LEA (cipher)

LEA

LEA encryption round function
General
Designers	Deukjo Hong, Jung-Keun Lee, Dong-Chan Kim, Daesung Kwon, Kwon Ho Ryu, Dong-Geon Lee
First published	2013
Cipher detail
Key sizes	128, 192, or 256 bits
Block sizes	128 bits
Structure	ARX (modular Addition, bitwise Rotation, and bitwise XOR)
Rounds	24, 28, or 32 (depending on key size)
Best public cryptanalysis
As of 2019, no successful attack on full-round LEA is known.

The Lightweight Encryption Algorithm (also known as LEA) is a 128-bit block cipher developed by South Korea in 2013 to provide confidentiality in high-speed environments such as big data and cloud computing, as well as lightweight environments such as IoT devices and mobile devices.^[1] LEA has three different key lengths: 128, 192, and 256 bits. LEA encrypts data about 1.5 to 2 times faster than AES, the most widely used block cipher in various software environments.

LEA is one of the cryptographic algorithms approved by the Korean Cryptographic Module Validation Program (KCMVP) and is the national standard of Republic of Korea (KS X 3246). LEA is included in the ISO/IEC 29192-2:2019 standard (Information security - Lightweight cryptography - Part 2: Block ciphers).

The block cipher LEA consisting of ARX operations (modular Addition: ${\displaystyle \boxplus }$, bitwise Rotation: ${\displaystyle \lll }$, ${\displaystyle \ggg }$, and bitwise XOR ${\displaystyle \oplus }$) for 32-bit words processes data blocks of 128 bits and has three different key lengths: 128, 192, and 256 bits. LEA with a 128-bit key, LEA with a 192-bit key, and LEA with a 256-bit key are referred to as “LEA-128”, “LEA-192”, and “LEA-256”, respectively. The number of rounds is 24 for LEA-128, 28 for LEA-192, and 32 for LEA-256.

Let ${\displaystyle P=P[0]\|P[1]\|P[2]\|P[3]}$ be a 128-bit block of plaintext and ${\displaystyle C=C[0]\|C[1]\|C[2]\|C[3]}$ be a 128-bit block of ciphertext, where ${\displaystyle P[i]}$ and ${\displaystyle C[i]}$ (${\displaystyle 0\leq i<4}$) are 32-bit blocks. Let ${\displaystyle K_{i}=K_{i}[0]\|K_{i}[1]\|K_{i}[2]\|K_{i}[3]\|K_{i}[4]\|K_{i}[5]}$ (${\displaystyle 0\leq i<Nr}$) be 192-bit round keys, where ${\displaystyle K_{i}[j]}$ (${\displaystyle 0\leq j<6}$) are 32-bit blocks. Here ${\displaystyle Nr}$ is the number of rounds for the LEA algorithm. The encryption operation is described as follows:

1. ${\displaystyle X_{0}[0]\|X_{0}[1]\|X_{0}[2]\|X_{0}[3]\leftarrow P[0]\|P[1]\|P[2]\|P[3]}$
2. for ${\displaystyle i=0}$ to ${\displaystyle Nr-1}$
   1. ${\displaystyle X_{i+1}[0]\leftarrow \left(\left(X_{i}[0]\oplus K_{i}[0]\right)\boxplus \left(X_{i}[1]\oplus K_{i}[1]\right)\right)\lll 9}$
   2. ${\displaystyle X_{i+1}[1]\leftarrow \left(\left(X_{i}[1]\oplus K_{i}[2]\right)\boxplus \left(X_{i}[2]\oplus K_{i}[3]\right)\right)\ggg 5}$
   3. ${\displaystyle X_{i+1}[2]\leftarrow \left(\left(X_{i}[2]\oplus K_{i}[4]\right)\boxplus \left(X_{i}[3]\oplus K_{i}[5]\right)\right)\ggg 3}$
   4. ${\displaystyle X_{i+1}[3]\leftarrow X_{i}[0]}$
3. ${\displaystyle C[0]\|C[1]\|C[2]\|C[3]\leftarrow X_{Nr}[0]\|X_{Nr}[1]\|X_{Nr}[2]\|X_{Nr}[3]}$

The decryption operation is as follows:

1. ${\displaystyle X_{Nr}[0]\|X_{Nr}[1]\|X_{Nr}[2]\|X_{Nr}[3]\leftarrow C[0]\|C[1]\|C[2]\|C[3]}$
2. for ${\displaystyle i=(Nr-1)}$ down to ${\displaystyle 0}$
   1. ${\displaystyle X_{i}[0]\leftarrow X_{i+1}[3]}$
   2. ${\displaystyle X_{i}[1]\leftarrow \left(\left(X_{i+1}[0]\ggg 9\right)\boxminus \left(X_{i}[0]\oplus K_{i}[0]\right)\right)\oplus K_{i}[1]}$
   3. ${\displaystyle X_{i}[2]\leftarrow \left(\left(X_{i+1}[1]\lll 5\right)\boxminus \left(X_{i}[1]\oplus K_{i}[2]\right)\right)\oplus K_{i}[3]}$
   4. ${\displaystyle X_{i}[3]\leftarrow \left(\left(X_{i+1}[2]\lll 3\right)\boxminus \left(X_{i}[2]\oplus K_{i}[4]\right)\right)\oplus K_{i}[5]}$
3. ${\displaystyle P[0]\|P[1]\|P[2]\|P[3]\leftarrow X_{0}[0]\|X_{0}[1]\|X_{0}[2]\|X_{0}[3]}$

The key schedule of LEA supports 128, 192, and 256-bit keys and outputs 192-bit round keys ${\displaystyle K_{i}}$ (${\displaystyle 0\leq i<Nr}$) for the data processing part.

