Zero-Knowledge Range Arguments for Signed Fractional Numbers from Lattices

Range proofs introduced by Brickell et al. at CRYPTO 1988, allow a prover to convince a verifier that the committed value belongs to an interval without revealing anything else. It has become an essential building block in various modern cryptographic protocols such as distributed ledgers, anonymous transactions, e-cash, e-voting, auction protocols, privacy-preserving certificate transparency, and many more. In this paper, we provide a zero-knowledge range argument system showing that a committed value is in a public or hidden range by constructing a zero-knowledge argument system to prove inequalities between signed fractional numbers as well as non-negative integers in the standard lattice settings. The complexity of our range arguments is only logarithmic in the size of the range. Negative numbers and fractional numbers play an important role in our everyday life, especially in financial loss, medical data, bank account balances, GPA and tax records, etc. It would be desirable to handle them in a privacy-preserving manner. Prior to this work, all the lattice-based zero-knowledge range argument systems only address a range of non-negative integers, whereas our range arguments can handle signed fractional numbers and fill an interesting research gap in the literature.