Efficient multiplicative-to-additive function from Joye-Libert cryptosystem and its application to threshold ECDSA

• Main Authors: XUE, Haiyang, AU, Ho Man, LIU, Mengling, CHAN, Yin Kwan, CUI, Handong, XIE, Xiang, YUEN, Hon Tsz, ZHANG, Chengru
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: Multiplicative-to-Additive function; Joye-Libert cryptosystem; Threshold ECDSA; Zero-knowledge proof; Information Security
• Online Access: https://ink.library.smu.edu.sg/sis_research/9187; https://ink.library.smu.edu.sg/context/sis_research/article/10192/viewcontent/3576915.3616595.pdf
• Institution: Singapore Management University

Threshold ECDSA receives interest lately due to its widespread adoption in blockchain applications. A common building block of all leading constructions involves a secure conversion of multiplicative shares into additive ones, which is called the multiplicative-to-additive (MtA) function. MtA dominates the overall complexity of all existing threshold ECDSA constructions. Specifically, O(n2) invocations of MtA are required in the case of n active signers. Hence, improvement of MtA leads directly to significant improvements for all state-of-the-art threshold ECDSA schemes.In this paper, we design a novel MtA by revisiting the Joye-Libert (JL) cryptosystem. Specifically, we revisit JL encryption and propose a JL-based commitment, then give efficient zero-knowledge proofs for JL cryptosystem which are the first to have standard soundness. Our new MtA offers the best time-space complexity trade-off among all existing MtA constructions. It outperforms state-of-the-art constructions from Paillier by a factor of 1.85 to 2 in bandwidth and 1.2 to 1.7 in computation. It is 7X faster than those based on Castagnos-Laguillaumie encryption only at the cost of 2X more bandwidth. While our MtA is slower than OT-based constructions, it saves 18.7X in bandwidth requirement. In addition, we also design a batch version of MtA to further reduce the amortised time and space cost by another 25%.