Query-Biased Preview over Outsourced and Encrypted Data

Algorithm 1

Secure additive coding for matrix.

Input 𝑚 random strings 𝐊=(𝐾₁,…,𝐾_𝑚) of length 𝑛⋅𝑁

𝐂𝐨𝐝𝐞_𝐊(𝑋_𝑚×𝑛):

 (1) check the validity of the input, continue if 𝑚_𝑖𝑗∈𝕊_𝑁 and for all 𝑗,

  ∑^𝑚_𝑘=1𝑐_𝑘𝑗≤𝑁, or output Ø otherwise

 (2) initialize a ciphertext matrix 𝐶_𝑚×𝑛=(𝑐_𝑖𝑗), each element is set to 0

  (𝑁 bits), and initialize 𝑛 cursors 𝑔₁,…,𝑔_𝑛 and set each 𝑔_𝑗=1 (𝑁 bits)

 (3) for  (𝑖=1;𝑖≤𝑚;𝑖++)  do

 (4) for  𝑗=1;𝑗≤𝑛;𝑗++  do

 (5)  for  𝑘=1;𝑘≤𝑥_𝑖𝑗;𝑘++  do

 (6)   𝑐_𝑖𝑗←𝑐_𝑖𝑗⊕𝑔_𝑗

 (7)   𝑔_𝑗←𝑔_𝑗<<1

 (8)  end for

 (9) end for

 (10) encrypt the ith row as 𝑐_𝑖←𝑐_𝑖⊕𝐾_𝑖

 (11) end for

 (12) output 𝐶_𝑚×𝑛

Decode _𝐾𝑖𝑐_𝑖:

 (1) initialize a temporary data row 𝐭=𝑡₁,…,𝑡_𝑛 with each element

  be 𝑁 bits, and set 𝐭=𝑐_𝑖⊕𝐾_𝑖

 (2) for each 𝑡_𝑗 in 𝐭, let the binary form of 𝑡_𝑗 be 𝑏_𝑁𝑏_𝑁−1…𝑏₁, then

   𝑥_𝑖𝑗=∑^𝑁_𝑘=1𝑏_𝑘

 (3) output 𝐱_𝐢=(𝑥_𝑖1,…,𝑥_𝑖𝑛)