# SM4 (cipher)

(Redirected from SM4 algorithm)
SM4
General
DesignersChinese Government
First published2006 (declassified; standardized March 21, 2012)
Cipher detail
Key sizes128 bits
Block sizes128 bits
Structureunbalanced Feistel network
Rounds32
Best public cryptanalysis
Linear and differential attacks against 22 rounds

SM4 (formerly SMS4) is a block cipher used in the Chinese National Standard for Wireless LAN WAPI (Wired Authentication and Privacy Infrastructure).

SM4 was a cipher proposed to for the IEEE 802.11i standard, but has so far been rejected by ISO. One of the reasons for the rejection has been opposition to the WAPI fast-track proposal by the IEEE.

The SM4 algorithm was invented by Lu Shuwang (Chinese: 吕述望). The algorithm was declassified in January, 2006, and it became a national standard (GB/T 32907-2016) in August 2016.

## Cipher detail

A few details of the SM4 cipher are:

• It has a block size of 128 bits.
• It uses an 8-bit S-box.
• The key size is 128 bits.
• The only operations used are 32-bit bitwise XOR, 32-bit circular shifts and S-box applications.
• Encryption or decryption of one block of data is composed of 32 rounds.
• Each round updates a quarter (i.e., 32 bits) of the internal state.
• A non-linear key schedule is used to produce the round keys.
• Decryption uses the same round keys as for encryption, except that they are in reversed order.

## Terms and definitions

### Word and byte

Define $Z_{2}^{e}$ as a vector set of e bits.

$Z_{2}^{32}$ is a word.

$Z_{2}^{8}$ is a byte.

### S-box

S-box is fixed for 8-bit input and 8-bit output, noted as Sbox(). As with AES, the S-box is based on the multiplicative inverse over GF(28). The affine transforms and polynomial bases are different from that of AES, but due to affine isomorphism it can be calculated efficiently given an AES Rijndael S-box.

### Keys and key parameters

The length of encryption keys is 128 bits, represented as $MK=(MK_{0},\ MK_{1},\ MK_{2},\ MK_{3})$ , in which $MK_{i}\ (i=0,\ 1,\ 2,\ 3)$ is a word.

A round key is represented as $(rk_{0},\ rk_{1},\ \ldots ,\ rk_{31})$ ,where each $rk_{i}(i=0,\ \ldots ,\ 31)$ is a word. It is generated by the encryption key.

$FK=(FK_{0},\ FK_{1},\ FK_{2},\ FK_{3})$ is a system parameter.

$CK=(CK_{0},\ CK_{1},\ \ldots ,\ CK_{31})$ is a fixed parameter, used to generate $rk_{i}$ .

$FK_{i}$ and $CK_{i}$ are words, used for extension of the algorithm.

## Remark

On March 21, 2012, the Chinese government published the industrial standard "GM/T 0002-2012 SM4 Block Cipher Algorithm", officially renaming SMS4 to SM4.

A description of SM4 in english is available as an Internet Draft. It contains a reference implementation in ANSI C.