# Difference between revisions of "Lightweight Block Ciphers"

Lightweight block ciphers are lightweight cryptographic primitives. On this page, we list 36 lightweight block ciphers and study their properties: properties of the algorithm (structure, block size, number of rounds, etc), hardware implementation properties and known attacks.

## Block Cipher Design

### Desirable Properties

The aim of a block cipher is to provide a keyed pseudo-random permutation which is then used as the building block of more complex protocols. For instance, coupled with a proper Mode of operation, they can be used to encrypt data. A "good" blockcipher must be fast and secure, i.e. it must be impossible for an adversary with realistic computing power to retrieve the key used even if she has access to a black-box capable of encrypting and decrypting the plaintext of her choice (security against chosen-ciphertext attack).

### Design Principles

There are two families of designs for block ciphers: Substitution-Permutation Networks and Feistel Networks. There are also specific constraints when designing lightweight blockciphers. First of all, memory is very expensive so that implementing S-boxes as look-up table can lead to a large hardware footprint. That is why these ciphers usually have no S-box at all (SIMON) or very small ones, only 4x4 (PRESENT).

#### Cost of Implementing Decryption

Implementing decryption alongside encryption should lead to an increase of the area necessary as it requires its own logic. However, depending on the mode of operation of the cipher, it may be possible to ignore the decryption algorithm: for instance, in the case of OFB, decryption is useless. Another way of reducing the additional cost is to build algorithms such that encryption and decryption are very similar. A first approach is to use involutions as components, for instance in KLEIN. The whole structure can be exploited to have involution related properties, for instance α-reflexivity in the case of PRINCE or differentiate encryption from decryption simply by a variation in the key-schedule (Feistel networks, mCrypton).

#### Fixed key?

The designers of symmetric block ciphers have different approaches regarding relted key attacks. The use-case of lightweight cryptography can lead to opposite views concerning the necessity of counter-measure to prevent such attacks.

• Because the key is likely to be "burnt" in the device, i.e. that it will not be possible to change it, there is no point in worrying about related key attacks: the probability for an attacker to obtain several devices keyed with appropriately related keys is too small to be of any importance.
• However, such block ciphers are very likely to be used to build compression functions for hash function with a Merkle-Damgård structure. In this context, resilience against related key attakcs is much more important.

## Summary

In the following table we list for each block cipher:

• Where it comes from (designers, year, conference/journal where it was introduced...),
• Its basic properties (key size, block size, structure...),
• Its known weaknesses (to the best of our knowledge),
• The properties of its best (to the best of our knowledge) hardware implementation.

Comparisons of the efficiency in time and space of their software implementation can be found in Survey and Benchmark of Lightweight Block Ciphers for Wireless Sensor Networks[1] and on the webpage of the BLOC project. Source code for most of these primitives can be found on the github account of the project.

