  Threshold cryptography is essential for many blockchain protocols. For
example, many protocols rely on threshold common coin to implement asynchronous
consensus, leader elections, and provide support for randomized applications.
Similarly, threshold signature schemes are frequently used for protocol
efficiency and state certification, and threshold decryption and threshold
time-lock puzzles are often necessary for privacy.
  In this paper, we study the interplay between threshold cryptography and a
class of blockchains that use Byzantine-fault tolerant (BFT) consensus
protocols with a focus on latency. More specifically, we focus on
blockchain-native threshold cryptosystem, where the blockchain validators seek
to run a threshold cryptographic protocol once for every block with the block
contents as an input to the threshold cryptographic protocol. All existing
approaches for blockchain-native threshold cryptosystems introduce a latency
overhead of at least one message delay for running the threshold cryptographic
protocol. In this paper, we first propose a mechanism to eliminate this
overhead for blockchain-native threshold cryptosystems with tight thresholds,
i.e., in threshold cryptographic protocols where the secrecy and reconstruction
thresholds are the same. However, many real-world proof-of-stake-based
blockchain-native threshold cryptosystems rely on ramp thresholds, where
reconstruction thresholds are strictly greater than secrecy thresholds. For
these blockchains, we formally demonstrate that the additional delay is
unavoidable. We then introduce a mechanism to minimize this delay in the
optimistic case. We implement our optimistic protocol for the proof-of-stake
distributed randomness scheme on the Aptos blockchain. Our measurements from
the Aptos mainnet show that the optimistic approach reduces latency overhead by
71%.
