Securely Outsourcing ID3 Decision Tree in Cloud Computing

Algorithm 5

Secure circuit protocol (SCP).

Input:   has , has

Output:  

1. CCS:

Randomly selects for commitment, and sends to and .

Generates the random number and share it secretly as , sends to , and sends to .

2. : Select seed for pseudo random function and send to .

3. and : Generate corresponding circuit based on function . Random

selection of and generate the following commitments for all and :

.

.

   and send the following information to :

.

.

4. CCS: Abort if and report different values for these items.

5. and :

   sends decommitment

, , and to CCS

   sends decommitment , , and to CCS.

6. CCS: For , compute , , for the appropriate . If any call to

returns , then abort. Similarly, CCS knows the values and , and aborts if or

can not open the corresponding commitments of and : , , and .

Run and , then broadcasts and to and .

7. and : Compute .