Presentation Cryptographic Properties Implementation Properties
name designers reference (design) block size key size structure rounds attacks Technology used area (#GE) throughput (Kb/s @ 100kHz) power consumption (µW) reference (implementation)
AES Rijmen et al. AES conference 98[2] 128 128 SPN 10
• Impossible differential[3], 7-rounds AES-128
• Related-key boomerang[4], full AES-192 and full AES-256
• Biclique[5] (full AES)
0.13µm 3100 80 -- ECRYPT[6]
192 12 -- -- -- -- --
256 14 -- -- -- -- --
Chaskey Cipher Mouha et. al. SAC'14[7] 128 128 ARX 8
• Differential-linear (6,7 rounds)[8]
-- -- -- -- --
CLEFIA Shirai et al. FSE 2007[9] 128 128 GFN 18
• Integral (12, 13, 14 rounds)[10]
• Improbable differentials (13, 14, 15 rounds)[11]
0.09µm 4950 355.6 -- ECRYPT[6]
192 22 -- -- -- -- --
256 26 -- -- -- -- --
DESLX Leander et al. FSE 2007[12] 64 184 Feistel 16 0.18 µm 2168 44.4 1.6 ECRYPT[6]
Fantomas Grosso et al. FSE'14[13] 128 128 SPN 12 -- -- -- -- --
GOST revisited Poschmann et al. CHES 10[14] 64 256 Feistel 32
0.18 µm 651 / 1017 24.24 / 200 -- Specification[14]
HIGHT Hong et al. CHES 06[16] 64 128 GFS 32
• Saturation (22 rounds)[17]
• Impossible diff. (26 rounds)[18]
• Related Key rectangle (full cipher)[19]
• Biclique (full cipher)[20]
0.25µm 3048 188.2 -- ECRYPT[6]
ITUbee Karakoç et al. LightSec'13[21] 80 80 Feistel 20 -- -- -- -- --
KASUMI ETSI 3GPP std[22] 64 128 Feistel 8
• Related-key boomerang (full-cipher)[23]
-- -- -- -- --
KLEIN Gong et al. SaP 12[24] 64 64 SPN 12
• Differential (KLEIN-64, 8 rounds)[25]
• Truncated Differential (KLEIN-64, full cipher)[26]
0.18 µm 1360 / 2032 -- -- Specification[24]
80 16 1530 / 2202 -- --
96 20 1700 / 2372 -- --
KATAN De Cannière et al. CHES 09[27] 32 80 stream-cipher-like 254
• Differential (KATAN32, 115 rounds)[28]
• Multi-dimensionnal MitM (175-rounds KATAN32, 130-rounds KATAN48 and 112-rounds KATAN64)[29]
• 3-subsets MitM (full cipher)[30]
0.13 µm 802 12.5 0.381 ECRYPT[6]
48 -- -- -- -- --
64 0.13 µm 1054 25.1 0.555 ECRYPT[6]
KTANTAN De Cannière et al. CHES 09[27] 32 80 stream-cipher-like 254 0.13 µm 462 12.5 0.146 ECRYPT[6]
48 -- -- -- -- --
64 0.13 µm 688 25.1 0.292 ECRYPT[6]
LBlock Wu et al. ACNS 11[31] 64 80 Feistel 32
• Related key impossible differential (22 rounds)[32]
• Zero-correlation (22 rounds)[33]
• Integral attack (22 rounds)[34]
• Impossible differential (21[35], 23[36] rounds)
0.18 µm 1320 200 -- Specification[31]
LEA Hong et al. WISA 13[37] 128 128 GFN 24 -- -- -- -- --
192 28
256 32
LED Guo et al. CHES 11[38] 64 64 SPN 32
• Ad Hoc (12 rounds of LED-64, 32 rounds of LED-128)[39]
0.18 µm 966 5.1 -- Specification[38]
128 48 1265 3.4 -- Specification[38]
MANTIS Beierle et al. CRYPTO 16[40] 64 128+64 (tweak) SPN 14
• Differential attack (10 rounds)[41]
-- -- -- -- --
mCrypton Lim et al. ISA 06[42] 64 64 SPN 12
• MitM[43] 7-rounds mCrytpon-64/96/128
• MitM[43] 8- and 9-rounds mCrytpon-128
0.13µm 2420[note 3] 482.3 -- Specification[42]
96 2681[note 3] -- --
128 2949[note 3] -- --
Midori Banik et al. Asiacrypt'15[44] 64 128 SPN 16 0.09µm[note 4] 1542 -- 60.6[note 5] Specification[44]
128 20 2522 -- 89.2[note 5]
MISTY1 Matsui FSE'97[45] 64 128 Feistel 8
• Integral via division property (full-cipher)[46][47]
-- -- -- -- --
Mysterion Journault et al. WCC 15[48] 128  ?[note 6] SPN 12 -- -- -- -- --
256  ?[note 6] 16 -- -- -- --
Noekeon Daemen et al. Nessie Workshop[49] 128 128 SPN 16
• Bit-pattern based integral, 5 rounds[50]
• Linear attack, 12 rounds (designers[49])
-- -- -- -- --
Piccolo Shibutani et al. CHES 11[51] 64 80 GFN 25
• Biclique (full Piccolo-80; 28-round Piccolo-128)[52]
• Related-key impossible diff[53], 14-rounds Piccolo-80, 21-rounds Piccolo-128
-- 683 / 1136 14.8 / 237.04 -- / -- Specification[51]
128 31 -- 758 / 1196 12.12 / 193.9 -- / --
PRESENT Bogdanov et al. CHES 07[54] 64 80 SPN 31
• Statistical saturation[55], up to 24-rounds
• Multi-dimensionnal linear[56], 26-rounds
• Truncated differential[57], 26-rounds
0.18 µm 1075 / 1570 11.7 / 200 1.4 / 2.78 Poschmann's PhD Thesis[58]
128 1391 / 1884 11.45 / 200 -- / 3.67
PRIDE Albrecht et al. CRYPTO 14[59] 64 128 SPN 20 -- -- -- -- --
PRINCE Borghoff et al. ASIACRYPT 12[59] 64 128 SPN 12
• Reflection attack[60], 6 rounds
• Sieve-in-the-Middle[61], 8 rounds
• Multiple differentials[62], 10 rounds
0.09 µm / 0.13 µm 3286 / 3491 529.9 / 533.3 4.5 / 5.8 Specification[59]
RC5-12 Rivest FSE 95[63] 32 0..2040 ARX 12
• Differential attack[64]
• Linear attack[65]
-- -- -- --
64
128
Rectangle Zhang et al. Sci China'15[66] 64 80 SPN 25
• Differential attack (18 rounds)[66]
0.13 µm 1599.5 -- Specification[66]
128 2063.5 --
RoadRunneR Baysal et. al. LightSec 15[67] 64 80 Feistel 10 -- -- -- -- --
128 12 -- -- -- --
Robin Grosso et al. FSE'14[13] 128 128 SPN 16
• Invariant subspace (weak key, full round)[68]
-- -- -- -- --
SEA Standaert et al. SCRAA 06[69] 96[note 7] 96 Feistel 93 0.13 µm 449[70] -- 3.218 MSQ07[71]
SKINNY Beierle et al. CRYPTO 16[40] 64 64/128/192[note 8] SPN 32/36/40 0.18 µm 1223/1696/2183 200.0/177.8/160.0 -- Specification[40]
128 128/256/384[note 8] 40/48/56 2391/3312/4268 320.0/266.7/228.6 -- Specification[40]
SIMECK Yang et al. CHES'15[72] 32 64 Feistel 32
• Differential (22/28/35 rounds SIMECK-32/48/64)[73][74]
0.13µm 549 / 765 5.6 / 88.9 0.417 / 0.606 Specification[72]
48 96 36 778 / 1117 5.0 / 120.0 0.576 / 0.875
64 128 44 1005 / 1484 4.2 / 133.3 0.754 / 1.162
SIMON Beaulieu et al. eprint.iacr 13[75] 32 64 Feistel 32
• Differential (up to 21/22/28/35/46 rounds SIMON-32/48/64/96/128)[76][77][78]
• Linear (20 rounds SIMON-32)[79]
• Impossible diff. (19/20/26 rounds SIMON-32/48/64)[79]
• Multi-Dim. Linear (23/25/31/38/53 rounds SIMON-32/48/64/96/128)[80]
-- -- -- -- Specification[75]
48 72 / 96 36 -- / 763 -- / 15.0 --
64 96 / 128 42 / 44 838 / 1000 17.8 / 16.7 --
96 96 / 144 52 / 54 984 / -- 14.8 / -- --
128 128 / 192 / 256 68 / 69 / 72 1317 / -- / -- 22.9 / -- / -- --
SPARX Dinu et al. ASIACRYPT 16[81] 64 SPN (ARX) 128 24
• Integral (15/22/24 rounds of SPARX-64/128, -128/128, -128/256)[81]
-- -- -- -- --
128 128/256 32/40 -- -- -- --
SPECK Beaulieu et al. eprint.iacr 13[75] 32 64 ARX 22
• Differential (up to 14/15/19/17/19 rounds SPECK-32/48/64/96/128)[76][82]
• Rectangle (11/12/14/16/18 rounds SPECK-32/48/64/96/128)[83]
-- -- -- -- Specification[75]
48 72 / 96 22 / 23 -- / 884 -- / 12.0 --
64 96 / 128 26 / 27 984 / 1127 14.5 / 13.8 --
96 96 / 144 28 / 29 1134 / -- 13.8 / -- --
128 128 / 192 / 256 32 / 33 / 34 1396 / -- / -- 12.1 / -- / -- --
TWINE Suzaki et al. Workshop on LC 11[84] 64 80 GFN 36
• Biclique (full cipher)[85]
• Zero-correlation (23-rounds)[86]
0.09 µm 1799 178 -- Specification[84]
128
• Biclique (full cipher)[85]
• Zero-correlation (25-rounds)[86]
2285 178 --
XTEA Needham et al. Note[87] 64 128 Feistel 64
• Related-key rectangle[88] 36 rounds
• MitM[89] 23 rounds
0.13 µm 3490 57.1 19.5 ECRYPT[6]
Zorro Gérard et al. CHES 13[90] 128 128 SPN 24
• Internal differentials (264 weak keys, full cipher)[91]
-- -- -- -- --

## Substitution-Permutation Network

The Substitution-Permutation Network (SPN) structure is the result of the seminal work of Shannon as it aims to provide both confusion and diffusion using two distinct operations. "Confusion" aims at making the relationship between the plaintext, the key and the ciphertext complicated while "Diffusion" focuses on achieving the avalanche-effect,i.e. a small modification on the plaintext must spread to the whole ciphertext. In an SPN, confusion is performed by a layer of S-boxes. An S-box is simply a permutation of a small subset of plaintext space and many are used in parallel to act upon the whole plaintext. Diffusion is achieved through the use of a permutation of the whole space, usually linear and sometimes called P-box. The best example of such a structure is Rijndael, the cipher which has been standardized by the American NIST to become the Advanced Encryption Standard (AES). This cipher had a great influence over the design of other primitives which we gathered in a group we call AES-like. However, it is possible to build a SPN-based cipher which is not as similar to the AES; such designs are presented in this section.

### AES-like

We put in this category the block ciphers having a structure derived from that of the AES. As it is the current encryption standard, the cryptographic community has been studying it closely since its publication in 1997 and, as of November 2013, it is still secure.

The lightweight authenticated cipher FIDES could also fit in this category. Furthermore, the stream cipher LEX[92] is based on the AES and serves as a basis for the design of other lightweight authenticated encryption schemes, namely ASC-1 and ALE.

