本文使用椭圆曲线加密体制,给出了公开可认证的门限秘密共享协议,构造了一个 公正的离线电子支付系统(被动匿名可撤回系统),该系统解决了委托人权力过于集中的问题,且委托人在最初公布其公开密钥后,完全是被动的,不卷入支付协议的实际操作中,只有在被要求时才去掉用户的匿名。 关键词: 非交互公开可认证;门限秘密共享;椭圆曲线加密;盲签名;电子支付系统 Abstract: In the paper, a non-interactive publicly verifiable protocol based on elliptic curves cryptography is proposed. It designs a off-line fair electronic payment system (electronic payment system with passive anonymity-revoking trustees). This protocol solves the power-centralized problem of trustees. After initially publicized their secret key, trustees will be passive, and does not involve in operation of the payment. They would revoke the customer's anonymity if only they were asked. Keywords: non-interactive publicly verifiable; threshold secret sharing scheme; elliptic curves cryptograph (ECC); blind signature; electronic payment system