Symmetrical algorithms:

These algorithms have only one key that is used for encrypt and decrypt. This is shown in the next figure.

As we said before, the algorithm is widely known, such as our padlock of the figure, but only the one who has the key (which is the secret) can operate it, yellow in our case. As we can see, the same key is used in both ends.

The key length gives the strength of the symmetric algorithms. Let’s imagine the example of the key of a padlock. If someone has to guess the shape of the key without having any clues, the longer the key, the better. It will have more variability of teeth and cracks. It is the same with the informatics concept: the longer the keys are (more bits), the safer it is. Symmetric algorithms are very quick to encrypt and decrypt a bunch of information, and that makes them suitable to encrypt a complete file, an executable program, or an image. The great limitation of symmetric algorithms happens when working with the same key becomes a problem. Justly, the distribution of the key among people who wish to operate between themselves supposes that they meet somewhere or that they have another confident way for distributing the key. In general, we say that they are handier in cases 1 to 1, where only two persons must know the same key. There are lots of symmetric algorithms –the blocks mentioned before as "public algorithm" – for example DES, Triple DES, AES, Blowfish, IDEA among others.

DES algorithm

No doubt, DES (Data Encryption Standard) is the symmetric algorithm mostly used until nowadays. It was created in 1974, and the USA government adopted it as standard in 1977. It became ANSI standard in 1981 Surprisingly, the original algorithm proposed by IBM had a 128 bits key, but the standard adopted, shortened it to 64 bits. The key is considered a little bit short for the actual computers. This was demonstrated in 1998, when different joint people used the brute force method, and broke it. However, this method is still considered strong since it hasn’t shown any theoretical debility.

The DES algorithm codifies plain text blocks of 64 bits, using a 64 bits key, and producing a ciphered text of also 64 bits.

Variants of the DES algorithm:

Many varieties have been tried on the DES algorithm, but they’ve shown very little or no improvement at all compared to the original. Some of them have even shown worse behaviors. The most used DES version is the one that points to solve the problem of the key length. This variety is called "Triple DES". On Triple DES, we encrypt with the k1 key, decrypt with k2, and encrypt once again with k1. The resultant key is the concatenation of k1 and k2, with a length of 112bits. Next picture shows this.

The decryption process is the opposite. Following the complete sequence of transformations, we can see that each stage deciphers what was ciphered with the same key, using the opposite algorithm, so the plain text is obtained again at the end.

Symmetric algorithms cryptoanalysis

DES has motivated different ways for cryptoanalysis. None of them has succeeded, but yet they have "professionalized" this activity, causing successful attacks to other algorithms. The easiest attack is the so called "brute force". It simply tries out all possible keys, since one of them produces the plaintext. Next table shows the time needed to try all possible combinations. easiest attack is the so called "brute force". It simply tries out all possible keys, since one of produces the plaintext. Next table shows the time needed to try all possible combinations.

It is then clear, that a key length of 128 bits or more, makes senseless to try all keys. On the table we can see the required time to try all combinations if a cipher is done every microsecond (a realistic speed nowadays) and if a million (106) ciphers are done every microsecond (reachable speed on the near future). It is useful to note that 109 is equivalent to a 1 followed by nine ceros.

The two most used schemas are based in having many plain texts and their correspondent ciphered ones. Using different keys each time we use DES –"session keys"-, brings more security to the algorithm. We will talk about them now.

Differential cryptoanalysis:

Its principle is to analyze two ciphered texts coming from two plain texts, which have special differences between them (number of bits). The ciphered texts are analyzed looking for keys that have high probability to produce those differences. Having analyzed more ciphered texts pairs, one of the keys will become the most probable.

Linear cryptoanalysis:

This method is based on making a logical XOR operation among some bits from the plain text, and then doing the same, but with a ciphered text. We make then XOR with both results from before, obtaining only one bit. If we do this procedure to many plain-ciphered pairs of texts, we can see whether we get more zeros or more ones. The presence of much more zeros than ones, or vice versa, is used to assign matching probabilities to the analyzed key.

Néstor Pisciota
Universidad Blas Pascal