Private balance-checking on blockchain accounts using private integer addition

A transaction record in a sharded blockchain can be represented as a two-dimensional array of integers with row-index associated to an account, column-index to a shard and the entry to the transaction amount. In a blockchain-based cryptocurrency system with coded sharding, a transaction record of a given epoch of time is encoded using a maximum-distance-separable code considering the entries as finite-field symbols. Each column of the resultant coded array is then stored in a server. In this paper, we propose a privacy-preserving multi-round protocol that allows a remote client to retrieve from a coded blockchain system the sum of transaction amounts belonging to two different epochs of time, but to the same ac-count. At the core of the protocol lies an algorithm for a remote client to privately compute a non-linear function referred to as integer addition of two finite-field symbols representing integer numbers, in the presence of curious-but-honest adversaries. Applying it to balance-checking in a cryptocurrency system, the protocol guarantees information-theoretic privacy on account number and shard number thereby ensuring perfect user anonymity, and also maintains confidentiality of half of the input bits on average. The protocol turns out to be a useful primitive for balance-checking in lightweight clients of a PolyShard-ed blockchain.