Forthcoming Articles http://www.jcr.cacrnet.org.cn EN-US http://www.jcr.cacrnet.org.cn/EN/current.shtml http://www.jcr.cacrnet.org.cn 5 This work mainly studies the construction of quantum circuit with low Toffoli-depth and low $T$-depth of SM4. For the S-box of SM4, based on the reclassification of its classical implementation obtained by using the tower field technique, the theoretical minimum of Toffoli-depth and $T$-depth of each part can be achieved by adding ancilla qubits. Among the rearranged operations of the classical implementation, the second part can be regarded as a 4-bit S-box. To construct quantum circuit for the second part, an NCT-based circuit with Toffoli-depth 2 that consumes 8 ancilla qubits is designed. For the construction of the Clifford+$T$-based circuit, the SAT-based method is applied and a $T$-depth-2 circuit of the second part is obtained. The above methods can effectively reduce the Toffoli-depth and $T$-depth of the complete circuit of the S-box under the condition of only adding finite qubits. Based on the above methods, the quantum circuit of the S-box of SM4 can be designed with Toffoli-depth of 8 and $T$-depth of 4, respectively. Finally, applying the above S-box circuit to the overall circuit of SM4, quantum circuit of SM4 with Toffoli-depth of 264 and $T$-depth of 132 is designed, respectively.]]> ]]> for peer-to-peer trading. A dual-side privacy-preserving model that calculates the average is first proposed. By employing data splitting and obfuscation methods, the model calculates the average value while ensuring the confidentiality of original bids. Additionally, a ring signature based on SM2 and a one-time address algorithm are designed to safeguard the anonymity of both trading parties. Building on the aforementioned model, this paper further presents a blockchain-assisted dual-side privacy-preserving multi-party computation scheme, known as DPC. DPC utilizes a price comparison mechanism grounded in Free-XOR garbled circuits to output the encrypted lower price. By deploying this mechanism on a directed acyclic graph (DAG) consortium blockchain, DPC enables concurrent on-chain supply and demand information and ensures the non-forgery of price comparison results. Based on the Miracl cryptographic library and C++ programming, we simulate and set up comparative experiments. The data show that DPC takes only 0.29 seconds to complete the average price computation for 80 participants, and the obfuscation ratio circuit’s even-gate overhead is reduced to a constant level, which outperforms existing comparable protocols.
]]> The public and transparent nature of data storage in blockchain ledgers poses a privacy breach risk on chain transaction data. Existing privacy protection schemes struggle to strike a balance between protecting users' privacy and regulating the behavior of malicious users. Moreover, the privacy protection scheme based on traditional public key cryptography may have security risks in the quantum environment. In response to the above issues, this study proposes a lattice-based regulatory privacy protection scheme on blockchain, which achieves the protection of normal user's identity and transaction amount, as well as the supervision of malicious user's identity and transaction amount. Also the study designs the supervision key generation algorithm with the secret sharing scheme, avoiding excessive rights of a single regulator; utilizes one-time keys and one-time addresses to connect both parties in a transaction, while hiding the recipient's address; designs a user identity public key proof with the R-LWE problem and R-BGV encryption algorithm to ensure the anonymity and supervision of the users' identity; and designs proof of transaction amount to ensure that the transaction amount is balanced and supervisable. Through the analysis of the correctness, security and performance of the scheme, it is proven that the proposed scheme can effectively protect transaction data privacy while resisting quantum interference and achieving supervision of transaction user's identity and transaction amount.]]>