We present the first treatment of non-interactive publicly-verifiable timestamping schemes in the Universal Composability framework. Similar to a simple construction by Mahmoody et al., we use non-parallelizable computational work that relates to elapsed time to avoid previous impossibility results on non-interactive timestamping. We extend these ideas to the UC-framework and show how to model verifiable delay functions (VDF) related to a global clock, and non-interactive timestamping, in the UC-framework. Furthermore, we present new constructions that are substantial improvements over Mahmoody et al.'s construction, such that any forged timestamps by the adversary are now limited to within a certain time-window that depends only on its ratio to compute VDFs more quickly and the time-window of corruption. Finally, we discuss natural applications for our construction in decentralized protocols.
In the Russian cards problem, Alice, Bob and Cath draw a, b and c cards, respectively, from a publicly known deck. Alice and Bob must then communicate their cards to each other without Cath learning who holds a single card. Solutions in the literature provide weak security, where Alice and Bob's exchanges do not allow Cath to know with certainty who holds each card that is not hers, or perfect security, where Cath learns no probabilistic information about who holds any given card. We propose an intermediate notion, which we call ε-strong security, where the probabilities perceived by Cath may only change by a factor of ε. We then show that a mild variant of the so-called geometric strategy gives ε-strong safety for arbitrarily small ε and appropriately chosen values of a, b, c. *
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