FogDedupe: A Fog-Centric Deduplication Approach Using Multi-Key Homomorphic Encryption Technique

Algorithm 5

Multi-key homomorphic encryption–based target-level deduplication.

Input: Input data blocks each with the size of 1024KB; Non-Redundant Tag (NR_T)

Output: Detecting the duplicate cipher chunks in the cloud storage.

Data Owner

  Begin

  1. The data owner receives the Non-Redundant Tag (NR_T) from the nearby fog node.

  2. Data owners generate keys to encrypt the data chunk

     a.  Data owner generates the value ‘n’ using Pseudo-Random Number

       Generator (PRNG), Here ‘n’ defines the message space and keyspace Z_n.

     b.  Data owner generates two random vectors ( and). Here, (a₀, a₁ …

       a_x-1) is used to represent the input message (m) and (b₀, b₁ … b_x-1) is

       used to represent the homomorphic output vector.

     c.  Data owners keep for decryption (i.e. Private Key) and sends to the

       Cloud Service Provider to perform additive homomorphic encryption on

       the ciphertext.

  3. Encrypts the data chunks using the private keys ()

     a.  Generate a random number r ∈ Z_n.

     b.  To encrypt a single data chunk ‘m’, Enc (m, r) = (m + r) mod n is used

       whereas to encrypt an array of input data chunks, Ciphertext () = Enc

       () is used.

     c.  Ciphertext () is transferred to the server along with homomorphic vector

        (b₀, b₁ … b_x-1).

  End

Cloud Service Provider

  Begin

   1.  CSP collects the index table information from the fog nodes.

   2.  Receives the information about the percentage of non-zero bit in the index table

     for each data chunk from the fog nodes.

   3.  Receives the ciphertext from the data owner along with vector (b₀, b₁ … b_x-1) and stores it as, (cipher text, offset) pair (i.e.) (c_i, b_i).

   4.  From the information gathered from Step. 2 (CSP side), Cloud Service Provider

     identifies the high risk (Possibility of redundancy) data chunks.

   5.  Additive Homomorphic operations are performed on high risk data chunks.

       a. Consider any two key value pair (t₁ and t₂) with high risk where t₁ = (c₁,

        o₁) and t_{2 =} (c₂, o₂), then the redundancy check can be performed using

        additive homomorphic encryption by calculating, t₁ + t₁ = (c₁ + c₂; o₁ +

        o₂) == t₂ + t₂ = (c₁ + c₂; o₁ + o₂) (this could be performed ‘n’ time for

        more accurate results)

   6.  If the values are the same, then the data chunks are decided to be redundant data

     chunks. So, the duplicate data block is removed.

End