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SCIENCE CHINA Information Sciences, Volume 62, Issue 3: 039108(2019) https://doi.org/10.1007/s11432-018-9474-3

High-efficient generation algorithm for large random active shield

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  • ReceivedJan 10, 2018
  • AcceptedMay 29, 2018
  • PublishedJan 8, 2019

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61376032) and Tianjin Science and Technology Project of China (Grant No. 15ZCZDGX00180).


References

[1] Shen C X, Zhang H G, Feng D G. Survey of information security. Sci China Ser F-Inf Sci, 2007, 50: 273-298 CrossRef Google Scholar

[2] Tria A, Choukri H. Invasive attacks. In: Encyclopedia of Cryptography & Security. Boston: Springer, 2011. 623--629. Google Scholar

[3] Xuan T N, Danger J L, Guilley S, et al. Cryptographically secure shield for security IPs protection. IEEE Trans Comput, 2017, 66: 354--360. Google Scholar

[4] Briais S, Cioranesco J M, Danger J L, et al. Random active shield. In: Proceedings of Workshop on Fault Diagnosis and Tolerance in Cryptography, Piscataway, 2012. 103--113. Google Scholar

[5] Briais S, Caron S, Cioranesco J M, et al. 3D hardware canaries. In: Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2012. 1--22. Google Scholar

[6] Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms. 3rd ed. Cambridge: MIT press, 2009. 65--97, 359--397. Google Scholar

  • Figure 1

    (a) Procedure of DPOA; (b) procedure of DCDPOA; (c) simulation results; (d) ET of three algorithms.

  •   

    Algorithm 1 DPOA

    Require:width $~W~$ and height $~H~$ $~(W,~H~\in~2\mathbb{N})~$;

    Output:final Hamiltonian path $~P_{F}~$;

    $~S_{B}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~8,~1~\le~j~\le~8,~~i,j~\in~2~\mathbb{N}~\right\}~$;

    $~P_{B}~\Leftarrow~{\rm~CM}(S_{B}~)~$;

    $~w~\Leftarrow~8~$, $~h~\Leftarrow~8~$;

    if $~W~\ge~H~$ then

    while $~h~<~H~$ do

    $~S_{\rm~ER}~\Leftarrow~\left\{~\left.~S(i,h+1)~\right|~1~\le~i~\le~8,~~i~\in~2\mathbb{N}+1~\right\}~$;

    $~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~ER}~)~$;

    $~h~\Leftarrow~h+2~$;

    end while

    while $~w~<~W~$ do

    $~S_{\rm~EC}~\Leftarrow~\left\{~\left.~S(w+1,j)~\right|~1~\le~j~\le~H,~~j~\in~2\mathbb{N}+1~\right\}~$;

    $~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~EC}~)~$;

    $~w~\Leftarrow~w+2~$;

    end while

    else

    while $~w~<~W~$ do

    $~S_{\rm~EC}~\Leftarrow~\left\{~\left.~S(w+1,j)~\right|~1~\le~j~\le~8,~~j~\in~2\mathbb{N}+1~\right\}~$;

    $~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~EC}~)~$;

    $~w~\Leftarrow~w+2~$;

    end while

    while $~h~<~H~$ do

    $~S_{\rm~ER}~\Leftarrow~\left\{~\left.~S(i,h+1)~\right|~1~\le~i~\le~W,~~i~\in~2\mathbb{N}+1~\right\}~$;

    $~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~ER}~)~$;

    $~h~\Leftarrow~h+2~$;

    end while

    end if

    $~P_{F}~\Leftarrow~P_{B}~$.

  •   

    Algorithm 2 DCDPOA

    Require:width $~W~$ and height $~H~$ $~(W,~H~\in~2\mathbb{N})~$;

    Output:final Hamiltonian path $~P_{F}~$;

    Solve $~\begin{cases} w~\times~N~+~4~\times~(N-1)~+p=W,~\\ N~\in~\mathbb{N},~~w,p~\in~2\mathbb{N}, \end{cases}~$and$~\begin{cases} h~\times~M~+~4~\times~(M-1)~+q=H,~\\ M~\in~\mathbb{N},~~h,q~\in~2\mathbb{N}, \end{cases}~$ get suitable $~N,w,p,M,h,q~$;

    for $~n=1:N~$

    for $~m=1:M~$

    $~P_{a}~\Leftarrow~{\rm~DP}(w,h)~$;

    if $~m==1~$ then

    $~P_{b}~\Leftarrow~P_{a}~$;

    else

    $~S_{\rm~CH}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~w,~h~\le~j~\le~h+4,\right.~$ $~~~~~~~~~~~\left.~i,~j~\in~2~\mathbb{N}+1~\right\}~$;

    $~P_{b}~\Leftarrow~{\rm~DP}(P_{a},~S_{\rm~CH},~P_{b})~$;

    end if

    end for

    if $~n==1~$ then

    $~P_{c}~\Leftarrow~P_{b}~$;

    else

    $~S_{\rm~CV}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~j~\le~\left[~h~\times~M~+~4~\times~(M-1)~\right],~\right.~$$~\left.~~~~~~~~~~~~~w~\le~i~\le~w+4,~~i,~j~\in~2~\mathbb{N}+1~\right\}~$;

    $~P_{c}~\Leftarrow~{\rm~DP}(P_{b},~S_{\rm~CV},~P_{c})~$;

    end if

    end for

    $~S_{\rm~RV}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~\left[~w~\times~N~+~4~\times~(N-1)~\right],~\right.~$ $~~~~~~~~~~~~\left[~h~\times~M~+~4~\times~(M-1)~\right]~\le~j~\le~H,~$ $~\left.~~~~~~~~~~~~i,j~\in~2~\mathbb{N}+1~\right\}~$;

    $~P_{c}~\Leftarrow~{\rm~DP}(P_{c},~S_{\rm~RV})~$;

    $~S_{\rm~RH}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~\left[~w~\times~N~+~4~\times~(N-1)~\right]~\le~i~\le~W,~\right.~$ $~\left.~~~~~~~~~~~~~1~\le~j~\le~H,~~i,j~\in~2~\mathbb{N}+1~\right\}~$;

    $~P_{c}~\Leftarrow~{\rm~DP}(P_{c},~S_{\rm~RH})~$;

    $~P_{F}~\Leftarrow~P_{c}~$.

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