#### AES

• Article: AES proposal: Rijndael, AES conference 98[2]
• Authors: Joan Daemen, Vincent Rijmen

The AES consists in 3 versions of the Rijndael cipher which have been standardized by the NIST. They are called AES-128, AES-192 and AES-256, the number corresponding to the key size. The internal state is always of 128 bits in the standard. An encryption consists in the following operations which are performed over the 128-bits internal state organized as a 4x4 matrix of bytes.

1. SubBytes: Each cell in the matrix is replaced by its image by a S-box. The AES S-box is S(x) = M(x-1)⊕C where the multiplicative inverse is taken in GF(28) (0 being mapped to 0), M is a matrix and C a constant. The inverse function is used because of its optimal non-linearity and differential spectrum (in even characteristic), properties which were known long before[93]. This S-box is also used for instance in PHOTON.
2. ShiftRows: The cells in the first row are left untouched, those in the second are shifted by 1 to the left, those in the third by 2 and those in the fourth by 3. This is to ensure diffusion between columns.
3. MixColumns: Each column is multiplied by an invertible MDS matrix to ensure diffusion between the rows.
4. AddRoundKey: The current subkey is xored in the internal state.

To have a visual explanation of the inner working of this cipher, the reader may refer to this flash animation by Enrique Zabala, Universidad ORT, Montevideo, Uruguay.

#### KLEIN

• Article: KLEIN: A New Family of Lightweight Block Ciphers, SaP 12[24]
• Authors: Zheng Gong, Svetla Nikova and Yee Wei Law
• Target: Hardware and Software

The 4x4 S-box used in the SubNibbles step is an involution. Furthermore, since all the S-boxes in the S-box layer are identical, it is possible to implement only one in hardware and put all protections against side-channel attacks in this unique place. The diffusion layer is made of two steps. The 16 4-bits nibbles are grouped into 8 bytes which are rotated two steps to the left so that the second byte becomes the last (RotateNibbles). Then, the bytes are split into two groups of 4 bytes which are considered like vectors of (GF(28))4 and multiplied by a matrix (MixNibbles). This last operation is very similar to the MixColumn operation of the AES.

The key-schedule is a Feistel Network involving at each round two calls to the S-box and a xoring of a round counter.

When discussing the key-schedule, the designers claim (Section 3.2.4[24]):

KLEIN will be used to construct block-cipher-based hash functions and message authentication codes[...]

They also tried to prevent related-key attacks and to provide easier masking to prevent side-channel attacks.

#### LED

The LED round function
• Article: The LED Block Cipher, CHES 11[38]
• Authors: Jian Guo, Thomas Peyrin, Axel Poschmann, and Matt Robshaw
• Target: Hardware and Software

Lightweight Encryption Device is a SPN heavily based on AES. Encryption is made of "steps" interleaved with xoring of the key, each "step" corresponding to 4 rounds. Each round is made of the xoring of a round constant and AES-style SubCells, ShitRows and MixColumnsSerial operations. The method used to design the MDS matrix used in the MixColumnsSerial was first used for the hash function PHOTON designed by the same team. The S-box used in the SubCells step is the PRESENT S-box.

An interesting characteristic of this design is the key schedule (or lack thereof): a key of 64 bits is xored with internal state as is while a key of 128 bits is cut into two subkeys of 64 bits which are used alternatively. Because of this, it is a variation of the Even-Mansour construction like in its best attack[39].

The authors provide a reference implementation as well as results on the efficiency of their algorithm at led.crypto.sg. Note that the algorithm presented in the proceedings of CHESS 2011 (link) has been modified slightly in the version available on eprint[38]. In particular, the definition of the round constants has been modified and an 80-bit version of the cipher was introduced.

#### Midori

A complete Midori64 encryption.
• Article: Midori: A Block Cipher for Low Energy Asiacrypt'15[44]
• Authors: Subhadeep Banik, Andrey Bogdanov, Takanori Isobe, Kyoji Shibutani, Harunaga Hiwatari, Toru Akishita, and Francesco Regazzoni
• Target: Hardware

Midori64 and Midori128 are two block ciphers designed to reduce energy consumption when implemented in hardware. They are both based on the same Midori structure. It uses an AES-like structure where the internal state is divided into a 4x4 matrix of nibbles (Midori64) or bytes (Midori128). Encryption then relies on 4 operations:

• SubCell: application of the 4- or 8-bit S-Boxes to each cell of the internal state. There are 4 different 8-bit S-Boxes built with an ASA-1 structure where S consists in the parallel application of a 4-bit S-Box (distinct from the one used in Midori64) and A is one of 4 different 8-bit permutations.
• ShuffleCell: A sophisticated replacement of the ShiftRow operation of the AES is used. A different permutation of the 4 cells is applied on each row. These were chosen so as to maximize diffusion.
• MixColumn: Each column is replaced by its image by a multiplication with an almost-MDS involution matrix M.
• KeyAdd: A key addition. The key schedule is very simple: for the 128-bit version, the master key is XOR-ed in the internal state along with a sparse round constant at every round. For the 64-bit version, the first half of the master key is XOR-ed in the internal state in odd rounds and the second in even rounds. The XOR of the two halves is used as whitening keys and, again, sparse round constants (equal to 0 except on the LSB of each nibble) are used.

The specification[44] contains a detailed analysis of the power consumption of this algorithm as well as comparison with other algorithms (namely AES, PRINCE, PRESENT, Noekeon and SIMON).

#### Mysterion

The Mysterion-128 round function
• Article: Improving the Security and Efficiency of Block Ciphers based on LS-Design WCC 15[48]
• Authors: Anthony Journault, François-Xavier Standaert and Kerem Varici.
• Target: Software

Mysterion explores the LS-design paradigm introduced by the designers of Fantomas and Robin and combines it with an AES-like structure to increase the security level. In particular, it uses a bit-sliced S-Box.

The internal state of the block cipher is organized into a 4×32 bit matrix for Mysterion-128 and a 4×64 bit matrix for Mysterion-256. These are subdivided into 4×8 blocks, so that the internal state of Mysterion-128 (resp. -256) consists in 4 (resp. 8) such blocks. A round consists in the following operations:

1. S-Box layer: the 4x4 "Class 13" S-Box identified by Ullrich et al.[94] is applied in parallel to each column of the internal state (much like in the Feistel function of RoadRunneR).
2. L-Box layer: the 8×8 L-Box is applied byte-wise in parallel on every row of every block: 4 (resp. 8) parallel applications/row for Mysterion-128 (resp. Mystertion-256).
3. ShiftColumns: this operation is similar in spirit to the ShiftRow operation of the AES. For Mysterion-256, the first column of each block is left unchanged, the second are rotated by one, etc. For Mysterion-128, the columns are grouped 2-by-2 so that the first 2 columns of each block are left unchanged, the next 2 are rotated by 2, etc. (see picture on the right).

#### SKINNY

One round of SKINNY encryption.
A circuit computing the S-Box S4.
• Article: The SKINNY Family of Block Ciphers and its Low-Latency Variant MANTIS, CRYPTO'16 [40]
• Authors: Christof Beierle, Jérémy Jean, Stefan Kolbl, Gregor Leander, Amir Moradi, Thomas Peyrin, Yu Sasaki, Pascal Sasdrich, and Siang Meng Sim
• Target: Hardware

SKINNY is a family of lightweight tweakable block ciphers designed so as to have the smallest hardware footprint. All members of the family are SPN consisting of several iterations of the following operations transforming a 4x4 matrix of 4-bit nibbles (64-bit variant) or bytes (128-bit variant). A picture summarizing this is given on the right.

