A Layered Searchable Encryption Scheme with Functional Components Independent of Encryption Methods

Algorithm 9

Range query component.

Build(𝑑,𝑉_𝑑):

(1) input a range document 𝑑 = (>𝑎₁, ≥𝑎₁,…, >𝑎_𝑖−1, ≥𝑎_𝑖−1, ≥𝑎_𝑖, =𝑎_𝑖, ≤𝑎_𝑖, <𝑎_𝑖+1, ≤𝑎_𝑖+1,…, <𝑎_𝑁, ≤𝑎_𝑁)

 and the mapping 𝑉_𝑑=(𝑣₁,…,𝑣_2𝑁+1). Here 𝑑 is the transformed form for the label 𝑎=𝑎_𝑖.

(2) initialize a bloom filter 𝐵 with all bits set to 0.

(3) for (𝑘=1;𝑘≤2𝑁+1;𝑘++) do

(4)  compute 𝑟 codewords 𝑦₁=ℎ₁(𝑑‖𝑣_𝑘),…,𝑦_𝑟=ℎ_𝑟(𝑑‖𝑣_𝑘).

(5)  insert the codewords 𝑦₁,…,𝑦_𝑟 into the bloom filter 𝐵.

(6) end for

(7) output a local functional structure 𝐿_𝑑=𝐵.

Filter(𝐶,𝐿,𝑉_𝑇):

(1) input 𝑛 ciphertexts 𝐶=(𝑐₁,…,𝑐_𝑛), the corresponding functional structures 𝐿=(𝐿₁,…,𝐿_𝑛),

 the mappings of the queried keywords 𝑉_𝑇=(𝑉₁,…,𝑉_𝑛)=(𝑣₁,…,𝑣_𝑛) (single keyword),

 where 𝑣_𝑖(1≤𝑖≤𝑛) is the mapping of “>𝑤”.

(2) for (𝑖=1;𝑖≤𝑛;𝑖++) do

(3)  compute 𝑟 codewords 𝑦₁=ℎ₁(𝑑‖𝑣_𝑖),…,𝑦_𝑟=ℎ_𝑟(𝑑‖𝑣_𝑖).

(4)  if all 𝑟 locations 𝑦₁,…,𝑦_𝑟 in bloom filter 𝐵_𝑖=𝐿_𝑖 are 1, then add 𝑐_𝑖 to 𝐶^′.

(5) end for

(6) output 𝐶^′.