A Blind Reversible Robust Watermarking Scheme for Relational Databases

Algorithm 3

Watermark detection.

Input: watermark relational database 𝑅^′_𝑊, parameters 𝐾,𝑔,𝛼, Mid and two pairs,

      (PP₁, CZP₁) and (PP₂, CZP₂).

Output: Watermarked status ∈{true, false}, recover the original database 𝑅

(1) 𝑆 = Tuple_Selection(𝑅,𝐾,𝑔);

(2) foreach tuple 𝑞∈𝑆 do

(3) attribute_index 𝑗=𝐹(𝑞.𝑃𝐾) mod 𝛼 // selected attribute 𝐴_𝑗

(4) mark_bit 𝑖𝑚𝑏=𝐹(𝑞.𝑃𝐾) mod 𝐿 // determine mark bit

(5) 𝑇 = Get2digits(𝐴_𝑗);

(6) insert 𝑇 into Seq;

(7) insert imb into Mark_Seq; //save index of the corresponding mark bit

(8)    end foreach;

(9)    Dif_Seq = Diff(Seq, Mid); // compute the difference sequence Dif_Seq

(10) for 𝑖=0 to 𝐿−1 do

(11) 𝑊^′[𝑖]=0; //reset watermark data

(12) count[𝑖][0] = 0; count[𝑖][1] = 0; //reset votes for 𝑊^′[𝑖] to be 0, 1 respectively

(13) end for;

(14) for 𝑖=0 to 𝐷𝑖𝑓_𝑆𝑒𝑞−1 do

(15) if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] = PP₁, then count[Mark_Seq[𝑖], 0] += 1;

(16) else

(17) if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] = PP₁ − 1, then count[Mark_Seq[𝑖], 1] += 1;

(18)           end if;

(19) if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] <= PP₁ − 1, then 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] = 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] + 1;

(20)          end if;

(21) end if;

(22) if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] = PP₂, then count[Mark_Seq[𝑖], 0] += 1;

(23) else

(24)           if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] = PP₂ + 1, then count[Mark_Seq[𝑖], 1] += 1;

(25)           end if;

(26)           if 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖] >= PP₂ + 1, then 𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖]=𝐷𝑖𝑓_𝑆𝑒𝑞[𝑖]−1;

(27)           end if;

(28) end if;

(29) end for;

(30) for 𝑖=0 to 𝐿−1 do

(31) if count[𝑖][0] + count[𝑖][1] = 0 then 𝑊^′[𝑖]=−1;

(32)   end if;

(33) if count[𝑖][1]/(count[𝑖][1] + count[𝑖][1]) > 𝜏 then 𝑊^′[𝑖]=1;

(34)   else 𝑊^′[𝑖]=0;

(35)   end if;

(36) end for;

(37) Regenerate the original watermark data 𝑊; // using (4)

(38) for 𝑖=0 to 𝐿−1 do //find the match between original watermark and

        detected watermark if 𝑊^′[𝑖]=𝑊[𝑖] then matchcount += 1;

(39)          end if;

(40) end for;

(41) if matchcount = 𝐿, then

(42)   return true; // suspected relational database 𝑅 is recovered successfully

(43) else

(44)   return false; // suspected relational database 𝑅 cannot be recovered

(45) end if;