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

Table 1

Notations.

Symbol	Description
𝑅	Database relation
PK	Primary key attribute
𝑟𝑖	The 𝑖th tuple
𝐴𝑗	The 𝑗th attribute
𝜂	Number of tuples in a database relation
𝜈	Number of attributes in a database relation
𝜔𝑑	Digit sub-watermark
𝜔𝑙	Length sub-watermark
𝜔𝑟	Range sub-watermark
𝜔𝑅	Watermark for database relation 𝑅
𝜔𝐶	Watermark certificate
SK	Secret key
𝑑𝑖	The 𝑖th digit
𝑙𝑗	The 𝑗th length
𝑟𝑘	The 𝑘th range
𝑓𝑑𝑖	Frequency for digit 𝑖 of data values
𝑓𝑙𝑗	Frequency for length 𝑗 of data values
𝑓𝑟𝑘	Frequency for range 𝑘 of data values
𝑟𝑓𝑑𝑖	Relative frequency for digit 𝑖 of data values
𝑟𝑓𝑙𝑗	Relative frequency for length 𝑗 of data values
𝑟𝑓𝑟𝑘	Relative frequency for range 𝑘 of data values
Δ𝑓𝑑𝑖	Change in frequency of digit 𝑖
Δ𝑓𝑙𝑗	Change in frequency for length j
Δ𝑓𝑟𝑘	Change in frequency for range k
Δℱ𝑑𝑖	Fractional change in digit frequency for digit 𝑖
Δℱ𝑙𝑗	Fractional change in length frequency for length j
Δℱ𝑟𝑘	Fractional change in range frequency for range 𝑘
CA	Certification authority
WAR	Watermark accuracy rate
WDR	Watermark distortion rate