Let ${\displaystyle K=K[0]\|K[1]\|K[2]\|K[3]}$ be a 128-bit key, where ${\displaystyle K[i]}$ (${\displaystyle 0\leq i<4}$) are 32-bit blocks. The key schedule for LEA-128 takes ${\displaystyle K}$ and four 32-bit constants ${\displaystyle \delta [i]}$ (${\displaystyle 0\leq i<4}$) as inputs and outputs twenty-four 192-bit round keys ${\displaystyle K_{i}}$ (${\displaystyle 0\leq i<24}$). The key schedule operation for LEA-128 is as follows:

1. ${\displaystyle T[0]\|T[1]\|T[2]\|T[3]\leftarrow K[0]\|K[1]\|K[2]\|K[3]}$
2. for ${\displaystyle i=0}$ to ${\displaystyle 23}$
   1. ${\displaystyle T[0]\leftarrow \left(T[0]\boxplus \left(\delta [i\mod 4]\lll i\right)\right)\lll 1}$
   2. ${\displaystyle T[1]\leftarrow \left(T[1]\boxplus \left(\delta [i\mod 4]\lll \left(i+1\right)\right)\right)\lll 3}$
   3. ${\displaystyle T[2]\leftarrow \left(T[2]\boxplus \left(\delta [i\mod 4]\lll \left(i+2\right)\right)\right)\lll 6}$
   4. ${\displaystyle T[3]\leftarrow \left(T[3]\boxplus \left(\delta [i\mod 4]\lll \left(i+3\right)\right)\right)\lll 11}$
   5. ${\displaystyle K_{i}\leftarrow T[0]\|T[1]\|T[2]\|T[1]\|T[3]\|T[1]}$

Let ${\displaystyle K=K[0]\|K[1]\|K[2]\|K[3]\|K[4]\|K[5]}$ be a 192-bit key, where ${\displaystyle K[i]}$ (${\displaystyle 0\leq i<6}$) are 32-bit blocks. The key schedule for LEA-192 takes ${\displaystyle K}$ and six 32-bit constants ${\displaystyle \delta [i]}$ (${\displaystyle 0\leq i<6}$) as inputs and outputs twenty-eight 192-bit round keys ${\displaystyle K_{i}}$ (${\displaystyle 0\leq i<28}$). The key schedule operation for LEA-192 is as follows:

1. ${\displaystyle T[0]\|T[1]\|T[2]\|T[3]\|T[4]\|T[5]\leftarrow K[0]\|K[1]\|K[2]\|K[3]\|K[4]\|K[5]}$
2. for ${\displaystyle i=0}$ to ${\displaystyle 27}$
   1. ${\displaystyle T[0]\leftarrow \left(T[0]\boxplus \left(\delta [i\mod 6]\lll i\right)\right)\lll 1}$
   2. ${\displaystyle T[1]\leftarrow \left(T[1]\boxplus \left(\delta [i\mod 6]\lll \left(i+1\right)\right)\right)\lll 3}$
   3. ${\displaystyle T[2]\leftarrow \left(T[2]\boxplus \left(\delta [i\mod 6]\lll \left(i+2\right)\right)\right)\lll 6}$
   4. ${\displaystyle T[3]\leftarrow \left(T[3]\boxplus \left(\delta [i\mod 6]\lll \left(i+3\right)\right)\right)\lll 11}$
   5. ${\displaystyle T[4]\leftarrow \left(T[4]\boxplus \left(\delta [i\mod 6]\lll \left(i+4\right)\right)\right)\lll 13}$
   6. ${\displaystyle T[5]\leftarrow \left(T[5]\boxplus \left(\delta [i\mod 6]\lll \left(i+5\right)\right)\right)\lll 17}$
   7. ${\displaystyle K_{i}\leftarrow T[0]\|T[1]\|T[2]\|T[3]\|T[4]\|T[5]}$

Let ${\displaystyle K=K[0]\|K[1]\|K[2]\|K[3]\|K[4]\|K[5]\|K[6]\|K[7]}$ be a 256-bit key, where ${\displaystyle K[i]}$ (${\displaystyle 0\leq i<8}$) are 32-bit blocks. The key schedule for LEA-192 takes ${\displaystyle K}$ and eight 32-bit constants ${\displaystyle \delta [i]}$ (${\displaystyle 0\leq i<8}$) as inputs and outputs thirty-two 192-bit round keys ${\displaystyle K_{i}}$ (${\displaystyle 0\leq i<32}$). The key schedule operation for LEA-256 is as follows:

