Whitehead's algorithm

Whitehead's algorithm

Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on a classic 1936 paper of J. H. C. Whitehead. It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity. == Statement of the problem == Let F n = F ( x 1 , … , x n ) {\displaystyle F_{n}=F(x_{1},\dots ,x_{n})} be a free group of rank n ≥ 2 {\displaystyle n\geq 2} with a free basis X = { x 1 , … , x n } {\displaystyle X=\{x_{1},\dots ,x_{n}\}} . The automorphism problem, or the automorphic equivalence problem for F n {\displaystyle F_{n}} asks, given two freely reduced words w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether there exists an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Thus the automorphism problem asks, for w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} . For w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} one has Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} if and only if Out ⁡ ( F n ) [ w ] = Out ⁡ ( F n ) [ w ′ ] {\displaystyle \operatorname {Out} (F_{n})[w]=\operatorname {Out} (F_{n})[w']} , where [ w ] , [ w ′ ] {\displaystyle [w],[w']} are conjugacy classes in F n {\displaystyle F_{n}} of w , w ′ {\displaystyle w,w'} accordingly. Therefore, the automorphism problem for F n {\displaystyle F_{n}} is often formulated in terms of Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} -equivalence of conjugacy classes of elements of F n {\displaystyle F_{n}} . For an element w ∈ F n {\displaystyle w\in F_{n}} , | w | X {\displaystyle |w|_{X}} denotes the freely reduced length of w {\displaystyle w} with respect to X {\displaystyle X} , and ‖ w ‖ X {\displaystyle \|w\|_{X}} denotes the cyclically reduced length of w {\displaystyle w} with respect to X {\displaystyle X} . For the automorphism problem, the length of an input w {\displaystyle w} is measured as | w | X {\displaystyle |w|_{X}} or as ‖ w ‖ X {\displaystyle \|w\|_{X}} , depending on whether one views w {\displaystyle w} as an element of F n {\displaystyle F_{n}} or as defining the corresponding conjugacy class [ w ] {\displaystyle [w]} in F n {\displaystyle F_{n}} . == History == The automorphism problem for F n {\displaystyle F_{n}} was algorithmically solved by J. H. C. Whitehead in a classic 1936 paper, and his solution came to be known as Whitehead's algorithm. Whitehead used a topological approach in his paper. Namely, consider the 3-manifold M n = # i = 1 n S 2 × S 1 {\displaystyle M_{n}=\#_{i=1}^{n}\mathbb {S} ^{2}\times \mathbb {S} ^{1}} , the connected sum of n {\displaystyle n} copies of S 2 × S 1 {\displaystyle \mathbb {S} ^{2}\times \mathbb {S} ^{1}} . Then π 1 ( M n ) ≅ F n {\displaystyle \pi _{1}(M_{n})\cong F_{n}} , and, moreover, up to a quotient by a finite normal subgroup isomorphic to Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} , the mapping class group of M n {\displaystyle M_{n}} is equal to Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} ; see. Different free bases of F n {\displaystyle F_{n}} can be represented by isotopy classes of "sphere systems" in M n {\displaystyle M_{n}} , and the cyclically reduced form of an element w ∈ F n {\displaystyle w\in F_{n}} , as well as the Whitehead graph of [ w ] {\displaystyle [w]} , can be "read-off" from how a loop in general position representing [ w ] {\displaystyle [w]} intersects the spheres in the system. Whitehead moves can be represented by certain kinds of topological "swapping" moves modifying the sphere system. Subsequently, Rapaport, and later, based on her work, Higgins and Lyndon, gave a purely combinatorial and algebraic re-interpretation of Whitehead's work and of Whitehead's algorithm. The exposition of Whitehead's algorithm in the book of Lyndon and Schupp is based on this combinatorial approach. Culler and Vogtmann, in their 1986 paper that introduced the Outer space, gave a hybrid approach to Whitehead's algorithm, presented in combinatorial terms but closely following Whitehead's original ideas. == Whitehead's algorithm == Our exposition regarding Whitehead's algorithm mostly follows Ch.I.4 in the book of Lyndon and Schupp, as well as. === Overview === The automorphism group Aut ⁡ ( F n ) {\displaystyle \operatorname {Aut} (F_{n})} has a particularly useful finite generating set W {\displaystyle {\mathcal {W}}} of Whitehead automorphisms or Whitehead moves. Given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} the first part of Whitehead's algorithm consists of iteratively applying Whitehead moves to w , w ′ {\displaystyle w,w'} to take each of them to an "automorphically minimal" form, where the cyclically reduced length strictly decreases at each step. Once we find automorphically these minimal forms u , u ′ {\displaystyle u,u'} of w , w ′ {\displaystyle w,w'} , we check if ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} . If ‖ u ‖ X ≠ ‖ u ′ ‖ X {\displaystyle \|u\|_{X}\neq \|u'\|_{X}} then w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} . If ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} , we check if there exists a finite chain of Whitehead moves taking u {\displaystyle u} to u ′ {\displaystyle u'} so that the cyclically reduced length remains constant throughout this chain. The elements w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} if and only if such a chain exists. Whitehead's algorithm also solves the search automorphism problem for F n {\displaystyle F_{n}} . Namely, given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} , if Whitehead's algorithm concludes that Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} , the algorithm also outputs an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Such an element φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} is produced as the composition of a chain of Whitehead moves arising from the above procedure and taking w {\displaystyle w} to w ′ {\displaystyle w'} . === Whitehead automorphisms === A Whitehead automorphism, or Whitehead move, of F n {\displaystyle F_{n}} is an automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} of F n {\displaystyle F_{n}} of one of the following two types: There is a permutation σ ∈ S n {\displaystyle \sigma \in S_{n}} of { 1 , 2 , … , n } {\displaystyle \{1,2,\dots ,n\}} such that for i = 1 , … , n {\displaystyle i=1,\dots ,n} τ ( x i ) = x σ ( i ) ± 1 {\displaystyle \tau (x_{i})=x_{\sigma (i)}^{\pm 1}} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the first kind. There is an element a ∈ X ± 1 {\displaystyle a\in X^{\pm 1}} , called the multiplier, such that for every x ∈ X ± 1 {\displaystyle x\in X^{\pm 1}} τ ( x ) ∈ { x , x a , a − 1 x , a − 1 x a } . {\displaystyle \tau (x)\in \{x,xa,a^{-1}x,a^{-1}xa\}.} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the second kind. Since τ {\displaystyle \tau } is an automorphism of F n {\displaystyle F_{n}} , it follows that τ ( a ) = a {\displaystyle \tau (a)=a} in this case. Often, for a Whitehead automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} , the corresponding outer automorphism in Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} is also called a Whitehead automorphism or a Whitehead move. ==== Examples ==== Let F 4 = F ( x 1 , x 2 , x 3 , x 4 ) {\displaystyle F_{4}=F(x_{1},x_{2},x_{3},x_{4})} . Let τ : F 4 → F 4 {\displaystyle \tau :F_{4}\to F_{4}} be a homomorphism such that τ ( x 1 ) = x 2 x 1 , τ ( x 2 ) = x 2 , τ ( x 3 ) = x 2 x 3 x 2 − 1 , τ ( x 4 ) = x 4 {\displaystyle \tau (x_{1})=x_{2}x_{1},\quad \tau (x_{2})=x_{2},\quad \tau (x_{3})=x_{2}x_{3}x_{2}^{-1},\quad \tau (x_{4})=x_{4}} Then τ {\displaystyle \tau } is actually an automorphism of F 4 {\displaystyle F_{4}} , and, moreover, τ {\displaystyle \tau } is a Whitehead automorphism of the second kind, with the multiplier a = x 2 − 1 {\displaystyle a=x_{2}^{-1}} . Let τ ′ : F 4 → F 4 {\displaystyle \tau ':F_{4}\to F_{4}} be a homomorphism such that τ ′ ( x 1 ) = x 1 , τ ′ ( x 2 ) = x 1 − 1 x 2 x 1 , τ ′ ( x 3 ) = x 1 − 1 x 3 x 1 , τ ′ ( x 4 ) = x 1 − 1 x 4 x 1 {\displaystyle \tau '(x_{1})=x_{1},\quad \tau '(x_{2})=x_{1}^{-1}x_{2}x_{1},\quad \tau '(x_{3})=x_{1}^{-1}x_{3}x_{1},\quad \tau '(x_{4})=x_{1}^{-1}x_{4}x_{1}} Then τ ′ {\displaystyle \tau '} is actually an inner automorphism of F 4 {\displaystyle F_{4}} given by conjugation by x 1 {\displaystyle x_{1}} , and, moreover, τ ′ {\displaystyle \

