A Fragile Zero Watermarking Scheme to Detect and Characterize Malicious Modifications in Database Relations

Table 20

Characterization of malicious attacks on range of data values (Deterministic).

(a) Characterization of malicious insertion attacks on range of data values (𝜂=10⁶, attack rate = 10%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	26.49	288506	26164	+9.97%	↑Low to High
1	100–999	48.73	2736731	45.43	494709	46373	+10.34%	↑Low to High
2	1000–9999	25.68	1442223	28.08	305806	26304	+9.41%	↑Low to High

(b) Characterization of malicious insertion attacks on range of data values (𝜂=10⁶, attack rate = 90%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	26.83	504566	242224	+92.33%	↑Low to High
1	100–999	48.73	2736731	45.27	851193	402857	+89.86%	↑Low to High
2	1000–9999	25.68	1442223	27.90	524663	245161	+87.71%	↑Low to High

(c) Characterization of malicious deletion attacks on range of data values (𝜂=10⁶, attack rate = 10%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	26.54	236532	−25810	−9.84%	↓High to Low
1	100–999	48.73	2736731	45.28	403562	−44774	−9.99%	↑Low to High
2	1000–9999	25.68	1442223	28.18	251104	−28398	−10.16%	↓High to Low

(d) Characterization of malicious deletion attacks on range of data values (𝜂=10⁶, attack rate = 90%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	27.08	26857	−235485	−89.76%	↓High to Low
1	100–999	48.73	2736731	50.18	49757	−398579	−88.90%	↑Low to High
2	1000–9999	25.68	1442223	22.74	22547	−256955	−91.93%	↓High to Low

(e) Characterization of malicious update attacks on range of data values (𝜂=10⁶, attack rate = 10%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	26.61	263370	1028	+0.39%	↑Low to High
1	100–999	48.73	2736731	45.97	454956	6620	+1.48%	↑Low to High
2	1000–9999	25.68	1442223	27.41	271271	−8231	−2.94%	↓High to Low

(f) Characterization of malicious update attacks on range of data values (𝜂=10⁶, attack rate = 90%)

Range No	𝑟𝑘	𝑟𝑓𝑟𝑘	𝑓𝑟𝑘	𝑟𝑓𝑟𝑘^′	𝑓𝑟𝑘^′	Δ𝑓𝑟𝑘	Δℱ𝑟𝑘	Characteristic
0	0–99	25.59	1436986	25.01	246838	−15504	−5.91%	↓High to Low
1	100–999	48.73	2736731	50.18	495248	46912	+10.46%	↑Low to High
2	1000–9999	25.68	1442223	24.81	244819	−34683	−12.41%	↓High to Low