Confusion (cryptology)

In cryptology, confusion is one of the two central principles for obfuscating the structures of plain text in the course of encryption or hashing . The other of these principles is diffusion . They go back to the American mathematician Claude Shannon .

purpose

As far as possible, no relationship should be discernible between plain text and ciphertext that could be exploited for an attack . Every change in the plain text should have an unpredictable effect on the ciphertext, and structures of the plain text should no longer be recognizable in the ciphertext. An example of the structure of plain text is the frequency of letters . If certain characters or bytes appear more frequently in plain text than others, nothing should be recognizable in the ciphertext.

realization

To achieve confusion, a cryptographic method must contain non-linear operations. A mapping of the input bits to a specific output bit is considered to be linear if the result is only calculated by additions in the field GF (2), i.e. by XORing input bits and possibly negating the result. In other words, the result can be expressed as a polynomial of degree 1 in the input bits. ${\ displaystyle f: \ {0.1 \} ^ {n} \ rightarrow \ {0.1 \}}$

It would therefore be a mistake to calculate the ciphertext bits only by XORing plaintext and key bits. A linear cryptanalysis would easily break such a procedure .

In contrast, the addition of two data words modulo , where the number of bits in a word is not linear . This is because the carry bit to the next point by AND operation is calculated of input, that is by multiplication in GF (2). ${\ displaystyle 2 ^ {e}}$ ${\ displaystyle e}$

A cryptographic method is usually constructed as a sequence of many similarly structured rounds. Each round consists in applying a round function to the data block. If every round contains non-linear operations, then the confusion increases with each additional round, i.e. H. the degree of the simplest polynomial with which the mapping of the input bits to a result bit can be expressed increases with the number of rounds. With a sufficient number of rounds, you can create enough confusion to make the process cryptographically secure.

It turns out that the alternating use of addition and bitwise XOR operation is cryptographically more effective than addition alone. Examples of block ciphers that only use addition and XOR to generate confusion are FEAL , TEA , XTEA and Threefish . A method consisting of only A ddition, R otation of data words and X OR are constructed such as Three Fish, also called ARX ciphers.

Many cryptographic methods contain S-boxes as components, which cause a lot of confusion, since one can largely freely choose how an a × b S-box maps the possible values of the input bits to the possible output values. S-boxes are z. B. used in the encryption methods DES , AES , Blowfish , CAST and Serpent . ${\ displaystyle 2 ^ {a}}$ ${\ displaystyle a}$ ${\ displaystyle 2 ^ {b}}$

Individual evidence

^ Klaus Pommerening: Linearity measures for Boolean maps. July 4, 2008, accessed August 9, 2020 .

[nonlin-1] Klaus Pommerening: Linearity measures for Boolean maps. July 4, 2008, accessed August 9, 2020 .