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An Efficient Elliptic Curve Discrete Logarithm based Trapdoor Hash Scheme without Key Exposure

The trapdoor hash function plays essential role in constructing certain secure digital signature, and signature scheme that composed by trapdoor hash function is widely applied in different fields. However, the key exposure problem of trapdoor hash scheme has brought great distress. In this paper, an efficient trapdoor hash scheme without key exposure based on elliptic curve discrete logarithm is put forward and its security is analyzed, the scheme satisfies the five properties of trapdoor hash functions: effective calculation, trapdoor collision, collision resistance, key exposure resistance and semantic security. Through comparing and analyzing with the existing schemes, it shows that the proposed scheme, which has only multiplicative complexity and removes the operations of  computing finite field element inverse, is more advantage in terms of safety and efficiency. Moreover, the scheme supports batch computation that it can greatly improve the efficiency of verification.