1. A New Approach of Signing Documents with Symmetric Cryptosystems and an Arbitrator Nol Premasathian inolhian@kmutt.ac.th Faculty of Science King Mongkut’s University of Technology Thonburi Bangkok, Thailand

2. Signing Documents Public Key Public Key Private Key Private Key

3. Signing Documents (Public Key) No trusted third party needed No trusted third party needed Problems with speed Problems with speed

4. Signing Documents (Private Key) A trusted third party needed A trusted third party needed Disputes dissolved by the trusted third party Disputes dissolved by the trusted third party

5. Existing Method The sender shares a private key with the arbitrator (sender’s key). The sender shares a private key with the arbitrator (sender’s key). The arbitrator shares a private key with the receiver (receiver’s key). The arbitrator shares a private key with the receiver (receiver’s key).

6. Existing Method (continue) The sender encrypts the message with the sender’s key and sends it to the arbitrator. The sender encrypts the message with the sender’s key and sends it to the arbitrator. The arbitrator decrypts the message, encrypts it with the receiver’s key and sends it to the receiver. The arbitrator decrypts the message, encrypts it with the receiver’s key and sends it to the receiver.

7. Existing Method (continue) The receiver decrypts the message and sends an acknowledgment encrypted with the receiver’s key to the arbitrator. The receiver decrypts the message and sends an acknowledgment encrypted with the receiver’s key to the arbitrator. The arbitrator decrypts the acknowledgment, encrypts it with the sender’s key and sends it to the sender. The arbitrator decrypts the acknowledgment, encrypts it with the sender’s key and sends it to the sender. The arbitrator keeps a record for the message and its acknowledgment. The arbitrator keeps a record for the message and its acknowledgment.

8. Existing Method (limitation) The arbitrator must keep a record of every sent message. The arbitrator must keep a record of every sent message. The arbitrator perceives the content of the message. The arbitrator perceives the content of the message.

9. Proposed Method There are three secret keys in the protocol: There are three secret keys in the protocol: Private key between the sender and the receiver (K m ) Private key between the sender and the receiver (K m ) Private key between the sender and the arbitrator (K s ) Private key between the sender and the arbitrator (K s ) Private key between the receiver and the arbitrator (K r ) Private key between the receiver and the arbitrator (K r )

10. Three transmissions From the sender to the arbitrator From the sender to the arbitrator From the arbitrator to the receiver From the arbitrator to the receiver From the receiver to the sender From the receiver to the sender

11. The protocol The sender sends K s (H(M)) and K m (M) to the arbitrator. The sender sends K s (H(M)) and K m (M) to the arbitrator. From K s (H(M)), the arbitrator can produce K r (K r (H(M))) and K s (H(K r (K r (H(M))))+H(M)). From K s (H(M)), the arbitrator can produce K r (K r (H(M))) and K s (H(K r (K r (H(M))))+H(M)). The arbitrator sends K m (M), K s (H(M)), K r (K r (H(M))), and K s (H(K r (K r (H(M))))+H(M)) to the receiver. The arbitrator sends K m (M), K s (H(M)), K r (K r (H(M))), and K s (H(K r (K r (H(M))))+H(M)) to the receiver.

12. The protocol (continue) The receiver verifies H(M) and sends K r (K r (H(M))) and K s (H(K r (K r (H(M))))+H(M)) to the sender to acknowledge the message The receiver verifies H(M) and sends K r (K r (H(M))) and K s (H(K r (K r (H(M))))+H(M)) to the sender to acknowledge the message The sender verify H(M) in K s (H(K r (K r (H(M))))+H(M)) with the original one and verify the validity of the acknowledgment. The sender verify H(M) in K s (H(K r (K r (H(M))))+H(M)) with the original one and verify the validity of the acknowledgment.

13. Signature and Acknowledgment K s (H(M)) is the signature of the message. K s (H(M)) is the signature of the message. K r (K r (H(M))) is the acknowledgment of the message K r (K r (H(M))) is the acknowledgment of the message

14. Conclusions The proposed method reduces the number of transmissions from four to three. The proposed method reduces the number of transmissions from four to three. The arbitrator does not perceive the content of the message. The arbitrator does not perceive the content of the message. The arbitrator needs not keep a record. The arbitrator needs not keep a record.