Cryptology ePrint Archive: Report 2021/775

Completeness Theorems for Adaptively Secure Broadcast

Ran Cohen and Juan Garay and Vassilis Zikas

Abstract: The advent of blockchain protocols has reignited the interest in adaptively secure broadcast, as it is by now well understood that broadcasting over a diffusion network allows an adaptive adversary to corrupt the sender depending on the message it attempts to send and change it. Hirt and Zikas [Eurocrypt '10] proved that this is an inherent limitation of broadcast in the simulation-based setting, i.e., that this task is impossible against an adaptive adversary corrupting a strict majority of the parties.

The contributions of this paper are two-fold. First, we devise a complete characterization of adaptively secure broadcast both in the property-based and in the simulation-based setting, and assuming a wide class of common setups. Our investigation reveals that, contrary to previous perception, the above limitation of adaptively secure broadcast is not an artifact of simulation-based security, but rather an inherent issue of adaptive security. In particular, we show that: (1) it also applies to the property-based broadcast definition adapted for adaptive adversaries, and (2) unlike other impossibilities in adaptive security this impossibility cannot be circumvented by adding a programmable random oracle.

Second, we turn to the resource-restricted cryptography (RRC) paradigm [Garay et al., Eurocrypt '20], which was proven useful in circumventing impossibility results, and ask whether it also affects the above negative result. We answer this question in the affirmative, by showing that time-lock puzzles (TLPs)---which can be viewed as an instance of RRC---indeed allow for achieving the property-based definition and circumvent the impossibility of adaptively secure broadcast. The natural question is then, do TLPs also allow for simulation-based adaptively secure broadcast against corrupted majorities? We answer this in the negative. Nonetheless, we show that a positive result can be achieved via a new, non-committing analogue of TLPs in the programmable random-oracle model.

As a contribution of independent interest, we also present the first (limited) composition theorem in the resource-restricted setting.

Category / Keywords: cryptographic protocols / Broadcast, adaptive security, cryptographic protocols

Date: received 8 Jun 2021, last revised 19 Feb 2022

Contact author: cohenran at idc ac il, garay at cse tamu edu, vzikas at cs purdue edu

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Version: 20220219:204835 (All versions of this report)

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