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SQUARE is an 8-round SPN structure block cipher and its round function and key schedule have been slightly modified to design building blocks of Rijndael. Key schedule of SQUARE is simple and efficient but fully affine, so we apply a related-key attack on it. We find a 3-round related-key differential trail with probability 2^{-28}, which has zero differences both on its input and output states, which is called *local collision* in [6]. By extending of this related-key differential, we construct a successful attack on full rounds of SQUARE. In this paper, we present a key recovery attack on full rounds of SQUARE using a related-key boomerang distinguisher. We construct a 7-round related-key boomerang distinguisher with probability 2^{-119} by finding *local collision*, and calculate its probability using *ladder switch* and *multiple path estimation* techniques. As a result, one round on top of the distinguisher is added to construct an attack on full rounds of SQUARE which recovers 16-bit key information with 2^{123} encryptions and 2^{121} data.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.1 pp.3-9

- Publication Date
- 2011/01/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E94.A.3

- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)

- Category
- Symmetric Cryptography

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Bonwook KOO, Yongjin YEOM, Junghwan SONG, "Related-Key Boomerang Attack on Block Cipher SQUARE" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 1, pp. 3-9, January 2011, doi: 10.1587/transfun.E94.A.3.

Abstract: SQUARE is an 8-round SPN structure block cipher and its round function and key schedule have been slightly modified to design building blocks of Rijndael. Key schedule of SQUARE is simple and efficient but fully affine, so we apply a related-key attack on it. We find a 3-round related-key differential trail with probability 2^{-28}, which has zero differences both on its input and output states, which is called *local collision* in [6]. By extending of this related-key differential, we construct a successful attack on full rounds of SQUARE. In this paper, we present a key recovery attack on full rounds of SQUARE using a related-key boomerang distinguisher. We construct a 7-round related-key boomerang distinguisher with probability 2^{-119} by finding *local collision*, and calculate its probability using *ladder switch* and *multiple path estimation* techniques. As a result, one round on top of the distinguisher is added to construct an attack on full rounds of SQUARE which recovers 16-bit key information with 2^{123} encryptions and 2^{121} data.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.3/_p

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@ARTICLE{e94-a_1_3,

author={Bonwook KOO, Yongjin YEOM, Junghwan SONG, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Related-Key Boomerang Attack on Block Cipher SQUARE},

year={2011},

volume={E94-A},

number={1},

pages={3-9},

abstract={SQUARE is an 8-round SPN structure block cipher and its round function and key schedule have been slightly modified to design building blocks of Rijndael. Key schedule of SQUARE is simple and efficient but fully affine, so we apply a related-key attack on it. We find a 3-round related-key differential trail with probability 2^{-28}, which has zero differences both on its input and output states, which is called *local collision* in [6]. By extending of this related-key differential, we construct a successful attack on full rounds of SQUARE. In this paper, we present a key recovery attack on full rounds of SQUARE using a related-key boomerang distinguisher. We construct a 7-round related-key boomerang distinguisher with probability 2^{-119} by finding *local collision*, and calculate its probability using *ladder switch* and *multiple path estimation* techniques. As a result, one round on top of the distinguisher is added to construct an attack on full rounds of SQUARE which recovers 16-bit key information with 2^{123} encryptions and 2^{121} data.},

keywords={},

doi={10.1587/transfun.E94.A.3},

ISSN={1745-1337},

month={January},}

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TY - JOUR

TI - Related-Key Boomerang Attack on Block Cipher SQUARE

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 3

EP - 9

AU - Bonwook KOO

AU - Yongjin YEOM

AU - Junghwan SONG

PY - 2011

DO - 10.1587/transfun.E94.A.3

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E94-A

IS - 1

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - January 2011

AB - SQUARE is an 8-round SPN structure block cipher and its round function and key schedule have been slightly modified to design building blocks of Rijndael. Key schedule of SQUARE is simple and efficient but fully affine, so we apply a related-key attack on it. We find a 3-round related-key differential trail with probability 2^{-28}, which has zero differences both on its input and output states, which is called *local collision* in [6]. By extending of this related-key differential, we construct a successful attack on full rounds of SQUARE. In this paper, we present a key recovery attack on full rounds of SQUARE using a related-key boomerang distinguisher. We construct a 7-round related-key boomerang distinguisher with probability 2^{-119} by finding *local collision*, and calculate its probability using *ladder switch* and *multiple path estimation* techniques. As a result, one round on top of the distinguisher is added to construct an attack on full rounds of SQUARE which recovers 16-bit key information with 2^{123} encryptions and 2^{121} data.

ER -