In cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, partitioning cryptanalysis is a form of cryptanalysis

Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

 for block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

s. Developed by Carlo Harpes in 1995, the attack is a generalization of linear cryptanalysis

Linear cryptanalysis

In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers...

. Harpes originally replaced the bit sums (affine transformation

Affine transformation

In geometry, an affine transformation or affine map or an affinity is a transformation which preserves straight lines. It is the most general class of transformations with this property...

s) of linear cryptanalysis with more general balanced

Balanced boolean function

.In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set...

 Boolean functions. He demonstrated a toy cipher that exhibits resistance against ordinary linear cryptanalysis but is susceptible to this sort of partitioning cryptanalysis. In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently-computable partitions

Partition of a set

In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...

 such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES

Data Encryption Standard

The Data Encryption Standard is a block cipher that uses shared secret encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 and which has subsequently enjoyed widespread use internationally. It is...

 and 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....

. A specific partitioning attack called mod n cryptanalysis

Mod n cryptanalysis

In cryptography, mod n cryptanalysis is an attack applicable to block and stream ciphers. It is a form of partitioning cryptanalysis that exploits unevenness in how the cipher operates over equivalence classes modulo n...

 uses the congruence classes modulo some integer for partitions.