A dealer-assisted weighted threshold Pointcheval–Sanders signature scheme from CRT-based weighted ramp secret sharing

Abstract Existing threshold Pointcheval–Sanders (PS) signature schemes largely assume equal-weight participants and therefore cannot directly express heterogeneous signing authority in semi-trusted multi-organization settings. This paper presents a dealer-assisted weighted threshold PS signing framework by integrating PS signatures with a Chinese Remainder Theorem (CRT)-based weighted ramp secret sharing (WRSS) mechanism. The main technical contribution is a CRT-to-PS integration method that converts weight-dependent modular shares into exponents while preserving the standard PS verification equation in prime-order bilinear groups. The WRSS base modulus is instantiated as the same prime order used by the bilinear-group scalar field, removing any modular mismatch between CRT reconstruction and PS exponentiation. As a result, the bit-length of each private-key share is proportional to the participant’s weight, and any signing subset whose total weight reaches the reconstruction threshold can jointly generate a valid PS signature. Meanwhile, any coalition whose total weight is at most the privacy threshold learns no information about the master secret beyond what is implied by the public key. We analyze the construction in the semi-honest model and in the WRSS-hybrid model, where the WRSS subroutines are idealized, and establish correctness, unforgeability, and randomization-based non-linkability. We further quantify the incremental computation and communication overhead introduced by the CRT-based weighting layer. The analysis separates CRT arithmetic from the bounded overflow-selection cost and includes heterogeneous-weight parameter tests. The proposed scheme is intended for dealer-assisted, semi-trusted, regulated multi-organization applications, such as joint authorization and credential-issuance workflows with policy-defined participant weights.