International Association
for Cryptologic Research

In 2011, Lindell proposed an efficient commitment scheme, with a non-interactive opening algorithm, in the Universal Composability (UC) framework. He recently acknowledged a bug in its security analysis for the adaptive case. We analyze the proof of the original paper and propose a simple patch of the scheme.

More interestingly, we then modify it and present a more efficient commitment scheme secure in the UC framework, with the same level of security as Lindell\'s protocol: adaptive corruptions, with erasures. The

security is proven in the standard model (with a Common Reference String) under the classical Decisional Diffie-Hellman assumption. Our proposal is the most efficient UC-secure commitment proposed to date (in

terms of computational workload and communication complexity).