Security and Trust Management by Sjouke Mauw & Mauro Conti

Author:Sjouke Mauw & Mauro Conti
Language: eng
Format: epub
ISBN: 9783030315115
Publisher: Springer International Publishing

Scalar product (Scalar) needs 6k, 4k, k, and addition, encryption, decryption, and exponential, respectively.

Exponential protocol (SExp.) employs 6, 7, 2, and addition, encryption, decryption, and exponential, respectively.

Distance protocol (Dist.) requires 2 and addition and exponential, respectively.

Given the above argument, the number of times that Relation 3 employs addition, encryption, decryption, and exponential operations can be approximated as follows:

(4)

We implemented addition, encryption, decryption, and exponential protocols using on a single machine running Ubuntu 14.04 LTS with 64-bit microprocessor and 8 GB of RAM. The cryptographic key length of Paillier is selected as NIST standard as 4096 bits. In our implementation, addition, encryption, and decryption for records required 8.3, 5.6, and 9 s, respectively. Moreover, by considering , each exponential operation needs 200 additions for element with -bit length equal to 20.

To assess the practical feasibility of our mechanism, we performed a number of experiments. Grosse et al. [10] showed that 50 adversarial instances are enough to infer a considerable MMD statistical distance between two datasets. Moreover, according to standard dimensioning technique, proposed in [19], the minimum size for a dataset to produce a reliable result is to dimension it as six times to the number of features. Therefore, to get a better insight on computation cost of the proposed approach, we consider the number of features to get their values as , while the number of data in training set (m) is set to six times of k. The number of adversarial instances (n) varies from 50 and gets its value as .

Figures 2 and 3 show the computation costs (in log-scale) for different values of n and k, respectively. As explained previously, m is considered as a dependent variable to the number of features (). From Fig. 2, it can be inferred that for fixed values of k and m, the required runtime increases linearly (with a slight slop) when n increases. On the other hand, for fixed value of n, when k varies from 20 to 200, the runtime increases from 0.5 h to 288 h. Figure 3 confirms that k has considerable impact on the computation cost. This result put the light on the fact that application of appropriate feature selection technique, prior to the adversarial instance detection over encrypted data, can noticeably reduce the computation cost.

Fig. 2.Computation time (in hour) for different values of adversarial instances (n).

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