SwissCovid

SwissCovid is a COVID-19 contact tracing app used for digital contact tracing in Switzerland. Use of the app is voluntary and based on a decentralized approach using Bluetooth Low Energy and Decentralized Privacy-Preserving Proximity Tracing (dp3t). == Development == The app was developed in collaboration with the FOPH by Federal Office for Information Technology, Systems and Communications FOITT, École polytechnique fédérale de Lausanne (EPFL) and the Swiss Federal Institute of Technology in Zurich (ETH) as well as other experts. == Non-interoperability with applications in European countries == There is an agreement between EU countries to make applications compatible. However, there is no legal basis for the SwissCovid application to be part of this portal even though technically speaking it is ready, according to Sang-Ill Kim, head of the digital transformation department of the Federal Office of Public Health. == Criticism == === Not full open source and dependence on Google and Apple === In June 2020, researchers Serge Vaudenay and Martin Vuagnoux published a critical analysis of the application, noting that it relies heavily on Google and Apple's exposure notification system, which is integrated into their respective Android and iOS operating systems. Since Google and Apple have not released the full source code of this system, this would call into question the truly open source nature of the application. The researchers note that the dp3t collective, which includes the developers of the application, has asked Google and Apple to release their code. Moreover, they criticize the official description of the application and its functionalities, as well as the adequacy of the legal basis for its effective operation. === Cyber attacks === Professor Serge Vaudenay and Martin Vuagnoux identify also various security vulnerabilities in the application. The system would thus allow a third party to trace the movements of a phone using the application by means of Bluetooth sensors scattered along its path, for example in a building. Another possible attack would be to copy identifiers from the phones of people who may be ill (for example, in a hospital), and to reproduce those identifiers in order to receive notification of exposure to COVID-19 and illegitimately benefit from quarantine (thus entitling them to paid leave, a postponed examination, or other benefits). The system would also allow a third party to use a phone using the application by means of Bluetooth sensors scattered along the way. Paul-Olivier Dehaye of Personaldata.io and professor Joel Reardon of the University of Calgary published in June 2020 several examples of AEM (Associated Encrypted Metadata) replay and manipulation attacks via software development kits (SDKs) found in benign third-party mobile applications downloaded by the general public and having the phone's Bluetooth access permissions and in September 2020 a paper indicating that "Bluetooth-based proximity tracing apps are fundamentally insecure with respect to an attacker leveraging a malevolent app or SDK". === Costs === According to a publication by the federal administration, "the costs of developing the software for the mobile phone application, the GR back-end and the code management system as well as the costs for access management for the cantonal doctors' services are estimated at a one-off amount of 1.65 million francs. However, the Zurich-based company Ubique, responsible for the development of the application, was finally awarded the mandate to develop the application for an amount of 1.8 million francs. Through the Botnar Foundation based in Basel, École polytechnique fédérale de Lausanne received 3.5 million Swiss francs for the development of the application

