Public-Key Hash Function for Blockchain

Abstract

Hash function is generally known as symmetric and private for use. However, when applying under public key infrastructure, it immediately yields a notion called chameleon hash function. Based on the chameleon hash, this chapter generalizes and formalizes the notion of public key hash (PKH) scheme by rigorous algorithmic design and security models of indistinguishability and collision-resistance. PKH is another form of the trapdoor commitment, which serves as a basic element for zero knowledge and IND-CCA2 secure public key encryption schemes. Notably, PKH (e.g. chameleon hash) has been recently used to build the redactable blockchain where block hash and transaction are supposed to be redacted without impairing consistency. To begin with, this chapter first review background information of PKH. Then, it instantiates by various PKH schemes: ACH, HCCH, PCH, TUCH and RCH which are mostly from our related works. By rich analysis of algorithmic design and proof techniques of security reduction, this chapter gives more empirical knowledge, insightful instruction and practising sources for the readers to follow. To summarize, PHK is considered as a basic primitive for many other cryptographic schemes. It is an easy starting point for a beginner to follow but can also extend to sophisticated design. The simplicity of the instantiated cases helps the reader quickly grasp and practise proof techniques given in this chapter