椭圆曲线密码体制(elliptic curve cryptosystem,ECC)依然是当前应用最广泛的公钥密码体制,其安全核心是椭圆曲线离散对数问题.本文提出了椭圆曲线离散对数的强不动点问题.利用强不动点假设,在随机预言模型下证明了 ECDSA(elliptic curve digital signature algorithm)的一个全域哈希变形方案是可以抵抗自适应选择消息下的存在伪造的.签名的聚合性质使得签名方案在诸如区块链、云存储等众多场景中发挥着重要作用,所以本文也讨论了这个全域哈希椭圆曲线签名方案的聚合性质.
Full domain Hash elliptic curve signature
The elliptic curve cryptosystem(ECC)remains the most widely used public key cryptosystem.The elliptic curve discrete logarithm problem is its security kernel.We propose a strong fixed point problem of elliptic curve discrete logarithm.Using the strong fixed point assumption,we prove that a full domain hash variant of ECDSA(elliptic curve digital signature algorithm)is secure against existential forgery under the adaptive chosen message attack under the random oracle model.The aggregation properties of signatures make signature schemes play important roles in many scenarios,such as blockchain and cloud storage;therefore,we also discussed the aggregatability of signatures of this variant of ECDSA.
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