Obscura-PQ: Post-Quantum Privacy-Preserving Protocol for the Algorand Blockchain Using Lattice-Based Linkable Ring Signatures

Abstract

Public blockchains expose the complete transaction graph, and the privacy protocols deployed to obscure it rely almost exclusively on elliptic-curve cryptography, whose discrete-logarithm foundations fall to Shor's algorithm. Because ledgers are immutable, every anonymity set published today under classical assumptions can be retroactively deanonymized by a future quantum adversary. Transitioning to post-quantum alternatives remains challenging, as strict smart-contract resource limits prohibit native on-chain verification of computationally intensive post-quantum proofs. To address these challenges, we present \emph{Obscura-PQ}, a decentralized, non-custodial post-quantum privacy protocol that verifies natively on the Algorand blockchain. Its core is a setup-free lattice linkable ring signature over the cyclotomic ring $\mathcal{R}_q = \mathbb{Z}_q[X]/(X^{512}+1)$. A deposit is a Ring-SIS binding commitment to a short secret; a withdrawal proves knowledge of a ring opening via an AOS/Borromean-style challenge chain over two response-sharing linear relations with rejection-sampled short responses, while publishing a deterministic Ring-LWE serial number for double-spend detection. We reduce double-spend soundness and linkability to Ring-SIS, theft resistance to Ring-SIS for honestly generated deposits, and anonymity to Ring-LWE and an explicit decisional linking assumption in the classical random-oracle model. To overcome strict on-chain opcode and storage limits, Obscura-PQ evaluates verification relations entirely in the NTT domain. We split forward NTTs across opcode-pooled execution phases and stream oversized proofs through refundable box storage, enabling $O(1)$ membership and double-spend checks. We provide a complete Algorand testnet implementation, demonstrating native on-chain verification of a post-quantum privacy protocol under strict smart-contract limits.