In cryptography

Cryptography

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

, E2 is a 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...

 which was created in 1998 by NTT

Nippon Telegraph and Telephone

, commonly known as NTT, is a Japanese telecommunications company headquartered in Tokyo, Japan. Ranked the 31st in Fortune Global 500, NTT is the largest telecommunications company in Asia, and the second-largest in the world in terms of revenue....

 and submitted to the AES competition.

Like other AES candidates, E2 operates on blocks of 128 bits, using a key of 128, 192, or 256 bits. It uses a 12-round Feistel network

Feistel cipher

In cryptography, a Feistel cipher is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel who did pioneering research while working for IBM ; it is also commonly known as a Feistel network. A large proportion of block...

. E2 has an input transformation and output transformation that both use modular multiplication

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....

, but the round function itself consists only of XORs and S-box

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 — Shannon's property of confusion...

 lookups. The single 8×8-bit S-box is constructed from the composition of an 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...

 with the discrete exponentiation

Exponentiation

Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

 x¹²⁷ over the finite field

Finite field

In abstract algebra, a finite field or Galois field is a field that contains a finite number of elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory...

 GF(2⁸). NTT adopted many of E2's special characteristics in Camellia

Camellia (cipher)

In cryptography, Camellia is a 128-bit block cipher jointly developed by Mitsubishi and NTT. The cipher has been approved for use by the ISO/IEC, the European Union's NESSIE project and the Japanese CRYPTREC project...

, which has essentially replaced E2.