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Table 2 Summary of complexities for our protocols and related protocols

From: Efficient privacy-preserving variable-length substring match for genome sequence

 

Btime

Bsize

Dtime

Dsize

Stime

Comm.

Round

ss-ROT (proposed)

0

0

\(\ell N\)

\(\ell N\)

\(\ell\)

\(\ell\)

\(\ell\)

Secure LPM (proposed)

\(\ell\)

\(\ell\)

\(\ell N\)

\(\ell N\)

\(\ell\)

\(\ell\)

\(\ell\)

[17, 19] (LPM by AHE)

−

−

−

−

\(\ell N\)

\(\ell \sqrt{N}\)

\(\ell\)

Baseline LPM

\(\ell ^2 N\)

\(\ell ^2 N\)

N

N

\(\ell ^2 N\)

\(\ell ^2 N\)

\(\log \ell +\log N\)

Secure LMEM (proposed)

\(\ell ^2\)

\(\ell ^2\)

\(\ell N\)

\(\ell N\)

\(\ell ^2\)

\(\ell ^2\)

\(\ell\)

Baseline LMEM

\(\ell ^3 N\)

\(\ell ^3 N\)

N

N

\(\ell ^3 N\)

\(\ell ^3 N\)

\(\log \ell +\log N\)

  1. BTime and Bsize are generation time and size of BTs. Dtime and Dsize are generation time for the shares of the database and size of the shares. Stime is the time for Search phase. Comm. is the size of data exchanged between computing nodes. Round is the number of data exchanges