1. SubCells (SC): each cell goes through an S-Box (the 4-bit S-Box S4 for the 64-bit variant the 8-bit S-Box S8 for the 128-bit variant).
2. AddConstants (AC): round constants derived using a 6-bit LFSR are added into the state.
3. AddRoundTweakey (ART): SKINNY is built using the TWEAKEY framework[95], round keys therefore depend on both the master key and the tweak and are called RoundTweakey. This operations adds such key material to half of the internal state.
4. ShiftRows (SR): The rows are rotated to the right according to their index, i.e. the first row is left unchanged, the second is rotated by 1, the third by 2 and the third by 3. This operation is identical to the one in the AES except for the direction of the rotation.
5. MixColumns (MC): Each column is multiplied by a binary matrix M given below.

The main idea behind this design is to provide as low an area in hardware as possible without sacrificing neither speed nor security. In particular, unlike for the NSA cipher SIMON, bounds are provided for the number of active S-Boxes in any differential trail in both the single-key and the related-key setting. These are obtained using a technique based on first transforming the existence of a trail into a MILP problem and then using a MILP solver to retrieve the result.

The components were chosen because of the good compromise they provide between cryptographic properties and hardware cost. The S-Boxes can be computed using a simple circuit (the one computing S4 is given on the right) and the matrix M is a simple binary matrix:

$M = \left[\begin{array}{cccc} 1 & 0 & 1 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 \end{array} \right].$

#### Zorro

• Article: Block Ciphers that are Easier to Mask: How Far Can we Go?, CHES'13[90]
• Authors: Benoit Gerard, Vincent Grosso, Maria Naya-Plasencia, Francois-Xavier Standaert
• Target: Software

Zorro is a modified version of the AES intended to be easy to mask (like Zorro, the masked hero). To achieve this, fewer calls to the S-box are made during each round and the S-box has been modified. To compensate, the number of rounds has been increased to 24. This design also borrows ideas from LED: there is no key schedule but, instead, the addition of round constants at each round. Besides, the execution is split into "steps" of 4 rounds and the key is added only at the end of a step. This the operation AK (add key) which consists simply in xoring the master key. No security claims are made regarding related key attacks.

Each round is made of 4 operations:

1. SB* which is a variant of the SubBytes operation where the S-box is applied to one row of the 4x4 bytes internal state,
2. AC is a round constant addition similar to the one used in LED,
3. SR is identical to ShiftRows,
4. MC is identical to MixColumns.

Much thought has been put in the design of the S-box: while retaining good cryptographic properties, it minimizes the number of multiplications necessary to compute it. It is based on a small 4-round Feistel cipher with mixing layer where the Feistel function is the monomial X3 in GF(24).

### Bit-Sliced S-Boxes

All block ciphers with an SPN structure that use a bit-sliced S-Box are put in this category. We call "bit-sliced S-Box" a non-linear layer consisting in the parallel application of several small non-linear functions which is supposed to be implemented using basic bitwise operations such as XOR, AND and OR. While Mysterion is classified as AES-like in this list, it also fits in this category. Similarly, the Feistel networks RoadRunneR and SEA use bit-sliced S-Boxes in their Feistel functions.

#### Fantomas/Robin

The components of a LS-design
• Article: LS-Designs: Bitslice Encryption for Efficient Masked Software Implementations, FSE'14[13]
• Authors: Grosso, V., Leurent, G., Standaert, F. X., & Varıcı, K.
• Target: Software

These block ciphers are two instances of so-called "LS-designs" where the internal state of the cipher is a matrix of s×L bits and where:

• the non-linear layer consists in the parallel applications of a s×s bits permutation (the S-Box) on each column of the matrix, and
• the linear layer consists in the application of a linear L×L bits permutation (the L-Box) on each line of the matrix.

This structure is intended to ease masking and thus to help thwart side-channel attacks when this cipher is implemented on a micro-controller. The S-Boxes of both ciphers (Fantomas and Robin) were chosen so as to be efficiently implemented in a bitslice fashion.

Robin uses involutions as both its L-Box and its S-Box but it is not the case for Fantomas. As a consequence, Robin has more rounds. Both have a 8×8 bits S-Box and a 16×16 bits L-Box.

#### Noekeon

The round function of Noekeon
• Article: The Noekeon Block Cipher, Nessie Proposal[49]
• Authors: Joan Daemen, Michaël Peeters, Gilles Van Assche, Vincent Rijmen
• Target: Software/Hardware

Noekeon is a Substitution-Permutation Network operating on blocks of 128 bits using a 128-bits key. It operates on 4 words of 32 bits except for the S-Box layer, "Gamma", which operates on 4-bits nibbles. The same round key is used in every round; how it is derived depends on whether related-key attacks must be considered or not. However, there exists related-key differentials for both key schedules[96] It uses the following operations.

• Gamma: Consists in applying a 4-bit involution S-Box on nibbles independently. Each of the 32 nibbles considered in Gamma is made of the bits of index i in each of the 4 words for all i in [0, 31]. This leads to a simple bitslice implementation of this layer. Most choices for Gamma generated using the same design criteria would have lead to weak ciphers but the one chosen in Noekeon does not[96].
• Theta: A linear layer which mixes words with each other and operates at the byte level. It has a Lai-Massey structure where the Lai-Massey function is linear: $x \mapsto x \oplus (x <<< 8) \oplus (x >>> 8)$. The round key is XOR-ed between the 2-steps of the Lai-Lassey operation.
• shift operations: Three of the four words are rotated by different offsets, namely 1, 5 and 2. Each rotations and their inverses are used.

A round constant is XOR-ed in the internal state before applying Gamma during encryption. Since the components are involution-based, decryption can be implemented using the same circuit as encryption. 16 rounds are used.

It is claimed to be suitable for implementation in hardware and on 8-bit processors.

The best attack by the designers is a linear attack based on a 2-rounds iterative linear trail covering 9 rounds, which is then extended to cover 12 rounds through key guessing.

#### PRIDE

The round function of PRIDE
• Article: Block Ciphers -- Focus On the Linear Layer (feat. PRIDE), CRYPTO'14[97]
• Authors: Martin R. Albrecht, Benedikt Driessen, Elif Bilge Kavun, Gregor Leander, Christof Paar and Tolga Yalcın
• Target: Software

PRIDE is the output of research focusing on the design of the linear layer in Substitution-Permutation Networks. Its main target is 8-bit micro-controllers. Specifically, the computer assisted search for components of the linear layer was optimized to look for permutations which can be efficiently implemented using the AVR instruction set.

To limit the overhead implied by the implementation of both encryption and decryption, its S-Box is an involution. Furthermore, it is implemented in a bit-sliced fashion and was chosen so as to minimize the number of instructions necessary to evaluate it.

The key-schedule is very similar to that of PRINCE: the master key is split in two halves, the first being used as whitening key and the second being used to derive subkeys XOR-ed in the internal state at every round. However, unlike in PRINCE, the post-whitening key is the same as the pre-whitening key and the subkeys are not derived by XOR-ing round constants but by adding round constants on some bytes using a regular addition modulo 256.

