Foundations of classical and quantum verifiable computing

近年来，正在生成和收集的数据的数量和敏感性出现了巨大的增长，例如基因测序、分布式存储服务和社交网络图。现代数据集的无处不在和庞大的规模迫切需要开发可扩展计算的新技术和方法。与此同时，作为部署分布式系统（如比特币和以太坊）基础的区块链技术的兴起，为开发去中心化协议提供了充足的动力，这些协议可能超越对集中金融控制的挑战，并通过为可用于公共利益的现实世界分布式系统提供基础，对社会产生深远影响。应对上述两种需求所带来的挑战的一个关键范例是可验证计算。这里的目标是允许以可扩展、安全和保护隐私的方式验证由第三方执行的计算。此外，随着量子计算的出现，验证也必须是后量子安全的。该提案的重点是推动经典和量子可验证计算及其实际应用的边界，将计算委托给云计算，以及区块链技术。它的主要目标是开发一个广泛的工具库，为应对大数据带来的挑战和对分散的点对点系统的需求开辟新的可能性。所提出的方法本质上是跨学科的，涉及密码学，复杂性理论，随机算法和量子信息的基本概念，以及依赖于编码理论，组合学和抽象代数的技术。

Recent years have seen a vast surge in the volume and sensitivity of data that are being generated and collected, e.g., in genetic sequencing, distributed storage services, and graphs of social networks. The ubiquity and sheer size of modern data sets raise an urgent need to develop new techniques and methodologies for scalable computation.At the same time, the rise of blockchain technology, which underlies deployed distributed systems such as Bitcoin and Ethereum, provides ample motivation for developing decentralised protocols that could go beyond challenging centralised financial control, and profoundly impact society by providing a foundation for real-world distributed systems that can be used for public benefit.A key paradigm for meeting the challenges imposed by both of the aforementioned desiderata is that of verifiable computing. Here, the goal is to allow verification of computation that is performed by a third-party, in a scalable, secure, and privacy-preserving way. Moreover, with the advent of quantum computing on the horizon, it is imperative that the verification would also be post-quantum secure.This proposal is focused on pushing the boundaries of classical and quantum verifiable computing and its real-world applications to delegation of computation to the cloud, as well as to blockchain technology. Its primary objective is to develop a wide arsenal of tools that would open new possibilities for meeting the challenges imposed by big data and the need for decentralised peer-to-peer systems.The proposed approach is inherently interdisciplinary, involving fundamental concepts in cryptography, complexity theory, randomised algorithms, and quantum information, as well as relying on techniques from coding theory, combinatorics, and abstract algebra.