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

Table 19

Characterization of malicious attacks on length of data values (deterministic).

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	7.08	77875	6790	+9.55%	↑Low to High
2	19.76	197605	19.80	217767	20162	+10.20%	↑Low to High
3	45.18	451787	45.32	498531	46744	+10.35%	↑Low to High
4	27.95	279523	27.80	305827	26304	+9.41%	↑Low to High

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	7.50	142584	71499	+100.58%	↑Low to High
2	19.76	197605	19.72	374737	177132	+89.64%	↑Low to High
3	45.18	451787	45.16	857986	406199	+89.91%	↑Low to High
4	27.95	279523	27.62	524693	245170	+87.71%	↑Low to High

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	7.19	64733	−6352	−8.94%	↓High to Low
2	19.76	197605	19.71	177421	−20184	−10.21%	↓High to Low
3	45.18	451787	45.19	406721	−45066	−9.98%	↓High to Low
4	27.95	279523	27.90	251125	−28398	−10.16%	↓High to Low

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	6.22	6221	−64864	−91.25%	↓High to Low
2	19.76	197605	21.19	21186	−176419	−89.28%	↓High to Low
3	45.18	451787	50.04	50039	−401748	−88.92%	↓High to Low
4	27.95	279523	22.55	22554	−256969	−91.93%	↓High to Low

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	6.85	68488	−2597	−3.65%	↓High to Low
2	19.76	197605	20.13	201333	3728	+1.89%	↑Low to High
3	45.18	451787	45.89	458869	7082	+1.57%	↑Low to High
4	27.95	279523	27.13	271310	−8213	−2.94%	↓High to Low

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

𝑙𝑗	𝑟𝑓𝑙𝑗	𝑓𝑙𝑗	𝑟𝑓𝑙𝑗^′	𝑓𝑙𝑗^′	Δ𝑓𝑙𝑗	Δℱ𝑙𝑗	Characteristic
1	7.11	71085	4.36	43599	−27486	−38.67%	↓High to Low
2	19.76	197605	20.97	209711	12106	+6.13%	↑Low to High
3	45.18	451787	50.16	501622	49835	+11.03%	↑Low to High
4	27.95	279523	24.51	245068	−34455	−12.33%	↓High to Low