On June 22, 2026, the White House issued Executive Order 14413, directing the federal government to accelerate the deployment of quantum computing and to assess "the implications for the migration to post-quantum cryptography." The order is the latest and loudest signal of a fact the legal system has not yet absorbed: the cryptographic assumptions behind nearly all digital proof carry an expiration date. Every electronic signature, every encrypted database, and every blockchain transaction rests on math that a sufficiently powerful quantum computer can break. When that computer arrives, adversaries will be able to forge the signatures and decrypt the records on which courts, regulators, and markets now rely. Data stolen today is already being warehoused for decryption tomorrow. Signatures trusted today may be forgeable tomorrow. This Article argues that the quantum transition forces the law to confront a distinction it has long been able to ignore: the difference between probabilistic verification (an intermediary's opinion, an AI confidence score, an auditor's judgment) and deterministic verification (a mathematical result that anyone can independently reproduce). Across digital identity, financial services, insurance, defense, supply chains, and digital assets, organizations prove claims through intermediaries whose honesty cannot be checked and whose methods cannot be reproduced. A small set of well-understood cryptographic tools can replace that fragmented apparatus: hardware-secured signing keys, Merkle tree timestamping, post-quantum signature standards, and zero-knowledge proofs. Together they produce verification that is reproducible, tamper-evident, and quantum-resistant from the outset. The Article makes three contributions. First, it reframes the “verification gap” as a legal problem rather than a technical one, showing how the Federal Rules of Evidence, the Daubert reliability standard, data breach liability doctrine, and fiduciary oversight duties each already point toward deterministic proof. Second, it shows that quantum risk is collapsing the legal defenses built on classical cryptography, most visibly the “it was encrypted” defense in breach litigation, while creating new disclosure and diligence obligations for boards. Third, it maps deterministic verification onto concrete applications in six sectors and proposes a regulatory framework, including a “deterministic assurance level” for evidentiary purposes and a public governance process for the rule schemas that translate law into machine-checkable criteria.
Ghanshyam Prasad Dubey, Ayush Giri, Daniel Arockiam, V. Sathya Priya
Federated learning has emerged as a transformative example in machine learning, allowing collaborative model training across decentralized devices while preserving data privacy. Federated learning (FL) has emerged as a ground-breaking paradigm in machine learning, allowing for collaborative model training across a network of decentralized devices while maintaining data privacy and security. Unlike typical centralized systems, FL keeps data localized on the clients' devices, meeting important privacy issues and legal constraints. We begin by explaining the fundamental principles of FL, such as the roles of clients and servers, the process of local training and model updates, and methods for aggregating these updates to enhance a global model. A strong emphasis is made on the numerous federated optimization algorithms that enable effective model training in a distributed environment. We also look at advanced privacy-preserving technologies like differential privacy and secure multi-party computing (SMPC), which are critical to FL's operation. This chapter provides a comprehensive exploration of federated learning, encompassing its foundational principles, methodologies, applications, and challenges by delving into the intricacies of federated learning techniques, like federated optimization algorithms, privacy-preserving mechanisms, and communication protocols. Through case studies and real-world examples, we highlight the diverse applications of federated learning across domains such as healthcare, finance, Internet of Things, and mobile devices. Moreover, we discuss the inherent challenges of federated learning, including communication overhead, privacy concerns, and heterogeneity of data distributions. By surveying recent advancements and research trends, we identify future directions for federated learning, emphasizing its potential to revolutionize distributed machine learning. This chapter serves as a comprehensive resource for researchers, practitioners, and enthusiasts seeking to understand and leverage the power of federated learning in decentralized intelligence.
In relation with Article 3 of the European Convention of Human Rights (ECHR, from now on), which prohibits torture and inhuman or degrading treatment or punishments, the European Court of Human Rights (ECtHR, from now on) has established there are no exceptions or limitations, no matter what the victim�s actions were. The ECHR has stated that the referred prohibition would be inefficient without an �effective official investigation� in those cases where the existence of torture is reported. The Spanish Constitutional Court has tried to comply thoroughly with the ECtHR�s Judgements. In this sense, we must note the broad and generous interpretation that the Spanish Constitutional Court has made of the prohibition of using proof obtained under torture. In spite of this, Spain suffered a sentence by the ECtHR for this reason in 2004. It involves the case Martinez Sala and others v Spain, Judgment of 2 November 2004. Now then, our Constitutional Court has been consistent with this Judgement of the ECtHR. The cases in which tortures are reported during detention cannot be approached without taking into account the fundamental right at stake, considered in Article 15 of the Spanish Constitution (CE from now on, for its initials in Spanish): right to life and to not suffer torture or inhuman or degrading treatment. This demand of reinforced motivation in judicial sentences which affect the content of an important fundamental right has had great importance in relation with the case of the filing of statement of torture since the STC 224/2007, of 22 October.