Paper 2021/329

Two Efficient and Regulatory Confidential Transaction Schemes

Min Yang, Changtong Xu, Zhe Xia, Li Wang, and Qingshu Meng

Abstract

With the development of Bitcoin, Ethereum and other projects, blockchain has been widely concerned with its outstanding characteristics such as non-centralization, collective maintenance, openness and transparency. Blockchain has been widely used in finance, logistics, copyright and other fields. However, as transactions are stored in plaintext in the blockchain for public verification, the privacy of users is not well guaranteed such that many financial applications can not be adopted widely. How to securely and economically protect the privacy of transactions is worth further research. In this paper, we have proposed two efficient and regulatory confidential transaction schemes using homomorphic encryption and zero-knowledge proof. ERCO, the first scheme, turns the standard ElGamal algorithm to be additively homomorphic and expands it into four ciphertexts such that $(m,r)$ in the transaction can be decrypted. Its security can be reduced to DDH assumption and the transaction size is less. PailGamal, the second scheme, is based on the combination of Paillier and ElGamal algorithms. Its security can be reduced to DDH assumption and it empowers regulators greater powers to obtain transaction-related specific content. In contrast to other ElGamal-based schemes, PailGamal makes any token amount directly decrypted without calculating a discrete logarithm problem. As any $(m,r)$ in transactions can be decrypted directly, game theory is applied to further reduce transaction size.