Analysis and Evaluation of Schemes for Secure Sum in Collaborative Frequent Itemset Mining across Horizontally Partitioned Data

Algorithm 1

Proposed algorithm for PPDFIM using Shamir’s secret sharing based on NoTP model and STTP model.

Setup:

The common random numbers are distinct publically available numbers in

a finite field of size where is a prime number and secret ().

The coefficients .

(1)    for each global candidate itemset to

(2)     for each party , () do

(3)     each party selects a random polynomial

(4)     compute the share of each party (, where

(5)      for   to (   do

(6)      send to party

(7)      receive the shares from every party

(8)      end for

(9)      compute

(10)   end for

(11)   if NoTP model is used

(12)    for each party , () do

(13)     for   to (   do

(14)     send to party

(15)     receive the results from every party

(16)     solve the set of equations to find the sum of secret values.

(17)    end for

(18)   end for

(19)   end if

(20)   else if  STTP model is used

(21)    for each party , () do

(22)    send to STTP

(23)    solve the set of p equations at STTP to find the sum of secret values.

(24)    end for

(25)    for each party , ()

(26)    STTP sends the final list of the computed sum of secret values to each party

(27)    end for

(28)   end if

(29)  end for