Embedding Reverse Links in a Blockchain

A.W. Roscoe, Pedro Antonino, Jonathan Lawrence
University College Oxford Blockchain Research Centre, The Blockhouse Technology Ltd

Blockchains provide extremely simple certainty looking backward in time because of the way each block contains a hash of its predecessor. This is not possible in the same way looking forward in time for various reasons, not the least of which is that when block ? is created, block ? + 1, and thus its hash, are unknown. Therefore blockchains rely on more complex mechanisms to establish what the successor of any given block is, and to ensure that alternatives – known as forks – cannot be introduced either close to the time of its creation or long after. These typically rely on chains of dependency and PKIs. In this paper we show how the concept of hooks can create something closely analogous to the usual hash links, only in the other direction. These represent a powerful mechanism to counteract attempts to insert forks from relatively old blocks, and are entirely internal to the blockchain. In understanding hooks we do some detailed combinatorial analysis of the game that good and bad agents play in blockchains, introducing criteria for relatively small collections of agents to make decisions, up to stochastic certainty.