门限最优的椭圆曲线数字签名算法及其应用  

Threshold-optimal ECDSA signature and its applications

作　　者：郭兆中 刘齐军 尹海波 徐茂智[1] GUO Zhaozhong;LIU Qijun;YIN Haibo;XU Maozhi(School of Mathematical Science,Peking University,Beijing 100871,China;Tianhe Guoyun Technology Co.,Ltd,Changsha 410100,China)

机构地区：[1]北京大学数学科学学院,北京100871 [2]湖南天河国云科技有限公司,湖南长沙410100

出　　处：《哈尔滨工程大学学报》2024年第8期1624-1631,共8页Journal of Harbin Engineering University

基　　金：国家重点研发计划(2022YFB2703002).

摘　　要：针对当前椭圆曲线门限签名算法交互次数多和计算复杂度高的问题,本文提出一种高效的椭圆曲线数字签名门限最优签名算法。新增了预处理过程,各节点再通过费尔德曼可验证秘密分享和一阶同态加密算法生成一套基础数据,应用于签名阶段的乘法和求逆运算,完成多项式“降次”。算法实现门限最优的性质,整个算法仅需4轮即可完成签名。结果表明:随着门限值由4提升至20,算法能够在1.232~19.66 s完成签名的生成;增加预计算阶段后,计算的效率提升至0.667~4.559 s;在安全环境下,单次签名速度则可以达到毫秒级,能够有效应用于区块链账户安全保护和跨链资产锁定,具有实际应用价值。Considering the high interaction and computational complexity of current elliptic curve digital signature algorithm threshold signature algorithms,this paper proposes a kind of high-efficiency threshold-optimal ECDSA signature algorithm.By introducing a preprocessing phase,a set of basic data can be generated through Feldman verifiable secret sharing and level-1 homomorphic encryption at each node,and such data can be used in the multiplication and inversion operations of the signature phase for lowering the polynomial order and ensuring threshold optimality.The whole protocol simply requires four rounds of interaction to generate a valid signature.The results show that,with the threshold value increasing from 4 to 20,the algorithm can generate a signature within 1.232~19.66 s.After the precomputation stage is introduced,the computational efficiency can be improved to 0.667~4.559 s.In a secure environment,the single signature generation speed can reach millisecond levels,which can be effectively applied to blockchain account security protection and cross-chain asset locking.The algorithm has practical application value.

关 键 词：椭圆曲线密码 数字签名 门限签名 同态加密 安全多方计算 区块链 数字资产 跨链 

分 类 号：O29[理学—应用数学]