Paper 2023/405

CaSCaDE: (Time-Based) Cryptography from Space Communications DElay

Abstract

Time-based cryptographic primitives such as Time-Lock Puzzles (TLPs) and Verifiable Delay Functions (VDFs) have recently found many applications to the efficient design of secure protocols such as randomness beacons or multiparty computation with partial fairness. However, current TLP and VDF candidate constructions rely on the average hardness of sequential computational problems. Unfortunately, obtaining concrete parameters for these is notoriously hard, as there cannot be a large gap between the honest parties’ and the adversary’s runtime when solving the same problem. Moreover, even a constant improvement in algorithms for solving these problems can render parameter choices, and thus deployed systems, insecure - unless very conservative and therefore highly inefficient parameters are chosen. In this work, we investigate how to construct time-based cryptographic primitives from communication delay, which has a known lower bound given the physical distance between devices: the speed of light. In order to obtain high delays, we explore the sequential communication delay that arises when sending a message through a constellation of satellites. This has the advantage that distances between protocol participants are guaranteed as positions of satellites are observable, so delay lower bounds can be easily computed. At the same time, building cryptographic primitives for this setting is challenging due to the constrained resources of satellites and possible corruptions of parties within the constellation. We address these challenges by constructing efficient proofs of sequential communication delay to convince a verifier that a message has accrued delay by traversing a path among satellites. As part of this construction, we propose the first ordered multisignature scheme with security under a version of the the discrete logarithm assumption, which enjoys constant-size signatures and, modulo preprocessing, computational complexity independent of the number of signers. Building on our proofs of sequential communication delay, we show new constructions of Publicly Verifiable TLPs and VDFs whose delay guarantees are rooted on physical communication delay lower bounds. Our protocols as well as the ordered multisignature are analysed in the Universal Composability framework using novel models for sequential communication delays and (ordered) multisignatures. A direct application of our results is a randomness beacon that only accesses expensive communication resources in case of cheating.