False shares in verifiable secret sharing with finite field commitments

Verifiable secret sharing (VSS) schemes [1–3] rely on the assumption that parties can not reliably fabricate false secret shares which pass the verification process. Here, we show that, for certain VSS implementations that use verification commitments bounded to a finite field, this assumption is incorrect. Let there be n shares of a secret and a threshold of t secret shares required to get the secret. Choose a finite field Zp and a generator g ∈ Zp. Each party associates with a unique non-zero identity i ∈ Zp and creates a secret random polynomial,