Achieving Security in Proof-of-Proof Protocol with Non-Zero Synchronization Time

Among the most significant problems that almost any blockchain faces are the problems of increasing its throughput (i.e., the number of transactions per unit of time) and the problem of a long waiting time before block confirmation. Thus, for example, in the most common BTC blockchain, according to various estimates, throughput is from 3 to 7 tps (transactions per second), and the average block confirmation time (block is considered confirmed if it has at least 6 blocks over it) is 1 h. At the same time, it is impossible to solve these problems directly by increasing the block size or increasing block generation intensity because this leads to essentially a decrease in the security of the blockchain in the first turn against double spend and splitting attacks. Such problems lead to the inconvenience of the practical use of cryptocurrencies to pay for goods and services. Proposed a few years ago, the PoP consensus protocol potentially helps to solve the problem of increasing blockchain throughput, although it was originally intended to ensure the stability of “young” blockchains, with “small” PoW, through the use of a secure blockchain, such as BTC. A blockchain that has provable security is called the security-provided blockchain (SPB), and one that uses SPB to achieve its security is called the security-inherited blockchain. In this paper, we give explicit formulas which describe how the number of confirmation blocks in the security-inherited blockchain, which is sufficient to achieve a given security level of this blockchain to a double spend attack, depends on the parameters of both blockchains. It is essential that we use a realistic model to obtain the results, taking into account the synchronization times of both blockchains. Such a model is much closer to the real situation, but at the same time, it leads to significant analytical difficulties in obtaining results. The obtained formulas are convenient for numerical calculations, the numerous examples of which are also given in this work.