Full domain Hash elliptic curve signature
Fangguo Zhang · Scientia Sinica Informationis · 2024
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.