Secret sharing schemes are fundamental cryptographic primitives with applications in secure multi-party computation and threshold cryptography. This talk introduces a secret sharing scheme tailored for lattice-based schemes that offers both short shares and small reconstruction coefficients. While its support is limited to small numbers of parties, we demonstrate the versatility of this scheme by applying it to two significant use cases:

1. Threshold Raccoon with Identifiable Aborts: We enhance the security of Threshold Raccoon by incorporating our secret sharing scheme to enable the identification of malicious parties that induce aborts. Our short sharing provides both a very natural and efficient construction.
2. Compact Threshold Signature Scheme: We construct a highly efficient threshold signature scheme based on the Fiat-Shamir with Aborts paradigm, leveraging our secret sharing scheme along with new simulation results to minimize the size of signatures.