cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

, integral cryptanalysis is a cryptanalytic attack that is particularly applicable to

block cipher In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called ''blocks''. Block ciphers are the elementary building blocks of many cryptographic protocols. They are ubiquitous in the storage a ...

s based on substitution–permutation networks. It was originally designed by

Lars Knudsen Lars Ramkilde Knudsen (born 21 February 1962) is a Denmark, Danish researcher in cryptography, particularly interested in the design and cryptanalysis, analysis of block ciphers, cryptographic hash function, hash functions and message authentic ...

as a dedicated attack against

Square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

, so it is commonly known as the Square attack. It was also extended to a few other ciphers related to Square: CRYPTON,

Rijndael The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant ...

, and

SHARK Sharks are a group of elasmobranch cartilaginous fish characterized by a ribless endoskeleton, dermal denticles, five to seven gill slits on each side, and pectoral fins that are not fused to the head. Modern sharks are classified within the ...

. Stefan Lucks generalized the attack to what he called a ''saturation attack'' and used it to attack Twofish, 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,

IDEA In philosophy and in common usage, an idea (from the Greek word: ἰδέα (idea), meaning 'a form, or a pattern') is the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophe ...

Camellia ''Camellia'' (pronounced or ) is a genus of flowering plants in the family Theaceae. They are found in tropical and subtropical areas in East Asia, eastern and South Asia, southern Asia, from the Himalayas east to Japan and Indonesia. There are ...

, Skipjack, MISTY1, MISTY2, SAFER++, KHAZAD, and ''FOX'' (now called IDEA NXT). Unlike

differential cryptanalysis Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can a ...

, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

s or even

multiset In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the ''multiplicity'' of ...

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 is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

References

* * * * * * * * * * * * Cryptographic attacks {{crypto-stub