#### Rectangle

The round function of Rectangle
• Article: RECTANGLE: A Bit-slice Ultra-Lightweight Block Cipher Suitable for Multiple Platforms, Science China Information Sciences'15[66]
• Authors: Wentao Zhang, Zhenzhen Bao, Dongdai Lin, Vincent Rijmen, Bohan Yang, Ingrid Verbauwhede
• Target: Hardware and software

Rectangle is a substitution permutation network. Its state is represented as a 4×16 matrix. The non-linear layer consists in the parallel application of a 4-bit S-Box on the columns of the state and the linear layer consists simply in applying a fixed rotation by a different amount on each row. There are two versions of this cipher. The first had a key schedule operating by storing the key in a matrix undergoing a round of encryption except that the S-Box is only applied on the first column[98]. It was vulnerable to a related-key differential attack against 19 rounds[99].

The latest version, as published in Science China'15[66], is not vulnerable to this attack anymore. Its key-schedule is different: it still relies on partially applying an S-Box layer to a key state but the overall operation has now a generalized Feistel structure. Compared to the older version, the key schedule of the latest version also performs better in software.

### Other SPN-based Structures

We put in this category the ciphers with a SPN structure which are not as close to the AES as the others, be it by the structure of the linear layer (e.g. PRESENT) of by their overall structure (e.g. PRINCE).

#### mCrypton

• Article: mCrypton – A Lightweight Block Cipher for Security of Low-Cost RFID Tags and Sensors, ISA 06[42]
• Authors: Chae Hoon Lim and Tymur Korkishko
• Target: Hardware

This cipher is a derivative of CRYPTON, a candidate of the AES competition. It has a structure close to that of Rijndael: it is a SPN with an internal space organised like a 4x4 matrix of nibbles of 4 bits. A round consists in the application of an S-box layer, a bit permutation within each column, a transposition of the matrix representing the state and, finally, xor-ing of the subkey. There are four different S-boxes, two being the inverse of the other two and they are all based on the inverse function in GF(24). Encryption and decryption are almost identical except for the key schedule.

#### MANTIS

The structure of MANTIS
• Article: The SKINNY Family of Block Ciphers and its Low-Latency Variant MANTIS, CRYPTO'16 [40]
• Authors: Christof Beierle, Jérémy Jean, Stefan Kolbl, Gregor Leander, Amir Moradi, Thomas Peyrin, Yu Sasaki, Pascal Sasdrich, and Siang Meng Sim
• Target: Hardware

Mantis is a tweakable block cipher with a 64-bit block size, 128-bit key and a 64-bit tweak. Much like PRINCE, from which it borrows the overall structure and the α-reflexivity, it is optimized for low latency. The key-schedule is also borrowed from PRINCE in the sense that the master key is cut in two halves, the first being used as an input and output whitening key and the second as a round key. However, additional operations are performed to take the tweak into account. The round function uses the following functions which operate on a 4x4 matrix of 4-bit nibbles (note that the last half of the rounds are the functionnal inverse of the first ones except for the round constants).

1. MixColumns: Each column is multiplied by a 4x4 binary matrix M.
2. PermuteCells: This operations plays the same role as the ShiftRow of the AES. However, it is more sophisticated than a mere rotation of the rows.
3. AddTweakey: Adds k1 (the second half of the masterkey) along with some tweak material to the internal state.
4. AddConstant: Round constants are added to the state. These were derived in a fashion very similar to those of PRINCE.
5. SubCells: The internal state goes through a layer of identical 4-bit S-Boxes.

Several of the components, namely the S-Box, the permutation used in PermuteCells and the matrix M have been borrowed from the low-energy cipher Midori.

The security claim is the same as for PRINCE: an adversary with 2d plaintext/ciphertext pair cannot recover the key in time less than 2126-n encryptions. Furthermore, while they do not claim related-key security because of the FX construction used, the designers do claim related-tweak security.

#### PRESENT

Two rounds of PRESENT encryption
• Article: PRESENT: An Ultra-Lightweight Block Cipher, CHES 07[54]
• Authors: A. Bogdanov, L.R. Knudsen, G. Leander, C. Paar, A. Poschmann, M.J.B. Robshaw, Y. Seurin, and C. Vikkelsoe
• Target: Hardware

This cipher is a SPN but, interestingly, it was not inspired by the AES. Indeed, while many SPN-based ciphers have permutation layers close in structure to that of the AES (see LED or mCrypton), that of PRESENT is completely different: it is bit oriented and is rather simple. It can be implemented in hardware using simple wiring. However, since bit-oriented permutations are not software-friendly, the target of PRESENT is clearly a hardware implementation. Its S-box was selected for its good cryptographic properties as well as for its small hardware footprint.

PRESENT is a very important design as it has been an inspiration for many others. For instance, its S-box has also been re-used by GOST revisited and LED as well as the lightweight hash function PHOTON. This cipher also inspired the design of two lightweight hash functions: DM-PRESENT and SPONGENT.

While only PRESENT-80 is described in the body of the CHES 07 article[54], PRESENT-128 and its modified key-schedule are described in the appendix. This cipher has been standardized and is part of the ISO-29192[100] with CLEFIA.

#### PRINCE

The PRINCE-core algorithm
• Article: PRINCE – A Low-latency Block Cipher for Pervasive Computing Applications, ASIACRYPT 12[59]
• Authors: Julia Borghoff, Anne Canteaut, Tim Guneysu, Elif Bilge Kavun, Miroslav Knezevic , Lars R. Knudsen, Gregor Leander, Ventzislav Nikov, Christof Paar, Christian Rechberger, Peter Rombouts, Søren S. Thomsen, and Tolga Yalcın
• Target: Hardware (low latency)

The main aim of the design of PRINCE is low latency.

There is no real key schedule: three 64 bits keys are derived from the 128 master key. Two are used as whitening keys and the third is simply xored in the internal state during encryption. To make the rounds behave differently from one another, different constants are xored in the internal state at each round. These constants RCi (i=0,..,11) are such that RCi⊕RC11-i=α where α is a constant derived from π. This property, combined with the fact that the first 5 rounds are the inverse of the last 5 mean that the decryption algorithm for key k is identical to an encryption with key k⊕α. This property is refered to as "α-reflexivity".

The authors challenge the symmetric cryptography community to attack (rounds-reduced versions of) this cipher and offer different rewards for "practical" attacks.

### ARX-Based SPN

#### SPARX

 SPECKEY, denoted Ak. Round function of SPARX-64/128
• Article: Design Strategies for ARX with Provable Bounds: SPARX and LAX[81]
• Authors: Daniel Dinu, Léo Perrin, Aleksei Udovenko, Vesselin Velichkov, Johann Großschädl and Alex Biryukov
• Target: software

Disclosure: the maintainers of this webpage are amongst the designers of SPARX. A page dedicated to this algorithm is available on this website (here).

SPARX is a family of ARX-based 64- and 128-bit block ciphers. Only addition modulo 216, 16-bit XOR and 16-bit rotations are needed to implement any version.

The SPARX ciphers have been designed according to the Long Trail Strategy put forward by its authors in the same paper. It can be seen as a counterpart of the Wide-Trail Strategy suitable for algorithms built using a large and weak S-Box rather than a small strong one. This method allows the designers to bound the differential and linear trial probabilities, unlike for all other ARX-based designs. The non-linearity is provided by SPECKEY, a 32-bit block cipher identical to SPECK-32 except for its key addition. The linear layer is very different from that of, say, the AES as it consists simply in a linear Feistel round for all versions.

