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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 61 , Issue 3 : 030312(2018) https://doi.org/10.1007/s11433-017-9132-y

Improving the efficiency of quantum hash function by dense coding of coin operators in discrete-time quantum walk

More info
  • ReceivedOct 3, 2017
  • AcceptedNov 8, 2017
  • PublishedJan 18, 2018
PACS numbers

Abstract


Funding

the National Natural Science Foundation of China(Grant,Nos.,61572053,61671087,U1636106,61602019)

and Beijing Natural Science Foundation(Grant,No.,4162005)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61572053, 61671087, U1636106, and 61602019), and Beijing Natural Science Foundation (Grant No. 4162005).


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  • Figure 1

    Circuit representation of the unitary operation at the ith iteration in the first QHF. The top n lines are the quantum register for storing the information about the position. The two lower lines are the two-bit message m2i1m2i, and the other line is the quantum register for storing the information about the coin.

  • Figure 2

    (Color online) Hash values of C1, C2, C3, C4, C5.

  • Figure 3

    Circuit representation of the unitary operation at the ith iteration in the second QHF. The top n lines are the quantum register for storing the information about the position. The three lower lines are the three-bit message, and the other line is the quantum register for storing the information about the coin.

  • Figure 4

    (Color online) Hash values of C1, C2, C3, C4, C5.

  • Table 1   Results for diffusion and confusion tests in the first QHF

    N=1024

    N=2048

    N=10000

    Mean

    B¯

    38.8545

    38.5542

    38.5839

    38.6642

    A¯

    69.2021

    69.2085

    69.1016

    69.1707

    T¯

    108.0566

    107.7627

    107.6855

    107.8349

    P (%)

    48.8944

    48.7614

    48.7265

    48.7941

    ΔT

    6.9318

    6.4671

    6.4822

    6.6270

    ΔP

    3.1366

    2.9263

    2.9331

    2.9987

  • Table 2   Results for diffusion and confusion tests in the second QHF

    N=1024

    N=2048

    N=10000

    Mean

    B¯

    41.4688

    41.3569

    42.5407

    41.7888

    A¯

    70.2764

    70.1060

    70.2384

    70.2069

    T¯

    111.7452

    111.4629

    112.7791

    111.9957

    P (%)

    50.5634

    50.4357

    51.0313

    50.6768

    ΔT

    7.8213

    8.5069

    8.2029

    8.1770

    ΔP

    3.5391

    3.8493

    3.7117

    3.7000

  • Table 3   Comparison between our schemes and other QW-based QHFs in terms of collision resistance

    No collision

    One collision

    Two collisions

    More collisions

    ref. [24]

    7688

    375

    1662

    275

    ref. [25]

    9367

    617

    16

    0

    ref. [26]

    9068

    889

    42

    1

    Our first scheme

    9914

    86

    0

    0

    Our second scheme

    9854

    71

    0

    75

  • Table 4   Comparison between our schemes and other QW-based QHFs in terms of resource consumption. Here, , and are 2×2 coin operators, and is a 4×4 coin operator

    The number of the particles

    Quantum operation

    The number of message bits

    ref. [24]

    2

    Sxy(IC2C2)

    1

    ref. [25]

    2

    Sxy(IC4)

    1

    ref. [26]

    1

    SyC2SxC2

    1

    Our first scheme

    1

    Sc(ICv)

    2

    Our second scheme

    1

    Sc(ICw)

    3

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