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SCIENCE CHINA Information Sciences, Volume 62, Issue 3: 032102(2019) https://doi.org/10.1007/s11432-017-9382-2

Related-tweakey impossible differential attack on reduced-round Deoxys-BC-256

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  • ReceivedDec 27, 2017
  • AcceptedFeb 28, 2018
  • PublishedJan 31, 2019

Abstract

Deoxys-BC is the internal tweakable block cipher of Deoxys, a third-round authenticated encryption candidate at the CAESAR competition. In this study, by adequately studying the tweakey schedule, we seek a six-round related-tweakey impossible distinguisher of Deoxys-BC-256, which is transformed from a 3.5-round single-key impossible distinguisher of AES, by application of the mixed integer linear programming (MILP) method. We present a detailed description of this interesting transformation method and the MILP-modeling process.Based on this distinguisher, we mount a key-recovery attack on 10 (out of 14) rounds of Deoxys-BC-256.Compared to previous results that are valid only when the key size $>204$ and the tweak size $<52$, our method can attack 10-round Deoxys-BC-256 as long as the key size $\geq174$ and the tweak size $\leq82$. For the popular setting in which the key size is 192 bits, we can attack one round more than previous studies.Note that this paper only gives a more accurate security evaluation and does not threaten the security of full-round Deoxys-BC-256.


Acknowledgment

This work was supported by National Key Research and Development Program of China (Grant No. 2017YFA0303903), National Natural Science Foundation of China (Grant No. 61672019), National Cryptography Development Fund (Grant No. MMJJ20170121), Zhejiang Province Key RD Project (Grant No. 2017C01062), Fundamental Research Funds of Shandong University (Grant No. 2016JC029), and China Postdoctoral Science Foundation (Grant No. 2017M620807).


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  • Figure 3

    Search for longer related-key differential.

  • Table 1   Cryptanalysis results for Deoxys-BC-256. Our attack can be mounted on Deoxys-BC-256 with a wider key size range. Because the cipher adopts the TWEAKEY framework (such as the tweak-updating mode, i.e., the tweak can be changed but the key stays the same), our attack is more efficient as the data complexity can be beyond full-codebook. A beyond-full-codebook attack on SKINNY was published in ; we give a more specified description about beyond-full-codebook attacks in Subsection .
    Primitive Number of rounds Tweak size Key size Time Data Attack type Ref.
    8/14 128 128 $\leq~2^{128}$ MitM [1]
    $\leq$ 8/14 128 128 $\leq~2^{128}$ Differential [1]
    Deoxys-BC-256 9/14 128 128 $2^{128}$ $2^{117}$ Rectangle [8]
    10/14 $<52$ $>204$ $2^{204}$ $2^{127.58}$ Rectangle [8]
    10/14 $\leq82$ $\geq174$ $2^{173.1}$ $2^{135}$ Impossible differential This paper
  • Table 2   $h$-permutation
    $i$ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    $h(i)$ 1 6 11 12 5 10 15 0 9 14 3 4 13 2 7 8
  • Table 3   Actual values of impossible differential conforming the distinguisher
    Round Index $\Delta~{\rm~TK}^1$ $\Delta~{\rm~TK}^2$ $\Delta~{\rm~STK}$ $\Delta~X$ $\Delta~Z$ $\Delta~W$
    1 8 0x3d 0x3d
    9 0x3d 0x47
    10 0x00 0x00
    11 0x00 0x7a
    2 8 0x66 0x5b 0x3d
    9 0x36 0x71 0x47
    11 0x7a
    3 9 0x66 0xb6 0xd0
    14 0x36 0xe3 0xd5
    4 14 0x66 0x6c 0x0a
    7 0x36 0xc6 0xf0
    5 7 0x66 0xd9 0xbf
    0 0x36 0x8d 0xbb 0x3e 0xd5
    1 0xba 0x2d
    2 0x00
    3 0x7c
    6 0 0x66 0xb3 0xd5
    1 0x36 0x1b 0x2d
    7 1 0x66 0x66 0x00
    6 0x36 0x36 0x00
    8 6 0x66 0xcd 0xab 0xab
    15 0x36 0x6d0x5b 0x5b

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