## Feistel Networks

### ARX-Based

ARX-based ciphers are designed using only modular Addition, Rotation and XOR. In particular, the only source of non-linearity is the modular addition. Algorithms built in this fashion are usually faster and smaller than S-Box-based algorithms in software, as well as having some inherit security against side-channel attacks as modular addition leaks less information than table look-ups. However, modular addition is not as attractive for designing hardware optimized algorithms due to its latency and "large" input and output size.

The SPARX block cipher is ARX-based but, due to its having a SPN structure, is put in said category.

The round function of the permutation of Chaskey.
• Article: Chaskey: An Efficient MAC Algorithm for 32-bit Microcontrollers, SAC'14[7]
• Authors: Nicky Mouha, Bart Mennink, Anthony Van Herrewege, Dai Watanabe, Bart Preneel and Ingrid Verbauwhede
• Target: Software

Chaskey (primitive's website) is a lightweight MAC algorithm optimised for 32-bit micro-controllers. It is based on a 128-bit block cipher, the Chaskey cipher, which uses ARX operations and an Even-Mansour structure. This means that there is no key schedule: the 128-bit master key is XOR-ed, then a public permutation is applied and then the master key is XOR-ed again. This simplicity is possible at the cost of a weaker security claim as in e.g. PRINCE or PRIDE because a generic attack exists with a time complexity of about 2128/D if the attacker obtains D plaintext-ciphertext pairs.

The code implementing it is very simple and is given below. It is similar to that of SipHash.

The original paper also suggests doubling the number of rounds of the Chaskey cipher to obtain an even more secure primitive, Chaskey-LTS (Long Term Security), with 16 rounds. It was later suggested[101], in reaction to Leurent's differential-linear attack[102], to use a variant with 12 rounds called Chaskey-12.

#include <stdint.h>
#define ROTL(x,b) (uint32_t)( ((x) >> (32 - (b))) | ( (x) << (b)) )

void encrypt(uint32_t v[4], uint32_t key[4]) {
int i;
for (i=0; i<4; i++) v[i] ^= key[i];
for (i=0; i<8; i++) {
v[0] += v[1]; v[1]=ROTL(v[1], 5); v[1] ^= v[0]; v[0]=ROTL(v[0],16);
v[2] += v[3]; v[3]=ROTL(v[3], 8); v[3] ^= v[2];
v[0] += v[3]; v[3]=ROTL(v[3],13); v[3] ^= v[0];
v[2] += v[1]; v[1]=ROTL(v[1], 7); v[1] ^= v[2]; v[2]=ROTL(v[2],16);
}
for (i=0; i<4; i++) v[i] ^= key[i];
}


#### HIGHT

The round function of HIGHT.
• Article: HIGHT: A New Block Cipher Suitable for Low-Resource Device, CHES 06[16]
• Authors: Deukjo Hong, Jaechul Sung, Seokhie Hong, Jongin Lim, Sangjin Lee, Bon-Seok Koo, Changhoon Lee, Donghoon Chang, Jesang Lee, Kitae Jeong, Hyun Kim, Jongsung Kim, and Seongtaek Chee
• Target: Hardware

HIGHT is an ARX based generalised Feistel network with whitening. The only operations used are addition and substraction modulo 28, xor and bitwise rotations. The subfunctions F0 and F1 consist in the xor of three different rotations of the input. The key schedule generates 8 bytes of whitening keys by selecting some bytes of the master key and 128 bytes of subkeys in a more complex way. Both during whitening and during encryption, addition and xor are used at the same time on different part of the internal state (see the round function on the right).

Unlike for instance TWINE, the permutation of the words after addition (or xoring) of the subkeys is a simple rotation.

The first author of HIGHT is also the first author of LEA.

#### LEA

The round function of LEA.
• Article: LEA: A 128-Bit Block Cipher for Fast Encryption on Common Processors, WISA 13[37]
• Authors: Hong, D., Lee, J. K., Kim, D. C., Kwon, D., Ryu, K. H., and Lee, D. G.
• Target: Software

LEA is a 128-bit block cipher operating on 4 branches of 32 bits each. The only operations used are 32-bit modular addition, XOR and rotation (ARX structure): the designers suppose that "the usage of 32-bit and 64-bit processors will grow rapidly compared to 8-bit and 16-bit ones" (see specification[37], Section 1.1). The round function is described in the picture on the right. Note that the key is added in both data-path going in each modular additions.

The key schedule also follows the ARX paradigm: constants are added modulo 232 to the key state and the different words are then rotated.

The first author of LEA is also the first author of HIGHT.

#### RC5

The RC5 round function.
• Article: The RC5 Encryption Algorithm, FSE 95[63]
• Authors: Ron Rivest
• Target: Software

RC5 is a an ARX (modular Addition, Rotation, Xor) two-branched Feistel network. It is "word oriented", meaning that all operations are performed over sub-blocks of size w; w being the bit length of one branch. Thus, RC5 can have a block size of 32, 64 or 128 corresponding respectively to w=16, w=32 and w=64. The key can be made of any number b of bytes between 0 and 255 and the number r of rounds is also a parameter so that an instance of RC5 should be denoted RC5-w/r/b. Here, we fix w=32 and b=16 so that RC5-r is a shortcut for RC5-32/r/16. Its most remarkable feature is the use of data-dependent rotations.

The key schedule derives an array of subkeys from the master key and "magic constants" derived from the mathematical constants e and the golden ratio.

Like for XTEA, we provide a pseudo-code for the encryption routine. It comes from Section 4.1 of the original paper[63]. A is the left branch, B is the right one and S is the array of the subkeys.

A = A + S[0]
B = B + S[1]
for i = 1 to r do
A = ((A ⊕ B) <<< B) + S[2×i]
B = ((B ⊕ A) <<< A) + S[2×i+1]


It has been an inspiration for the AES competition finalist RC6. This algorithm is patented by RSA security.

#### SIMECK

The SIMECK round function.
• Article: The Simeck Family of Lightweight Block Ciphers, CHES'15[72]
• Authors: Gangqiang Yang, Bo Zhu, Valentin Suder, Mark D. Aagaard, and Guang Gong
• Target: Hardware

SIMECK is a family of block ciphers heavily inspired by the SIMON family of block ciphers. Indeed, the round function is the same up to a change in the rotation indices: rotations by 1, 8 and 2 bits are replaced by rotations by 0, 5 and 1 bit. The key schedule re-uses the round function, much like in SPECK, hence the name of the primitive.

The security claim of this cipher is based on that of SIMON: SIMECK is intended to be as secure as SIMON. Note that the designers of SIMECK are not affiliated to the National Security Agency (unlike the designers of SIMON and SPECK).

The change in the rotations and the key schedule allow an improved hardware implementation: SIMECK requires a smaller area than SIMON when implemented in hardware.

#### SIMON and SPECK

 Round function of SIMON Round function of SPECK
• Article: The SIMON and SPECK Families of Lightweight Block Ciphers, eprint.iacr.org, 2013[75]
• Authors: Ray Beaulieu, Douglas Shors, Jason Smith, Stefan Treatman-Clark, Bryan Weeks, and Louis Wingers (NSA)
• Target: Hardware (SIMON) and software (SPECK)

These ciphers have been designed by the American National Security Agency (NSA). They are both Feistel networks with two branches but differ by the design of their Feistel function. They are both almost ARX construction, meaning that they rely on Addition, word Rotation and Xor, although SIMON uses And gates instead of additions. Both perform exceptionnally well in both hardware and software, although SIMON is supposed to be more hardware-oriented and SPECK more software-oriented. Unlike all other ciphers' specification, no security analysis whatsoever is provided.

