Efficient Verifiably Encrypted ECDSA-Like Signatures and Their Applications
Xiao Yang, Mengling Liu, Man Ho Au, Xiapu Luo, Qingqing Ye
Abstract
Verifiably encrypted signature (VES) allows a signer to encrypt a signature under the public key of a trusted third party (aka adjudicator) in a verifiable manner. Recently, Yang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> proposed a practical verifiably encrypted signature scheme for ECDSA and initiated the study of escrow protocol for Bitcoin via VES. This paper generalizes and improves the VES scheme of Yang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , such that it covers a family of signatures with similar structures, including ECDSA, Schnorr and their variants. Our construction is very efficient: comparing with Yang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> ’s construction, the size of the resulting VES (for ECDSA) is reduced by more than 25 times. The only caveat is that the adjudicator is required to store a look-up table of size around 270MB. Our scheme naturally gives rise to escrow protocols for mainstream cryptocurrencies that employ ECDSA-like signatures to authorise transaction, including Bitcoin, Ethereum, Cardano, Chainlink, etc.