Cryptology ePrint Archive: Report 2019/403

While there is a substantial body of literature on the problem of hashing to elliptic curves, much of this work does not apply to Barreto-Lynn-Scott curves. Moreover, the work that does apply has the unfortunate property that fast implementations are complex, while simple implementations are slow.

In this work, we address these issues. First, we show a straightforward way of adapting the ``simplified SWU'' map of Brier et al. to BLS12-381. Second, we describe optimizations to this map that both simplify its implementation and improve its performance; these optimizations may be of interest in other contexts. Third, we implement and evaluate. We find that our work yields constant-time hash functions that are simple to implement, yet perform within 9% of the fastest, non--constant-time alternatives, which require much more complex implementations.