##### SIMON

Hardware-oriented, this blockcipher relies only on the following operations: and, rotation, xor. It is a classical Feistel network where the Feistel function consists in applying basic operations on the branch, xoring the in subkey and then xoring the result with the other branch.

##### SPECK

Software-oriented, this blockcipher relies only on the following operations: addition, rotation, xor (ARX construction). The structure of the round function is a typical ARX structure similar to the one of the block cipher Threefish used by the hash function Skein[103].

#### XTEA

• Article: Tea Extensions[87]
• Authors: Needham R. and Wheeler D.
• Target: Software

XTEA is a cipher designed so as to be described by the smallest amount of code. It is an improvement of a previous design called TEA which had identical goals but several weaknesses. To illustrate the compactness of the C-code describing encryption, we provide below a possible implementation (suggested on the wikipedia page of XTEA).

#include <stdint.h>

/* take 64 bits of data in v[0] and v[1] and 128 bits of key[0] - key[3] */

void encipher(unsigned int num_rounds, uint32_t v[2], uint32_t const key[4]) {
unsigned int i;
uint32_t v0=v[0], v1=v[1], sum=0, delta=0x9E3779B9;
for (i=0; i < num_rounds; i++) {
v0 += (((v1 << 4) ^ (v1 >> 5)) + v1) ^ (sum + key[sum & 3]);
sum += delta;
v1 += (((v0 << 4) ^ (v0 >> 5)) + v0) ^ (sum + key[(sum>>11) & 3]);
}
v[0]=v0; v[1]=v1;
}


### Two Branched

In this category, we put all the Feistel networks operating on blocks of size 2n for which the Feistel function maps n bits to n bits that are not based on the ARX paradigm.

#### DESLX

• Article: New Lightweight DES Variants, FSE 07[12]
• Authors: Gregor Leander, Christof Paar, Axel Poschmann, and Kai Schramm
• Target: Hardware

This cipher is a modified version of DES. The 8 S-boxes have been replaced by unique one to make it easier to implement. Besides, the S-box was chosen so as to achieve better resilience against linear and differential attacks. Another modification is the use of a FX structure to increase the security: parts of the keys are used as whitening keys in the input and in the output.

The idea of using an old design from an era when hardware optimization was critical was also used in GOST revisited.

#### GOST revisited

The GOST round function.
• Article: 256 Bit Standardized Crypto for 650 GE – GOST Revisited, CHES 10[14]
• Authors: Axel Poschmann, San Ling, and Huaxiong Wang
• Target: Hardware

The GOST used to be a sovietic counterpart for the American NIST. It still exists as a standards organization for countries of the former USSR. In cryptography, GOST usually refers to the block cipher GOST standard, a 64 bit two-branch Feistel network with a Feistel function using eight unspecified S-boxes. GOST revisited consists simply in the block cipher described in the GOST standard such that it uses eight copies of the PRESENT S-box. The idea of using such an old design is to benefit from the cryptanalytic scrutiny it has already been subject to. Besides, the GOST cipher had already been standardized for 20 years when the paper was published. The approach consisting in modifying an old standard is similar to that of the designers of DESLX.

There is no real key schedule, different blocks of the master key are used at each round. The Feistel function is simply a modular addition of the key (modulo 232), an S-box layer and rotation by 11-bits. This very simple structure and the lack of a key schedule explain the very small hardware footprint of the cipher.

The authors compare the footprint of GOST using their S-box layer and the one used by the Central Bank of Russian Federation and, interestingly, the difference is not so big (identical throughput and 800 or 1000 GE depending on the speed/area tradeoff).

#### ITUbee

A complete ITUbee encryption.
• Article: ITUbee: A Software Oriented Lightweight Block Cipher, Lightweight Cryptography for Security and Privacy 13[21]
• Authors: Ferhat Karakoç, Hüseyin Demirci, and A. Emre Harmancı
• Target: Software

ITUbee is a block cipher using 20 rounds of a Feistel structure with key whitening at the beginning and end of the encryption. Its structure is summarized in the figure on the right where:

• L is a multiplication by a simple 5x5 square matrix operating on bytes,
• S is a substitution layer using the S-Box of the AES,
• F(x) = S(L(S(x))).

Its use of a Feistel function based on a small SPN is reminiscent of the Generalized Feistel Network Piccolo. Chunks of the master key are used directly during encryption; the only key schedule consists in adding round constant in a fashion similar to LED or PRINCE. Another Feistel Network with a SASASAS structure as its Feistel function was published later: RoadRunneR.

Its main features are low power consumption and low memory requirement in software (8-bits microcontroller) according to simulations on the AVR ATiny45 microcontroller. The authors claim resilience against related key attacks. Unlike many lightweight block ciphers which have a block length of 64 bits, ITUbee uses blocks of 80 bits.

#### KASUMI/MISTY

A description of the recursive structure of MISTY1 (KASUMI is similar to MISTY1) and MISTY2.
##### MISTY
• Article: New Block Encryption Algorithm MISTY, Fast Software Encryption 97[45]
• Authors: Minoru Matsui
• Target: Software and Hardware

MISTY is a set of two 64-bit block ciphers using 4n rounds (usually, 4n=8) with a Feistel structure for MISTY1 and MISTY-like (i.e. the non linear permutation is applied on a branch directly) for MISTY2 along with specific key dependent transformation applied on the branches between the rounds. The structure of the non-linear function is itself a 3-round Feistel Network and the Feistel function used in this second layer has a MISTY-like structure. This recursive structure is shown in the picture on the right. At the final level, 7- and 9-bit bijective S-Boxes are used. While uncommon, this choice allows the S-Boxes to be both APN and bent, a task significantly harder to achieve on 8-bit[note 9].

The design criteria for MISTY is clearly stated:

1. MISTY should have a numerical basis for its security,
2. MISTY should be reasonably fast in software on any processor,
3. MISTY should be sufficiently fast in hardware implementation.

The key schedule of MISTY re-uses a component used during encryption, namely the so-called FI function corresponding to a 3-round unbalanced MISTY-like structure using the 7- and 9-bit S-Boxes.

##### KASUMI

KASUMI is a variant of MISTY1 allowing a more efficient hardware implementation. Its specification can be obtained from the etsi.org website[22]. It is referred to as A5/3 in this specification. It is identical to MISTY1 with 8 rounds (the default) except for its key schedule which simply rotates the bits of the master key and XORs round constants. This simplification lead to a vulnerability against related-key attacks[23] which is not present in MISTY1.

#### LBlock

 A high level view of the LBlock encryption. The Feistel function of Lblock.
• Article: LBlock: A Lightweight Block Cipher, ACNS 11[31]
• Authors: Wenling Wu and Lei Zhang
• Target: Hardware and Software

This Feistel Network has two branches of 32 bits and a "twist": the branch which is xored with the output of the F function is first rotated by 8 bits. The Feistel function is made of a xor with a subkey, a layer of 8 distinct 4x4 S-boxes and a word permutation shuffling 4-bit words. The permutation used in the Feistel function and the bit rotation of one of the branch make this design very similar to TWINE as explained in the TWINE specification[84].

