In cryptography

Cryptography

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

, mod n cryptanalysis is an attack

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...

 applicable to block

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...

 and stream cipher

Stream cipher

In cryptography, a stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream . In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of successive digits varies during the encryption...

s. It is a form of partitioning cryptanalysis

Partitioning cryptanalysis

In cryptography, partitioning cryptanalysis is a form of cryptanalysis for block ciphers. Developed by Carlo Harpes in 1995, the attack is a generalization of linear cryptanalysis. Harpes originally replaced the bit sums of linear cryptanalysis with more general balanced Boolean functions...

 that exploits unevenness in how the cipher

Cipher

In cryptography, a cipher is an algorithm for performing encryption or decryption — a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...

 operates over equivalence classes (congruence classes) modulo n

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

. The method was first suggested in 1999 by John Kelsey

John Kelsey (cryptanalyst)

John Kelsey is a cryptographer currently working at NIST. His research interests include cryptanalysis and design of symmetric cryptography primitives , analysis and design of cryptographic protocols, cryptographic random number generation, electronic voting, side-channel attacks on cryptography...

, Bruce Schneier

Bruce Schneier

Bruce Schneier is an American cryptographer, computer security specialist, and writer. He is the author of several books on general security topics, computer security and cryptography, and is the founder and chief technology officer of BT Managed Security Solutions, formerly Counterpane Internet...

, and David Wagner and applied to RC5P (a variant of RC5

RC5

In cryptography, RC5 is a block cipher notable for its simplicity. Designed by Ronald Rivest in 1994, RC stands for "Rivest Cipher", or alternatively, "Ron's Code"...

) and M6

M6 (cipher)

In cryptography, M6 is a block cipher proposed by Hitachi in 1997 for use in the IEEE 1394 FireWire standard. The design allows some freedom in choosing a few of the cipher's operations, so M6 is considered a family of ciphers....

 (a family of block ciphers used in the FireWire standard). These attacks used the properties of binary addition and bit rotation modulo a Fermat prime.

Mod 3 analysis of RC5P

For RC5P, analysis was conducted modulo 3. It was observed that the operations in the cipher (rotation and addition, both on 32-bit words) were somewhat biased over congruence classes mod 3. To illustrate the approach, consider left rotation by a single bit:

Then, because

we can deduce that

Thus left rotation by a single bit has a simple description modulo 3. Analysis of other operations (data dependent rotation and modular addition) reveals similar, notable biases. Although there are some theoretical problems analysing the operations in combination, the bias can be detected experimentally for the entire cipher. In (Kelsey et al., 1999), experiments were conducted up to seven rounds, and based on this they conjecture that as many as nineteen or twenty rounds of RC5P can be distinguished from random using this attack. There is also a corresponding method for recovering the secret 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 produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...

.

Against M6 there are attacks mod 5 and mod 257 that are even more effective.