1-Round Distributed Key Generation With Efficient Reconstruction Using Decentralized CP-ABE

Abstract

Distributed key generation (DKG) is widely used in multi-party computation and decentralized applications. DKG has two phases, namely sharing and reconstruction. Most of the prior DKG protocols need at least 2 rounds for the sharing phase, in case some party raises a dispute. The existing 1-round DKG protocol [Fouque <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , PKC’01], built based on a publicly verifiable secret sharing (PVSS) scheme, assumes a static adversary model and its reconstruction phase requires <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{2})$ </tex-math></inline-formula> communication complexity. Motivated by the observation that a ciphertext-policy attribute-based encryption (CP-ABE) scheme hides secret sharing (SS) in ciphertext, we utilize decentralized CP-ABE to achieve the first adaptively secure 1-round DKG protocol. Firstly, a CP-ABE scheme enables the ciphertexts in DKG to be externally decrypted, making our protocol superior to the PVSS-based DKG protocol in reconstruction. The communication and computation complexities are both lowered to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula> thanks to the constant-sized decryption key and the proposed batch decryption. The use of CP-ABE also makes our DKG protocol storage-friendly, i.e., the parties store no ciphertext after the sharing phase. Secondly, we add non-interactive zero-knowledge (NIZK) proofs to make the CP-ABE ciphertext publicly verifiable by leveraging the sigma protocol and the Fiat-Shamir heuristic. Thirdly, we demonstrate our protocol’s feasibility by presenting a proof-of-concept implementation over Ethereum, which is used as a public channel and a trustworthy computation platform. The implementation is a non-trivial task due to Ethereum’s incompatibility with the bilinear mapping group.