The key schedule involves two additional S-boxes which are different from the ones used in the Feistel function.

• Article: RoadRunneR: A Small And Fast Bitslice Block Cipher For Low Cost 8-bit Processors, LightSec 2015[67]
• Authors: Adnan Baysal and Sühap Şahin
• Target: Software

RoadRunneR is a Feistel Network which uses a SPN as its Feistel function. The non-linear layer of the Feistel funciton is based on the bitsliced implementation of its S-Box as can be seen for instance in the LS strategy introduced for Robin and Fantomas. The designers had the following goals:

1. Implementation efficiency in 8-bit CPUs,
2. No table and SRAM usage,
4. Provable security like in wide trail design strategy.

The key schedule is very simple: 32-bit chunks of the master key are used one after another. Once the end of the key is reached, the first bits are used again. Round constants are added to prevent slide attacks.

The Feistel function has a SPN structure consisting in 4 S-Box layers, 3 linear layers (much like ITUbee) and 3 key additions. The 4-bit S-Box was chosen for the very simple circuit that can be used to compute it as well as its good cryptographic properties. It was found in a previous work by Ullrich et al.[94] and is also used by Mysterion. The linear layer is applied on 4 bytes separately and consists in the xor of three different rotations of its input (in a fashion similar to the F0 and F1 functions of HIGHT): $x \mapsto x \oplus (x <<< 1) \oplus (x <<< 2)$.

#### SEA

The SEA round function.
• Article: SEA: A Scalable Encryption Algorithm for Small Embedded Applications, Smart Card Research and Advanced Applications 06[69]
• Authors: Francois-Xavier Standaert, Gilles Piret, Neil Gershenfeld, and Jean-Jacques Quisquater
• Target: Software and Hardware

SEA is a block cipher which can have an arbitrary block size n (as long as n=6b for some b), word size w and number of rounds nr. A complete description of the algorithm (round function and update of the key) is given on the figure on the right which comes from the original paper[69]. It is based on the following operations:

• Bitwise XOR
• Application of an S-box S. Interestingly, S is a 3x3 S-box.
• Rotation of the words in a vector of words
• Bit rotation inside a word

### Generalized Feistel Networks (GFN)

#### CLEFIA

The CLEFIA encryption and its subroutines.
• Article: The 128-Bit Blockcipher CLEFIA, FSE 07[9]
• Authors: Taizo Shirai, Kyoji Shibutani, Toru Akishita, Shiho Moriai, and Tetsu Iwata
• Target: Hardware and Software

This cipher is intended for use in DRM protocols. Its "lightweightness" can be debated as an area of 4950 GE is significant. The designers of CLEFIA worked for Sony and some of them were involved in the creation of Piccolo.

CLEFIA has been standardized and is part of the ISO-29192[100] with PRESENT.

#### Piccolo

The Piccolo encryption.
• Article: Piccolo: an ultra-lightweight blockcipher, CHES 11[51]
• Authors: Shibutani, K., Isobe, T., Hiwatari, H., Mitsuda, A., Akishita, T., & Shirai, T.
• Target: Hardware

Piccolo is a GFS with 4 16-bits branches which employs a sophisticated permutation for the diffusion layer instead of a simple shift (like TWINE and as opposed to CLEFIA) as well as whitening. Note that although the branches of the Fesitel structure are made of 16 bits, the permutation operates on words of 8 bits.

The Feistel function is a small SPN where the permutation layer is a multiplication by the same matrix as the one used in the MixNibbles operation in the AES and KLEIN --- although in a different field. The 4x4 S-box was designed especially for Piccolo and, while still having decent non-linearity and differential uniformity, has a tiny hardware footprint: it can be implemented using only 4 NOR gates, 3 XOR gates and 1 XNOR gate. A small SPN is also used as the Feistel function in ITUbee.

The designers work for Sony and several of them worked on CLEFIA.

#### TWINE

The round function of TWINE.
• Article: TWINE: A Lightweight, Versatile Block Cipher, Workshop on Lightweight Crypto 11[84]
• Authors: Tomoyasu Suzaki, Kazuhiko Minematsu, Sumio Morioka, and Eita Kobayashi
• Target: Hardware and software

TWINE is a generalised Feistel structure (GFS) with 16 4-bits branches. The Feistel function, called 8 times per round, consists simply in xoring a subkey and applying a 4x4 S-box. The key schedule itself is also a GFS.

The diffusion layer is not a simple circular shift, like for instance in CLEFIA and HIGHT, it is a more sophisticated permutation to speed-up diffusion. It is based on Suzaki et al.'s Improving the Generalized Feistel (FSE 10)[104]: the permutation used in TWINE requires only half as much rounds as a circular shift for a one sub-block difference to diffuse to all the sub-blocks. The S-box is based on the inverse function in GF(24), just like the one of the AES which is based on the inverse function in GF(28).

The designers of TWINE worked at NEC Corporation, a Japanese company. While a priori different due to its 2-branched nature, LBlock actually has a structure very similar to TWINE.

## Other Designs

#### KTANTAN and KATAN

The structure of a round of KATAN/KTANTAN.
• Article: KATAN and KTANTAN — A Family of Small and Efficient Hardware-Oriented Block Ciphers, CHES 09[27]
• Authors: Christophe De Cannière, Orr Dunkelman, and Miroslav Knezevic
• Target: Hardware

The optimization of the physical footprint is at the core of these two designs, at the cost of some speed. The only difference between the two families is the key schedule: in KTANTAN, the key is included in the hardware and cannot be changed. The design is based on a variant of the stream cipher trivium called bivium.

The structure of the encryption is best described by the designers themselves:

The structure of the KATAN and the KTANTAN ciphers is very simple — the plaintext is loaded into two registers (whose lengths depend on the block size). Each round, several bits are taken from the registers and enter two nonlinear Boolean functions. The output of the Boolean functions is loaded to the least significant bits of the registers (after they were shifted). Of course, this is done in an invertible manner. To ensure sufficient mixing, 254 rounds of the cipher are executed.

Several attacks based on Meet-in-the-Middle related concepts have been successfully applied on these ciphers[29][30]. They exploit the slow diffusion of the key material to the internal state throughout the rounds.

The hash function QUARK borrows ideas from these ciphers.

## Notes

1. Since the S-box used has better properties than the ones of the DES, attacks on DES may not be applicable to DESLX. Furthermore, no attack exists (to the best of our knowledge) on DESLX with its full FX structure.
2. To the best of our knowledge.
3. Encryption only.
4. The figures for Midori correspond to an encryption-only implementation.
5. Note that the implementation proposed uses a 10 MHz frequency (unlike the other ciphers in this table).
6. The paper in which Mysterion was introduced does not describe a key schedule, only a round function (and a number of round).
7. The blocksize of SEA can actually be chosen arbitrarily among multiples of 6. 96 bits is the smallest size considered in the paper about the hardware implementation of SEA (MSQ07).
8. Note that SKINNY is built using the TWEAKEY framework which makes little distinction between the key and the tweak. Thus, the key sizes actually correspond to the sum of the key and the tweak length.
9. In fact, whether an 8-bit APN permutation exist is still an open problem.

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