Two-Round Trip Schnorr Multi-signatures via Delinearized Witnesses

We construct a two-round Schnorr-based signature scheme (DWMS) by delinearizing two pre-commitments supplied by each signer. DWMS is a secure signature scheme in the algebraic group model (AGM) and the random oracle model (ROM) under the assumption of the hardness of the one-more discrete logarithm problem and the 2-entwined sum problem that we introduce in this paper. Our new m-entwined sum problem tweaks the k-sum problem in a scalar field using the associated group. We prove the hardness of our new problem in the AGM assuming the hardness of the discrete logarithm problem in the associated group. We believe that our new problem simplifies the security proofs of multi-signature schemes that use the delinearization of commitments.