Artificial intelligence safety institute

An artificial intelligence safety institute is a type of state-backed organization aiming to evaluate and ensure the safety of advanced artificial intelligence (AI) models, also called frontier AI models. AI safety gained prominence in 2023, notably with public declarations about potential existential risks from AI. During the AI Safety Summit in November 2023, the United Kingdom and the United States both created their own AISI. During the AI Seoul Summit in May 2024, international leaders agreed to form a network of AI Safety Institutes, comprising institutes from the UK, the US, Japan, France, Germany, Italy, Singapore, South Korea, Australia, Canada and the European Union. In 2025, the UK's AI Safety Institute was renamed the "AI Security Institute", and its US counterpart became the Center for AI Standards and Innovation (CAISI). == Timeline == In 2023, Rishi Sunak, the Prime Minister of the United Kingdom, expressed his intention to "make the UK not just the intellectual home but the geographical home of global AI safety regulation" and unveiled plans for an AI Safety Summit. He emphasized the need for independent safety evaluations, stating that AI companies cannot "mark their own homework". During the summit in November 2023, the UK AISI was officially established as an evolution of the Frontier AI Taskforce, and the US AISI as part of the National Institute of Standards and Technology. Japan followed by launching an AI safety institute in February 2024. Politico reported in April 2024 that many AI companies had not shared pre-deployment access to their most advanced AI models for evaluation. Meta's president of global affairs Nick Clegg said that many AI companies were waiting for the UK and the US AI Safety Institutes to work out common evaluation rules and procedures. An agreement was indeed concluded between the UK and the US in April 2024 to collaborate on at least one joint safety test. Initially established in London, the UK AI Safety Institute announced in May 2024 that it would open an office in San Francisco, where many AI companies are located. This is part of a plan to "set new, international standards on AI safety", according to UK's technology minister Michele Donelan. == International network == At the AI Seoul Summit in May 2024, the European Union and other countries agreed to create their own AI safety institutes, forming an international network. In July 2025, the international network held an exercise to explore issues with evaluating AI agents, especially when it came to leaking sensitive information or cybersecurity. Network members also met at NeurIPS 2025 in the city of San Diego. == Specific institutes == === Australia === The Albanese government announced the creation of the Australian AI Safety Institute on 25 November 2025. === Canada === Canada announced in April 2024 that it would create an AI safety institute, and such an institute was officially founded in November 2024. The institute is housed under Innovation, Science and Economic Development Canada, though it also partners with the Canadian Institute for Advanced Research (CIFAR). It is supported by a budget of CA$50,000,000 for a five-year timespan. === European Union === The EU AI office, founded in May 2024, is a member of the international network of AI safety institutes. === France === On 31 January 2025, the government of France created the Institut national pour l'évaluation et la sécurité de l'intelligence artificielle (INESIA), or the National Institute for AI Evaluation and Security. === India === The Ministry of Electronics and Information Technology held consultations with Meta Platforms, Google, Microsoft, IBM, OpenAI, NASSCOM, Broadband India Forum, Software Alliance, Indian Institutes of Technology (IITs), The Quantum Hub, Digital Empowerment Foundation, and Access Now on October 7, 2024, in relation to the establishment of the AI Safety Institute. The decision was made to shift focus from regulation to standards-setting, risk identification, and damage detection—all of which require interoperable technologies. The AISI may spend the ₹20 crore allotted to the Safe and Trusted Pillar of the IndiaAI Mission for the initial budget. Future funding may come from other components of the IndiaAI Mission. UNESCO and MeitY began consulting on AI Readiness Assessment Methodology under Safety and Ethics in Artificial Intelligence from 2024. It is to encourage the ethical and responsible use of AI in