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Lattice-Based Encrypted Verifiably Encryption Signature Scheme for the Fair and Private Electronic Commence

To achieve the fairness and the privacy of the e-commence, and also to consider the quantum security of the e-commence, a lattice-based encrypted verifiably encryption signature scheme (EVES) is proposed in this paper. We achieve the strong unforgeability and the opacity properties in the standard model over lattice without the help of the lattice-based delegation technologies which is one of main tools to achieve the standard model security for the lattice-based cryptography. It is shown that the proposed scheme can be used to design a fair and privacy-preserving e-commence system in cloud, not only for business-to-customer business(B2C) but also for customer-to-customer business(C2C). The main reason is that the verifier can read the details of the EVES by easily computation operations before the EVES is verified. Then the seller who acts as a verifier in EVES scheme can ask a proxy sever to deal the business for him. Then the seller does not need to keep online for most of time. Moreover, we compare the proposed EVES with some known lattice-based VES schemes. Besides the proposed scheme achieves the more cryptographic functions, such as EVES vs VES and standard model vs random oracle model etc., the proposed scheme even has some advantage about the computation cost compared with known lattice-based VES schemes.