Composable Long-Term Security with Rewinding
Long-term security, a variant of Universally Composable (UC) security introduced by Müller-Quade and Unruh (TCC ’07, JoC ’10), allows to analyze the security of protocols in a setting where all hardness assumptions no longer hold after the protocol execution has finished. Such a strict notion is highly desirable when properties such as input privacy need to be guaranteed for a long time, e.g. with zero-knowledge proofs for secure electronic voting. Strong impossibility results rule out so-called long-term-revealing setups, e.g. a common reference string (CRS), to achieve long-term security, with known constructions for long-term security requiring hardware assumptions, e.g. signature cards. We circumvent these impossibility results with new techniques, enabling rewinding-based simulation in a way that universal composability is achieved. This allows us to construct a long-term-secure composable commitment scheme in the CRS-hybrid model, which is provably impossible in the notion of Müller-Quade and Unruh. We base our construction on a statistically hiding commitment scheme in the CRS-hybrid model with CCA-like properties. To provide a CCA oracle, we cannot rely on super-polynomial extraction techniques and instead extract the value committed to via rewinding. To this end, we incorporate rewinding-based commitment extraction into the UC framework via a helper in analogy to Canetti, Lin and Pass (FOCS 2010), allowing both adversary and environment to extract statistically hiding commitments. Our new framework provides the first setting in which a commitment scheme that is both statistically hiding and universally composable can be constructed from standard polynomial-time hardness assumptions and a CRS only. We also prove that our CCA oracle is k-robust extractable. This asserts that extraction is possible without rewinding a concurrently executed k-round protocol. Consequently any k-round (standard) UC-secure protocol remains secure in the presence of our helper. Finally, we prove that building long-term-secure oblivious transfer (and thus general two-party computations) from long-term-revealing setups remains impossible in our setting. Still, our long-term-secure commitment scheme suffices for natural applications, such as long-term secure and composable (commit-and-prove) zero-knowledge arguments of knowledge.