combinations, or any derivative thereof.

### Dictionary Attack[edit]

A dictionary attack is a common password cracking technique, relying largely on the weak passwords selected by average computer users. For instance, if an attacker had somehow accessed the hashed password files through various malicious database manipulations and educated searching on an online store, he would then write a program to hash one at a time all words in a dictionary (of, for example any or all languages and common derivative passwords), and compare these hashes to the real password hashes he had obtained. If the hashes match, he has obtained a password.

#### Pre-Computation Dictionary Attack[edit]

The simple dictionary attack method quickly becomes far too time-consuming with any large number of password hashes, such as an online database would yield. Thus, attackers developed the method of pre-computation. In this attack, the attacker has already hashed his entire suite of dictionaries, and all he need do is compare the hashes. Additionally, his task is made easier by the fact that many users will select the same passwords. To prevent this attack, a database administrator must attach unique 32-bit salts to the users passwords before hashing, thus rendering precompution useless.

## Responses to Brute Force Attacks[edit]

There are a number of ways to mitigate brute force attacks. For example:

- Changing a key frequently in response to an attempt to try all possible keys would require an attacker to start over assuming he knew the key was changed or finish attempting all possible keys before starting the attack again from the beginning.
- A system could rely on a time out or lock out of the system after so many attempts at guessing the key. Systems that time out can simply block further access, lock a user account, contact the account owner, or even destroy the clear text information.
- 2 step verification is a method of requiring a second key to enter the system. This complicates a brute force attack since the attacker must not only guess one key but then guess a second possibly equally complex key. The most common implementation of this is to ask for further authentication "What's your first dogs name?". There is a new trend on the horizon for systems to utilize two step verification through a time based key that is emailed or texted and having access to an account or particular electronic device serves as a secondary key.