**Chapter 7: Conclusion**

**6.4 Performance Analysis of Processing Time**

**6.4.3 Results of Response Phase**

When the server receives the challenge message, the response message is computed on the basis of the received challenge, the stored blocks, and tags (the details can be found in Section 4.2.1.2 of Chapter 4). Therefore, the processing time of the response phase is incurred on the server. This section presents implementation results of response phase with probability of detection 90%, 95%, and 99%.

Figure 6.12 shows the impact of file size on the processing time of the response mes-sages for 16 bit signature. When the auditor sends a challenge message, including 230 blocks to achieve 90% probability, the computation time changes from 7.56 to 7.99 sec-ond. For 95% probability of detection, the computation time is around 10 seconds and for 99% probability, the computation time is increasing from 15.24 to 15.87 second. There-fore, it can be concluded that the computation time is roughly constant and is independent from size of file.

The impact of probability of detection on the computation time of the response mes-sages is also evaluated when the length of signature is 16 bits. Figure 6.13 demonstrates that by increasing the probability of detection, the number of the requested blocks are also increasing, which caused additional processing time to be incurred on the prover. For ex-ample, the imposed computation on the server during the response phase of 10 MB file, are 7.56 second for 90% probability. When the probability of detection increases to 95%

the processing time is also increasing to 9.95 second. In 99% probability, the processing time reaches the 15.24 second. The graph also shows that the processing time of 50 MB file reaches 7.99 s, 10.22 s, and 15.73 s for 90%, 95%, and 99% probability of detection respectively.

Figure 6.14 illustrates the impact of normal file size on the computation time dur-ing the response phase with 32 bits as the length of signature. As it is clear, when the

Figure 6.12: The Impact of Normal File Size on Processing Time during Response Phase when signature length is 16.

probability of detection is 90%, the processing time fluctuates between 7.65, and 8.22 s.

By augmenting the probability to 95%, the processing time varies slightly from 9.91 s to 10.49 s. Finally, a slight increase cost is also observed during the response phase of normal file size with 99% probability (between 15.19 s, and 15. 78 s).

The effect of the different probability of detection on the processing time of response phase for normal file size with 32 bit signature is shown in Figure 6.15. It can be seen when the size of file is 10 MB, the processing time is about 7.65 s, 9.91 s, and 15.19 s for 90%, 95%, and 99% probability of detection respectively. By augmenting the size of file, the computation time of response phase is slightly increasing, for example; the processing time in 50 MB file size is 8.22 s, 10.49 s, and 15.78 s on the basis of the amount of detection probabilities.

Figure 6.16 displays the impact of the file size on the processing time of response

Figure 6.13: The Impact of Probability of Detection on Processing Time during Response Phase for Normal File Size When Signature Length is 16.

phase for 64 bit signature. It can be seen that the size of file has an inconsiderable effect on the processing time of the response phase. For instance, when the probability of detection is 90%, 95%, or 99%, the processing time is about 7.85 s, 1026 s, or 15.48 s respectively.

The effect of probability of detection on processing time is also illustrated in Figure 6.17 for 64 bit probability. The computation time for the file with size 10 MB, is around 7.68 s, 9.89 s, and 15.19 s for different probability of detection. When the size of file reaches 50 MB, the processing time approaches to 7.84 s, 10.49 s, and 15.81 s regarding to probability of detection.

The effect of file size on the processing time for 128 bit signature is analyzed in Fig-ure 6.18. This graph demonstrates that the size of file has not been considerable influence on the processing time of response phase. For example, the processing time for 90%, 95%, and 99% of the probability is approximately 7.75 s, 10.52 s, and 15.84 s orderly.

Figure 6.14: The Impact of Normal File Size on Processing Time during Response Phase when signature length is 32.

Figure 6.15: The Impact of Probability of Detection on Processing Time during Response Phase for Normal File Size When Signature Length is 32.

Figure 6.16: The Impact of Normal File Size on Processing Time during Response Phase when signature length is 64.

The impact of probability of detection on processing time of response phase for 128 signatures is revealed in Figure 6.19. Regarding to this graph, when the size of file is 10 MB, the processing time is around 7.68 s, 9.92 s, and 15.26 s for different rate of probability. As such, the processing time for 50 MB file size is 7.94 s, 10.60 s, and 16.12 s respectively.

The processing time of the response phase is also analyzed for 256 bit signature to show the impact of file size on it in Figure 6.20. Similar to Figure 6.18, the processing time for different file size is approximately constant. For example, when the probability of detection is 90%, 95%, or 99%, the processing time of normal file size is around 7.58 s, 10.26 s, and 15.57 s orderly.

The effect of probability of detection on the processing time of response phase is also evaluated in Figure 6.21 for 256 bit signature. Clearly, the processing time depends

Figure 6.17: The Impact of Probability of Detection on Processing Time during Response Phase for Normal File Size When Signature Length is 64.

Figure 6.18: The Impact of Normal File Size on Processing Time during Response Phase when signature length is 128.

Figure 6.19: The Impact of Probability of Detection on Computation Time during Re-sponse Phase for Normal File Size When Signature Length is 128.

Figure 6.20: The Impact of Normal File Size on Computation Time during Response Phase When Signature Length is 256.

Figure 6.21: The Impact of Probability of Detection on Processing Time during Response Phase for Normal File Size When Signature Length is 256.

on probability of detection directly.

Figure 6.22 compares the processing time of response phase for different size of signature and probability of detection when the size of input file is from 10 MB to 50 MB. The graph demonstrates that the processing time of the response phase only depends on the probability of detection. Moreover, the length of signature has a negligible effects on the processing time of this step.

The processing time experiment of the response phase is also conducted for the large-scale file size of input file (1, 5, and 10 GB) to prove that the processing time of response phase is independent of the size of the file. Figure 6.23 displays that the computation time of such files are around 7.8, 10.6, and 16.1 when the probabilities of detection are 90%, 95%, and 99% respectively. Moreover, Figure 6.24 shows the impact of probability of detection on processing time during the response phase for large-scale file sizes. As it is clear, by increasing the number of the probability, the processing time is also increasing.

Figure 6.22: The Comparison of Processing Time for Different Normal File Size, Proba-bility of Detection, and Signature Length during the Response Phase.

Figure 6.23: The Impact of Large Scale Files on Processing Time during Response Phase When Signature Length is 256.

Figure 6.24: The Impact of Probability of Detection on Processing Time during Response Phase for Large Scale Files When Signature Length is 256.