UC-Secure Star DKG for Non-Exportable Key Shares with VSS-Free Enforcement
2026-02-25 • Cryptography and Security
Cryptography and Security
AI summaryⓘ
The authors study how a group of devices can securely create and share a secret key so that no single device can misuse it alone. They focus on a setting where the secret parts stay protected inside special hardware modules that prevent exporting keys. To ensure security without revealing secrets, they combine new verification methods and mathematical proofs that work straight through the process without rewinding. Their construction, called Star DKG, enables a setup where a central service and any one device together can approve actions, useful for secure multi-device wallets. They prove this scheme is secure under standard cryptographic assumptions with reasonable communication and computation costs.
Distributed Key GenerationVerifiable Secret SharingNon-Exportable KeysThreshold WalletsTrusted Execution EnvironmentsUniversal ComposabilityZero-Knowledge ProofsFischlin ProtocolDiscrete Logarithm ProblemDiffie-Hellman Assumption
Authors
Vipin Singh Sehrawat
Abstract
Distributed Key Generation (DKG) lets parties derive a common public key while keeping the signing key secret-shared. UC-secure DKG requires a verifiable-sharing enforcement layer -- classically satisfied via Verifiable Secret Sharing (VSS) and/or commitment-and-proof mechanisms -- for secrecy, uniqueness, and affine consistency. We target the Non-eXportable Key (NXK) setting enforced by hardware-backed key-isolation modules (e.g., TEEs, HSM-like APIs), formalized via an ideal KeyBox (keystore) functionality $\mathcal{F}_{KeyBox}$ that keeps shares non-exportable and permits only attested KeyBox-to-KeyBox sealing. With confidentiality delegated to the NXK boundary, the remaining challenge is enforcing transcript-defined affine consistency without exporting or resharing shares. State continuity rules out rewinding-based extraction, mandating straight-line techniques. We combine (i) KeyBox confidentiality; (ii) Unique Structure Verification (USV), a publicly verifiable certificate whose certified scalar never leaves the KeyBox yet whose public group element is transcript-derivable; and (iii) Fischlin-based UC-extractable NIZK arguments of knowledge in a gRO-CRP (global Random Oracle with Context-Restricted Programmability) model. We construct Star DKG (SDKG), a UC-secure scheme for multi-device threshold wallets where a designated service must co-sign but cannot sign alone, realizing a 1+1-out-of-$n$ star access structure (center plus any leaf) over roles (primary vs. recovery) with role-based device registration. In the $\mathcal{F}_{KeyBox}$-hybrid and gRO-CRP models, under DL and DDH assumptions with adaptive corruptions and secure erasures, SDKG UC-realizes a transcript-driven refinement of the standard UC-DKG functionality. Over a prime-order group of size $p$, SDKG incurs $\widetilde{O}(n\log p)$ communication overhead and $\widetilde{O}(n\log^{2.585}p)$ bit-operation cost.