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Confusion and diffusion
 
 
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In cryptography
Cryptography

Cryptography is the practice and study of hiding information. In modern times cryptography is considered a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering....
, confusion and diffusion are two properties of the operation of a secure cipher
Cipher

In cryptography, a cipher is an algorithm for performing encryption and decryption — a series of well-defined steps that can be followed as a procedure....
 which were identified by Claude Shannon
Claude Elwood Shannon

Claude Elwood Shannon , an United States of America electronic engineer and mathematician, is known as "the father of information theory".Shannon is famous for having founded information theory with one landmark paper published in 1948....
 in his paper, "Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems

Communication Theory of Secrecy Systems is a paper published by Claude Shannon discussing cryptography from the viewpoint of information theory....
" published in 1949.

In Shannon's original definitions, confusion refers to making the relationship between the key
Key (cryptography)

In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would have no result....
 and the ciphertext as complex and as involved as possible; diffusion refers to the property that redundancy in the statistics of the plaintext
Plaintext

In cryptography, plaintext is the information which the sender wishes to transmit to the receiver. Before the computer era, plaintext simply meant text in the language of the communicating parties....
 is "dissipated" in the statistics of the ciphertext.

Diffusion is associated with dependency of bits of the output on bits of the input.






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In cryptography
Cryptography

Cryptography is the practice and study of hiding information. In modern times cryptography is considered a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering....
, confusion and diffusion are two properties of the operation of a secure cipher
Cipher

In cryptography, a cipher is an algorithm for performing encryption and decryption — a series of well-defined steps that can be followed as a procedure....
 which were identified by Claude Shannon
Claude Elwood Shannon

Claude Elwood Shannon , an United States of America electronic engineer and mathematician, is known as "the father of information theory".Shannon is famous for having founded information theory with one landmark paper published in 1948....
 in his paper, "Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems

Communication Theory of Secrecy Systems is a paper published by Claude Shannon discussing cryptography from the viewpoint of information theory....
" published in 1949.

In Shannon's original definitions, confusion refers to making the relationship between the key
Key (cryptography)

In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would have no result....
 and the ciphertext as complex and as involved as possible; diffusion refers to the property that redundancy in the statistics of the plaintext
Plaintext

In cryptography, plaintext is the information which the sender wishes to transmit to the receiver. Before the computer era, plaintext simply meant text in the language of the communicating parties....
 is "dissipated" in the statistics of the ciphertext.

Diffusion is associated with dependency of bits of the output on bits of the input. In a cipher with good diffusion, flipping an input bit should change each output bit with a probability of one half (this is termed the Strict Avalanche Criterion
Avalanche effect

In cryptography, the avalanche effect refers to a desirable property of cryptographic algorithms, typically block ciphers and cryptographic hash functions....
).

Substitution
Substitution cipher

In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth....
 (a plaintext
Plaintext

In cryptography, plaintext is the information which the sender wishes to transmit to the receiver. Before the computer era, plaintext simply meant text in the language of the communicating parties....
 symbol is replaced by another) has been identified as a mechanism for primarily confusion (see S-box); conversely transposition
Transposition (mathematics)

In informal language, a transposition is a function that swaps two elements of a set. More formally, given a finite set Set , a transposition is a permutation such that there exist indices such that , and for all other indices This is often denoted as ...
 (rearranging the order of symbols, see P-box
Permutation box

In cryptography, a permutation box is a Method of bit-shuffling used to permute or Transposition bits across Substitution box inputs, retaining Confusion and diffusion while Transposition ....
) is a technique for diffusion, although other mechanisms are also used in modern practice, such as linear transformations (e.g. in Rijndael). Product cipher
Product cipher

In cryptography, a product cipher is a popular type of block cipher that works by executing in sequence a number of simple transformations such as substitution cipher, transposition cipher, and modular arithmetic....
s use alternating substitution
Substitution cipher

In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth....
 and transposition phases to achieve both confusion and diffusion respectively.

See also

  • Substitution-permutation network
    Substitution-permutation network

    In cryptography, an SP-network, or substitution-permutation network , is a series of linked mathematical operations used in block cipher algorithms such as Advanced Encryption Standard....