XSOC-QSIG/TQ: Threshold Quorum Authorization, Design and Security Argument

XSOC-QSIG/TQ is the threshold quorum authorization mode in the XSOC-QSIG family, rooted in DSKAG deterministic symmetric key agreement and the NIE identity engine. A custody set of n members at threshold t shares a secret vector over a prime field. For an operation, public coefficients are derived from the operation, the CGA lineage, the epoch, and the secret-vector identifier, and each member returns a single field element that is its Shamir share of an authorization value reconstructed only by a quorum. Member contributions are authenticated by a 30-byte DSKAG authenticator and attested and revocable through NIE; the on-chain gate verifies a post-quantum module-SIS commitment, reconstructs robustly against a corrupted minority, and consumes each one-time secret. This deposit contains the design and implementation plan and its security argument. The argument proves threshold secrecy and the limited-use bound information-theoretically and reduces quorum unforgeability to post-quantum assumptions: the DSKAG authenticator, NIE attestation, and module-SIS commitment binding. The threshold layer is information-theoretic; the deployed system rests on the stated post-quantum and setup assumptions. The construction generalizes the degree-one, single-use affine authorization gate to degree t-1 with up to m-1 uses per secret vector and a dual attribution-and-commitment barrier.