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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....
, integral cryptanalysis is a cryptanalytic attack
Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so....
 that is particularly applicable to 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....
s based on 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....
s. It was originally designed by Lars Knudsen
Lars Knudsen

Lars Ramkilde Knudsen is a Denmark researcher in cryptography, particularly interested in the design and cryptanalysis of block ciphers, cryptographic hash function and message authentication codes ....
 as a dedicated attack against 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....
, so is commonly known as the Square attack. It was also extended to a few other ciphers related to Square: CRYPTON
CRYPTON

In cryptography, CRYPTON is a block cipher submitted as a candidate for the Advanced Encryption Standard . It is very efficient in hardware implementations and was designed by Chae Hoon Lim of Future Systems Inc....
, Rijndael, and SHARK
Shark

Sharks are a type of fish with a full Cartilage skeleton and a highly Streamlines, streaklines and pathlinesd body. They respire with the use of five to seven gill slits....
. Stefan Lucks
Stefan Lucks

Stefan Lucks is a researcher in the fields of communications security and cryptography. Lucks is known for his attack on Triple DES, and for extending Lars Knudsen's Square attack to Twofish, a cipher outside the Square family, thus generalising the attack into integral cryptanalysis....
 generalized the attack to what he called a saturation attack and used it to attack Twofish
Twofish

In cryptography, Twofish is a Symmetric-key algorithm block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard process, but was not selected for standardisation....
, which is not at all similar to Square, having a radically different Feistel network structure.






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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....
, integral cryptanalysis is a cryptanalytic attack
Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so....
 that is particularly applicable to 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....
s based on 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....
s. It was originally designed by Lars Knudsen
Lars Knudsen

Lars Ramkilde Knudsen is a Denmark researcher in cryptography, particularly interested in the design and cryptanalysis of block ciphers, cryptographic hash function and message authentication codes ....
 as a dedicated attack against 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....
, so is commonly known as the Square attack. It was also extended to a few other ciphers related to Square: CRYPTON
CRYPTON

In cryptography, CRYPTON is a block cipher submitted as a candidate for the Advanced Encryption Standard . It is very efficient in hardware implementations and was designed by Chae Hoon Lim of Future Systems Inc....
, Rijndael, and SHARK
Shark

Sharks are a type of fish with a full Cartilage skeleton and a highly Streamlines, streaklines and pathlinesd body. They respire with the use of five to seven gill slits....
. Stefan Lucks
Stefan Lucks

Stefan Lucks is a researcher in the fields of communications security and cryptography. Lucks is known for his attack on Triple DES, and for extending Lars Knudsen's Square attack to Twofish, a cipher outside the Square family, thus generalising the attack into integral cryptanalysis....
 generalized the attack to what he called a saturation attack and used it to attack Twofish
Twofish

In cryptography, Twofish is a Symmetric-key algorithm block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard process, but was not selected for standardisation....
, which is not at all similar to Square, having a radically different Feistel network structure. Forms of integral cryptanalysis have since been applied to a variety of ciphers, including Hierocrypt
Hierocrypt

In cryptography, Hierocrypt-L1 and Hierocrypt-3 are block ciphers created byToshiba in 2000. They were submitted to the NESSIE project, but were not selected....
, IDEA
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....
, Camellia
Camellia (cipher)

In cryptography, Camellia is a block cipher that has been evaluated favorably by several organisations, including the European Union's NESSIE project , and the Japanese CRYPTREC project ....
, Skipjack
Skipjack (cipher)

In cryptography, Skipjack is a block cipher — an algorithm for encryption — developed by the United States National Security Agency ....
, MISTY1
MISTY1

In cryptography, MISTY1 is a block cipher designed in 1995 by Mitsuru Matsui and others for Mitsubishi Electric. MISTY1 is one of the selected algorithms in the European NESSIE project, and has been recommended for Japanese government use by the CRYPTREC project....
, MISTY2, SAFER++, KHAZAD, and FOX (now called IDEA NXT
IDEA NXT

In cryptography, the IDEA NXT algorithm is a block cipher designed by Pascal Junod and Serge Vaudenay of EPFL . It was conceived between 2001 and 2003, the project was originally named FOX and was published in 2003....
).

Unlike differential cryptanalysis
Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions....
, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses set
Set

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics....
s or even multiset
Multiset

In mathematics, a multiset is a generalization of a Set . A Element of a multiset can have more than one Element , while each member of a set has only one membership....
s of chosen plaintexts of which part is held constant and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation. This contrast between the differences of pairs of texts and the sums of larger sets of texts inspired the name "integral cryptanalysis", borrowing the terminology of calculus
Calculus

Calculus is a branch of mathematics that includes the study of limit , derivatives, integrals, and infinite series, and constitutes a major part of modern university education....
.