#  SCIENCE CHINA Information Sciences, Volume 63 , Issue 3 : 139102(2020) https://doi.org/10.1007/s11432-018-9818-y

## Theoretical analysis of persistent fault attack Fan ZHANG 1,2,3,4, Guorui XU 1,3,4,*, Ziyuan LIANG 1,3,4, Kui REN 3,4
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• ReceivedDec 30, 2018
• AcceptedMar 1, 2019
• PublishedFeb 10, 2020
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### Abstract

There is no abstract available for this article. ### Acknowledgment

This work was supported in part by Open Fund of State Key Laboratory of Cryptology (MMKFKT201805), Zhejiang Key RD Plan(2019C03133), Major Scientific Research Project of Zhejiang Lab (2018FD0ZX01), Young Elite Scientists Sponsorship Program by CAST(17-JCJQ-QT-045), Alibaba-Zhejiang University Joint Institute of Frontier Technologies.

Appendixes A–C.

### References

 Zhang F, Lou X X, Zhao X J, et al. Persistent fault analysis on block ciphers. IACR Trans Cryptograph Embed Syst, 2018, 2018: 150--172. Google Scholar

 Joye M, Tunstall M. Fault Analysis in Cryptography. Berlin: Springer, 2012. Google Scholar

 Ferrante M, Saltalamacchia M. The coupon collector's problem. Mater Matemàtics, 2014, 2014: 1--35. Google Scholar

 Flajolet P, Gardy D, Thimonier L. Birthday paradox, coupon collectors, caching algorithms and self-organizing search. Discrete Appl Math, 1992, 39: 207-229 CrossRef Google Scholar

• Figure 1

(Color online) (a) Distribution of values in ciphertexts; (b) error rate and number of ciphertexts for all cases.

•

Algorithm 1 Pseudo code to distinguish two special values

Require:$n,~j,~\text{value}[i]$ $(~0~\leq~i~\leq~j)$;

$\text{count}[n]~\Leftarrow~[0..0];$ $\text{value}_{\min}~\Leftarrow~0;$ $~\text{value}_{\max}~\Leftarrow~0$;

for $i~\Leftarrow~0$ TO $j-1$

$\text{count}[\text{value}[i]]~\Leftarrow~\text{count}[\text{value}[i]]~+~1$;

end for

for $\text{value}~\Leftarrow~0$ TO $N-1$

if $\text{count}[\text{value}]~\leq~\text{count}[\text{value}_{\min}]$ then

$\text{value}_{\min}~\Leftarrow~\text{value}$;ELSIF$\text{count}[\text{value}]~>~\text{count}[\text{value}_{\max}]$

$\text{value}_{\max}~\Leftarrow~\text{value}$;

end if

end for

return $\text{value}_{\min},~\text{value}_{\max}$.