| PT-SCESW scheme is a series of algorithms namely Setup, Encryption, Auditing, Comparison |
| phases, which are shown as follows: |
| Setup Phase. The DO chooses a security parameter , range parameter and master key |
| to generate a public parameter . The DO runs KeyGen to produce the secret key |
| and public key . Setup phase outputs the secret key , public key , public parameter |
| and master key . Setup phase contains KeyGen algorithm in SCESW scheme. The DO |
| shares with others and preserves as a secret. |
| Encryption Phase |
| (i) Par, Der: system definitions are similar to SCESW scheme, as shown |
| in Algorithm 3. |
| (ii) Enc: given a security parameter , range parameter , master |
| key , public key , private key and num , the DO runs the |
| algorithm to output a ciphertext , set and the metadata. Then file and set will |
| be sent by the DO to the CSP. The metadata might be signed and kept by the DO. |
| Auditing Phase |
| (i) ChalGen: given the secret parameter , the verifier outputs auditing |
| challenge for the query. |
| (ii) ProofGen: given the DO’s public parameter , file , set and |
| auditing challenge , the TPA outputs the auditing proof to verify that the CSP |
| owns the outsourced file correctly. |
| (iii) ProofCheck: given the DO’s public key , |
| evidence , metadata and auditing challenge , the TPA outputs correct or . |
| If the proof passes the verification, the function outputs correct; otherwise, the |
| function outputs and the system stops to work. At last, TPA sends the auditing |
| report to the verifier. |
| Comparison Phase |
| (i) Cmp: system definition is similar to SCESW scheme, as illustrated |
| in Algorithm 3. |