1. ${\displaystyle T[0]\|T[1]\|T[2]\|T[3]\|T[4]\|T[5]\|T[6]\|T[7]\leftarrow K[0]\|K[1]\|K[2]\|K[3]\|K[4]\|K[5]\|K[6]\|K[7]}$
2. for ${\displaystyle i=0}$ to ${\displaystyle 31}$
   1. ${\displaystyle T[6i\mod 8]\leftarrow \left(T[6i\mod 8]\boxplus \left(\delta [i\mod 8]\lll i\right)\right)\lll 1}$
   2. ${\displaystyle T[6i+1\mod 8]\leftarrow \left(T[6i+1\mod 8]\boxplus \left(\delta [i\mod 8]\lll \left(i+1\right)\right)\right)\lll 3}$
   3. ${\displaystyle T[6i+2\mod 8]\leftarrow \left(T[6i+2\mod 8]\boxplus \left(\delta [i\mod 8]\lll \left(i+2\right)\right)\right)\lll 6}$
   4. ${\displaystyle T[6i+3\mod 8]\leftarrow \left(T[6i+3\mod 8]\boxplus \left(\delta [i\mod 8]\lll \left(i+3\right)\right)\right)\lll 11}$
   5. ${\displaystyle T[6i+4\mod 8]\leftarrow \left(T[6i+4\mod 8]\boxplus \left(\delta [i\mod 8]\lll \left(i+4\right)\right)\right)\lll 13}$
   6. ${\displaystyle T[6i+5\mod 8]\leftarrow \left(T[6i+5\mod 8]\boxplus \left(\delta [i\mod 8]\lll \left(i+5\right)\right)\right)\lll 17}$
   7. ${\displaystyle K_{i}\leftarrow T[6i\mod 8]\|T[6i+1\mod 8]\|T[6i+2\mod 8]\|T[6i+3\mod 8]\|T[6i+4\mod 8]\|T[6i+5\mod 8]}$

The eight 32-bit constant values ${\displaystyle \delta [i]}$ (${\displaystyle 0\leq i<8}$) used in the key schedule are given in the following table.

Constant values used in the key schedule

${\displaystyle i}$	0	1	2	3	4	5	6	7
${\displaystyle \delta [i]}$	0xc3efe9db	0x44626b02	0x79e27c8a	0x78df30ec	0x715ea49e	0xc785da0a	0xe04ef22a	0xe5c40957

As of 2019, no successful attack on full-round LEA is known. As is typical for iterated block ciphers, reduced-round variants have been attacked. The best published attacks on LEA in the standard attack model (CPA/CCA with unknown key) are boomerang attacks and differential linear attacks. The security margin to the whole rounds ratio is greater than 37% against various existing cryptanalytic techniques for block ciphers.

LEA has very good performance in a general-purpose software environment. In particular, it is possible to encrypt at a rate of about 1.5 to 2 times on average, compared to AES, the most widely used block cipher in various software environments. The tables below compare the performance of LEA and AES using FELICS (Fair Evaluation of Lightweight Cryptographic Systems),^[3] a benchmarking framework for evaluation of software implementations of lightweight cryptographic primitives.

Test vectors for LEA for each key length are as follows.^[5] All values are expressed in hexadecimal form.

• LEA-128
  • Key: 0f 1e 2d 3c 4b 5a 69 78 87 96 a5 b4 c3 d2 e1 f0
  • Plaintext: 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
  • Ciphertext: 9f c8 4e 35 28 c6 c6 18 55 32 c7 a7 04 64 8b fd
• LEA-192
  • Key: 0f 1e 2d 3c 4b 5a 69 78 87 96 a5 b4 c3 d2 e1 f0 f0 e1 d2 c3 b4 a5 96 87
  • Plaintext: 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f
  • Ciphertext: 6f b9 5e 32 5a ad 1b 87 8c dc f5 35 76 74 c6 f2
• LEA-256
  • Key: 0f 1e 2d 3c 4b 5a 69 78 87 96 a5 b4 c3 d2 e1 f0 f0 e1 d2 c3 b4 a5 96 87 78 69 5a 4b 3c 2d 1e 0f
  • Plaintext: 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f
  • Ciphertext: d6 51 af f6 47 b1 89 c1 3a 89 00 ca 27 f9 e1 97

LEA is free for any use: public or private, commercial or non-commercial. The source code for distribution of LEA implemented in C, Java, and Python can be downloaded from KISA's website.^[6] In addition, LEA is contained in Crypto++ library, a free C++ class library of cryptographic schemes.^[7]

LEA is one of the cryptographic algorithms approved by the Korean Cryptographic Module Validation Program (KCMVP).^[8]

LEA is included in the following standards.

• KS X 3246, 128-bit block cipher LEA (in Korean)^[5]

• ISO/IEC 29192-2:2019, Information security - Lightweight cryptography - Part 2: Block ciphers^[9]