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Substitution-permutation network

 

 
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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....
, an SP-network, or substitution-permutation
Permutation

In several fields of mathematics the term permutation is used with different but closely related meanings. They all relate to the notion of mapping the element s of a set to other elements of the same set, i.e., exchanging elements of a set....
 network (SPN), is a series of linked mathematical operations used in block cipher
Block cipher

In cryptography, a block cipher is a symmetric key algorithm cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation....
 algorithms such as AES
Advanced Encryption Standard

In cryptography, the Advanced Encryption Standard is an encryption standard adopted by the Federal government of the United States. The standard comprises three block ciphers, AES-128, AES-192 and AES-256, adopted from a larger collection originally published as Rijndael. Each AES cipher has a 128 bit block size, with key sizes of 128...
.

These networks consist of S-boxes
Substitution box

In cryptography, an S-box is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the Key and the ciphertext — Claude Shannon property of confusion and diffusion....
 and P-boxes
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 ....
 that transform blocks of input bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s into output bits. It is common for these transformations to be operations that are efficient to perform in hardware, such as exclusive or
Exclusive disjunction

The Logical connective exclusive disjunction, also called exclusive or , is a type of logical disjunction on two operands that results in a value of true if and only if exactly one of the operands has a value of true....
 (XOR) and bitwise rotation.

S-boxes substitute or transform input bits into output bits.






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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....
, an SP-network, or substitution-permutation
Permutation

In several fields of mathematics the term permutation is used with different but closely related meanings. They all relate to the notion of mapping the element s of a set to other elements of the same set, i.e., exchanging elements of a set....
 network (SPN), is a series of linked mathematical operations used in block cipher
Block cipher

In cryptography, a block cipher is a symmetric key algorithm cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation....
 algorithms such as AES
Advanced Encryption Standard

In cryptography, the Advanced Encryption Standard is an encryption standard adopted by the Federal government of the United States. The standard comprises three block ciphers, AES-128, AES-192 and AES-256, adopted from a larger collection originally published as Rijndael. Each AES cipher has a 128 bit block size, with key sizes of 128...
.

These networks consist of S-boxes
Substitution box

In cryptography, an S-box is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the Key and the ciphertext — Claude Shannon property of confusion and diffusion....
 and P-boxes
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 ....
 that transform blocks of input bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s into output bits. It is common for these transformations to be operations that are efficient to perform in hardware, such as exclusive or
Exclusive disjunction

The Logical connective exclusive disjunction, also called exclusive or , is a type of logical disjunction on two operands that results in a value of true if and only if exactly one of the operands has a value of true....
 (XOR) and bitwise rotation.

S-boxes substitute or transform input bits into output bits. A good S-box will have the property that changing one input bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
 will change about half of the output bits. It will also have the property that each output bit will depend on every input bit. P-boxes take the S-box outputs of one round, permute or transpose bits, and feed them into the S-box inputs of the next round. In addition, at each round 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....
 is combined using some group operation, typically XOR. While a single typical S-box adds only a limited amount of diffusion and a single typical P-box only adds a limited amount of confusion, a well-designed SP network has enough rounds that changing any input bit changes every output bit of the entire message with equal probability.

For a given amount of confusion and diffusion
Confusion and diffusion

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Elwood Shannon in his paper, "Communication Theory of Secrecy Systems" published in 1949....
, a SP network has more parallelism and so can be computed faster on modern CPUs than a Feistel network.

See also

  • 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....
  • Square
    Square (cipher)

    In cryptography, Square is a block cipher invented by Joan Daemen and Vincent Rijmen. The design, published in 1997, is a forerunner to the Rijndael algorithm, which has been adopted as the Advanced Encryption Standard....
  • International Data Encryption Algorithm
    International Data Encryption Algorithm

    In cryptography, the International Data Encryption Algorithm is a block cipher designed by Xuejia Lai and James Massey of ETH Zurich and was first described in 1991....