industries. The study will find areas where government can become involved, especially in attempts to strengthen institutional and regulatory capabilities. Minister for Electronics & Information Technology Ashwini Vaishnaw announced the creation of an IndiaAI Safety Institute on January 30, 2025, to ensure the ethical and safe application of AI models. The institute will promote domestic R&D that is grounded in India's social, economic, cultural, and linguistic diversity and is based on Indian datasets. With the help of academic and research institutions, as well as private sector partners, the institute will follow the hub-and-spoke approach to carry out projects within Safe and Trusted Pillar of the IndiaAI Mission. It operates under a "hub-and-spoke" model with collaboration from academic institutions (e.g., IITs), tech firms, and international organizations like UNESCO. === Japan === The Japan AISI (or J-AISI) was founded in February 2024. Part of the Information Technology Promotion Agency, it employs about 23 people. The institute consists of the Council of AISI, the AISI Steering Committee, and a secretariat with six teams. Akiko Murakami (previously of IBM Japan and Sompo Japan) serves as the institute's executive director, and Kenji Hiramoto and Suguru Nishimura serve as the institute's two deputy executive directors. === Kenya === Kenya agreed to join the international network of AI safety institutes, but the country has not announced any details yet. It is the only African state in the network. === Singapore === The Digital Trust Centre was initially founded in June 2022. In May 2024, it was renamed to the Singapore AISI. Part of Nanyang Technological University, the institute partners with Infocomm Media Development Authority and is supported by an investment of S$10,000,000 per year. === South Korea === South Korea announced in May 2024 that it would create an AI safety institute under the umbrella of the Electronics and Telecommunications Research Institute. It will be supported by a tentative investment of somewhere between 10 and 20 million South Korean won per year, and employ at least 30 people. The institute was founded in November 2024 and is based in Bundang District within the city of Seongnam. === United Kingdom === The United Kingdom founded in April 2023 a safety organisation called Frontier AI Taskforce, with an initial budget of £100 million. In November 2023, it evolved into the AI Safety Institute, and continued to be led by Ian Hogarth. The AISI is part of the United Kingdom's Department for Science, Innovation and Technology. The United Kingdom's AI strategy aims to balance safety and innovation. Unlike the European Union which adopted the AI Act, the UK is reluctant to legislate early, considering that it may lower the sector's growth, and that laws might be rendered obsolete by technological progress. In May 2024, the institute open-sourced an AI safety tool called "Inspect", which evaluates AI model capabilities such as reasoning and their degree of autonomy. In February 2025, the UK body was renamed the AI Security Institute. Observers saw the name change as a signal that the institute will not focus on ethical issues such as algorithmic bias or freedom of speech in AI applications. === United States === The US AISI was founded in November 2023 as part of the National Institute of Standards and Technology (NIST). This happened the day after the signature of the Executive Order 14110. In February 2024, Joe Biden's former economic policy adviser Elizabeth Kelly was appointed to lead it. In February 2024, the US government created the US AI Safety Institute Consortium (AISIC), regrouping more than 200 organizations such as Google, Anthropic or Microsoft. In March 2024, a budget of $10 million was allocated. Observers noted that this investment is relatively small, especially considering the presence of many big AI companies in the US. The NIST itself, which hosts the AISI, is also known for its chronic lack of funding. Biden administration's request for additional funding was met with further budget cuts from congressional appropriators. Under President Trump, plans for members of the agency to attend the February 2025 AI Action Summit in Paris were scrapped. The US and the UK refused to sign the summit's final communique. US Vice President JD Vance said "pro-growth AI policies" should be prioritised over safety. The name of the agency was changed in June 2025 to the Center for AI Standards and Innovation

