## Cryptology ePrint Archive: Report 2021/329

Two Efficient Regulatory Confi dential Transaction Schemes

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

Abstract: Blockchain has been widely used in finance, logistics, copyright and other fields with its outstanding characteristics such as non-centralization, collective maintenance, openness, transparency and non-tamperability. However, as transactions are stored in plaintext in the blockchain for public verification, the anonymity and privacy of users can not be guaranteed and this hampers many financial applications. How to protect the privacy of transactions is worthy further research.

In this paper, we have proposed two regulatory and efficient confidential transaction schemes using homomorphic encrytion and zero-knowledge proof. The first one improves the efficiency of the existing ElGamal based scheme while preserves its privacy. The second one employs the Paillier encryption with homomorphic property and it empowers regulators with greater power to obtain transaction-related specific content. The core of ElGamal based scheme is the Modified ElGamal algorithm, which changes the form of the standard ElGamal algorithm and expands it into four ciphertexts such that $(m,r)$ in the transaction can be decrypted. The Paillier based scheme is mainly to combine Paillier encryption with ElGamal encryption. Contrast to other ElGamal based scheme, the combination makes any token amount can be 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. In our construction, transactions are about 1.1KB.

Category / Keywords: cryptographic protocols / zero knowledge