A weakness of unforgeability is found in Ma and Chen scheme, and the root cause is the susceptive linear design in the scheme. In order to avoid the weakness and susceptive linear design, an improvement by means of two mechanisms including quadratic residue and composite discrete logarithm is proposed, which can defeat the forgery attacks in Ma and Chen scheme. The new scheme remains good confidentiality, public verifiability and efficiency.
The secure socket layer/ transport layer security（SSL/TLS） handshake protocol uses public key cryptographic algorithms such as RSA for key establishment. Typically, public key cryptographic algorithm is computational intensive due to the modular multiplications. Therefore, SSL/TLS servers often become swamped while performing public key decryptions when the simultaneous requests increase quickly. A batch RSA decryption algorithm was proposed. The novel algorithm provides the reasonable response time and optimizes server performance significantly. The decryption speedup is proportional to the batch size b, for instance, the speedup factor is 4, while in Shacham＇s scheme the acceleration rate is only 2.5 when b = 4.
A key problem of electronic commerce （for short e-commerce） is fair exchange which guarantees that at the end of the transaction, either both parties involved in the trausaction receive each other＇s items or none do. A non-interactive optimistic fair exchange e-commerce protocol model based on the publicly verifiable secret sharing is presented. The main idea of our exchange protocol is to interchange verifiable and recoverable keys of the symmetric encryption for participants＇ items. So it is especially suitable for exchange of large-size items. Furthermore, our protocol is efficient and simple as it does not need interactive proof system which has been adopted by a large quantity of previously proposed fair exchange protocols. Based on a modified （2,2） secret sharing scheme, a concrete non-interactive fair exchange e-commerce protocol is designed.