Semantic analysis (knowledge representation)

Semantic analysis is a method for eliciting and representing knowledge about organisations. Initially the problem must be defined by domain experts and passed to the project analyst(s). The next step is the generation of candidate affordances. This step will generate a list of semantic units that may be included in the schema. The candidate grouping follows where some of the semantic units that will appear in the schema are placed in simple groups. Finally the groups will be integrated together into an ontology chart. Semantic analysis always starts from the problem definition which if not clear, require the analyst to employ relevant literature, interviews with the stakeholders and other techniques towards collecting supplementary information. All assumptions made must be genuine and not limiting the system.

GPT-5.3-Codex

GPT-5.3-Codex (Generative Pre-trained Transformer 5.3 Codex) is a large language model (LLM) announced and released by OpenAI on February 5, 2026. It is made as a competitor to Claude's Opus 4.6, focusing on code generation, speed and the ability to search repositories, run terminal commands and at the same time, debug code. In technical benchmarks, it is reported that GPT-5.3 Codex is 25% faster than Opus 4.6. GPT-5.3 Codex is available in the Codex app and on the web; access via API is also planned. According to OpenAI, GPT-5.3-Codex is the company's "first model that was instrumental in creating itself." On February 12, 2026, GPT-5.3-Codex-Spark was released in a research preview, which is a smaller version of GPT-5.3-Codex which supports text-only input. As of February 2026, GPT-5.3-Codex is only available for ChatGPT Pro ($200/month) subscribers.

Content Security Policy

Content Security Policy (CSP) is a computer security standard introduced to prevent cross-site scripting (XSS), clickjacking and other code injection attacks resulting from execution of malicious content in the trusted web page context. It is a Candidate Recommendation of the W3C working group on Web Application Security, widely supported by modern web browsers. CSP provides a standard method for website owners to declare approved origins of content that browsers should be allowed to load on that website—covered types are JavaScript, CSS, HTML frames, web workers, fonts, images, embeddable objects such as Java applets, ActiveX, audio and video files, and other HTML5 features. == Status == The standard, originally named Content Restrictions, was proposed by Robert Hansen in 2004, first implemented in Firefox 4 and quickly picked up by other browsers. Version 1 of the standard was published in 2012 as W3C candidate recommendation and quickly with further versions (Level 2) published in 2014. As of 2023, the draft of Level 3 is being developed with the new features being quickly adopted by the web browsers. The following header names are in use as part of experimental CSP implementations: Content-Security-Policy – standard header name proposed by the W3C document. Google Chrome supports this as of version 25. Firefox supports this as of version 23, released on 6 August 2013. WebKit supports this as of version 528 (nightly build). Chromium-based Microsoft Edge support is similar to Chrome's. X-WebKit-CSP – deprecated, experimental header introduced into Google Chrome, Safari and other WebKit-based web browsers in 2011. X-Content-Security-Policy – deprecated, experimental header introduced in Gecko 2 based browsers (Firefox 4 to Firefox 22, Thunderbird 3.3, SeaMonkey 2.1). A website can declare multiple CSP headers, also mixing enforcement and report-only ones. Each header will be processed separately by the browser. CSP can also be delivered within the HTML code using a meta tag, although in this case its effectiveness will be limited. Internet Explorer 10 and Internet Explorer 11 also support CSP, but only sandbox directive, using the experimental X-Content-Security-Policy header. A number of web application frameworks support CSP, for example AngularJS (natively) and Django (middleware). Instructions for Ruby on Rails have been posted by GitHub. Web framework support is however only required if the CSP contents somehow depend on the web application's state—such as usage of the nonce origin. Otherwise, the CSP is rather static and can be delivered from web application tiers above the application, for example on load balancer or web server. === Bypasses === In December 2015 and December 2016, a few methods of bypassing 'nonce' allowlisting origins were published. In January 2016, another method was published, which leverages server-wide CSP allowlisting to exploit old and vulnerable versions of JavaScript libraries hosted at the same server (frequent case with CDN servers). In May 2017 one more method was published to bypass CSP using web application frameworks code. == Mode of operation == If the Content-Security-Policy header is present in the server response, a compliant client enforces the declarative allowlist policy. One example goal of a policy is a stricter execution mode for JavaScript in order to prevent certain cross-site scripting attacks. In practice this means that a number of features are disabled by default: Inline JavaScript code