| Algorithm: = Modify_or_Insert_Block (, ). |
| Input: the appointed block location , and the new block . |
| Output: the new of the updated MHT. |
| User: compute ; ; |
| transmit to CSP; |
| CSP: compute |
| if then |
| if mark = modify then |
| ; |
| else |
| ; |
| end if |
| compute ; |
| send to user; |
| end if |
| User: compute ; |
| if then |
| compute ; |
| if then |
| authorize CSP to execute update operation; |
| end if |
| end if |
| CSP:  if mark = modify then |
| , , are replaced by , , in the outsourced file ; |
| update the MHT stored in cloud by recalculating all the nodes on the path from |
| the th leaf node to the ; |
| else |
| insert , into after , , respectively; |
| update the MHT by replacing with the th primordial leaf node that is transformed into |
| a parent node having the left-child leaf and the right-child leaf , and then recalculating all the |
| nodes on the path from to the ; |
| end if |
| User: transmit () to TPA; |
| TPA: according to the mark, update the MHT stored at TPA side by the same way as CSP; |
| send to user the root of the updated MHT , denoted by ; |
| User: if then |
| update the , stored in her local, with ; |
| end if |
| return ; |
