This is a comparison of non-linear video editing software applications. See also a more complete list of video editing software. == General information == This table gives basic general information about the different editors: === Active === === Discontinued / Inactive === ==== Definition ==== professional: used for full length Hollywood movies; professional (small): mainly used for paid commercials, short films or podcasts/YouTube channels; prosumer: Mainly targeting private use, anything that can do more than just trimming a film; basic: trimming a film; == System requirements == This table lists the operating systems that different editors can run on without emulation, as well as other system requirements. Note that minimum system requirements are listed; some features (like High Definition support) may be unavailable with these specifications. "Unix" includes the similar Linux, BSD and Unix-like operating systems. == High definition/High resolution import == The table below indicates the ability of each program to import various High Definition video or High resolution video formats for editing. == Feature set == == Output options == Please note that recording to Blu-ray does not imply 1080@50p/60p . Most only support up to 1080i 25/30 frames per second recording. Also not all formats can be output.
Robotic process automation
Robotic process automation (RPA) is a form of business process automation that is based on software robots (bots) or artificial intelligence (AI) agents. RPA should not be confused with artificial intelligence as it is based on automation technology following a predefined workflow. It is sometimes referred to as software robotics (not to be confused with robot software). In traditional workflow automation tools, a software developer produces a list of actions to automate a task and interface to the back end system using internal application programming interfaces (APIs) or dedicated scripting language. In contrast, RPA systems develop the action list by watching the user perform that task in the application's graphical user interface (GUI) and then perform the automation by repeating those tasks directly in the GUI. This can lower the barrier to the use of automation in products that might not otherwise feature APIs for this purpose. RPA tools have strong technical similarities to graphical user interface testing tools. These tools also automate interactions with the GUI, and often do so by repeating a set of demonstration actions performed by a user. RPA tools differ from such systems in that they allow data to be handled in and between multiple applications, for instance, receiving email containing an invoice, extracting the data, and then typing that into a bookkeeping system. == Historic evolution == As a form of automation, the concept has been around for a long time in the form of screen scraping, so long that to early PC users the reminder of it often blurs with the idea of malware infection. Yet compared to screen scraping, RPA is much more extensible, consisting of API integration into other enterprise applications, connectors into ITSM systems, terminal services and even some types of AI (e.g. machine learning) services such as image recognition. It is considered to be a significant technological evolution in the sense that new software platforms are emerging which are sufficiently mature, resilient, scalable and reliable to make this approach viable for use in large enterprises (who would otherwise be reluctant due to perceived risks to quality and reputation). == Use == The hosting of RPA services also aligns with the metaphor of a software robot, with each robotic instance having its own virtual workstation, much like a human worker. The robot uses keyboard and mouse controls to take actions and execute automations. Normally, all of these actions take place in a virtual environment and not on screen; the robot does not need a physical screen to operate, rather it interprets the screen display electronically. The scalability of modern solutions based on architectures such as these owes much to the advent of virtualization technology, without which the scalability of large deployments would be limited by the available capacity to manage physical hardware and by the associated costs. The implementation of RPA in business enterprises has shown dramatic cost savings when compared to traditional non-RPA solutions. === RPA actual use === Banking and finance process automation Mortgage and lending processes Customer care automation eCommerce merchandising operations Social media marketing Optical character recognition applications Data extraction process Fixed automation process Manual and repetitive tasks automation Voice recognition and digital dictation software linked to join up business processes for straight through processing without manual intervention Specialised remote infrastructure management software featuring automated investigation and resolution of problems, using robots for the first line IT support Chatbots used by internet retailers and service providers to service customer requests for information. Also used by companies to service employee requests for information from internal databases Presentation layer automation software, increasingly used by business process outsourcers to displace human labour Interactive voice response (IVR) systems incorporating intelligent interaction with callers == Impact on employment == According to Harvard Business Review, most operations groups adopting RPA have promised their employees that automation would not result in layoffs. Instead, workers have been redeployed to do more interesting work. One academic study highlighted that knowledge workers did not feel threatened by automation: they embraced it and viewed the robots as team-mates. The same study highlighted that, rather than resulting in a lower "headcount", the technology was deployed in such a way as to achieve more work and greater productivity with the same number of people. Conversely, however, some analysts proffer that RPA represents a threat to the business process outsourcing (BPO) industry. The thesis behind this notion is that RPA will enable enterprises to "repatriate" processes from offshore locations into local data centers, with the benefit of this new technology. The effect, if true, will be to create high-value jobs for skilled process designers in onshore locations (and within the associated supply chain of IT hardware, data center management, etc.) but to decrease the available opportunity to low-skilled workers offshore. On the other hand, this discussion appears to be healthy ground for debate as another academic study was at pains to counter the so-called "myth" that RPA will bring back many jobs from offshore. === Impact on society === Academic studies project that RPA, among other technological trends, is expected to drive a new wave of productivity and efficiency gains in the global labour market. Although not directly attributable to RPA alone, Oxford University conjectures that up to 35% of all jobs might be automated by 2035. There are geographic implications to the trend in robotic automation. In the example above where an offshored process is "repatriated" under the control of the client organization (or even displaced by a business process outsourcer) from an offshore location to a data centre, the impact will be a deficit in economic activity to the offshore location and an economic benefit to the originating economy. On this basis, developed economies – with skills and technological infrastructure to develop and support a robotic automation capability – can be expected to achieve a net benefit from the trend. In a TEDx talk hosted by University College London (UCL), entrepreneur David Moss explains that digital labour in the form of RPA is likely to revolutionize the cost model of the services industry by driving the price of products and services down, while simultaneously improving the quality of outcomes and creating increased opportunity for the personalization of services. In a separate TEDx in 2019 talk, Japanese business executive, and former CIO of Barclays bank, Koichi Hasegawa noted that digital robots can be a positive effect on society if we start using a robot with empathy to help every person. He provides a case study of the Japanese insurance companies – Sompo Japan and Aioi – both of whom introduced bots to speed up the process of insurance pay-outs in past massive disaster incidents. Meanwhile, Professor Willcocks, author of the LSE paper cited above, speaks of increased job satisfaction and intellectual stimulation, characterising the technology as having the ability to "take the robot out of the human", a reference to the notion that robots will take over the mundane and repetitive portions of people's daily workload, leaving them to be used in more interpersonal roles or to concentrate on the remaining, more meaningful, portions of their day. It was also found in a 2021 study observing the effects of robotization in Europe that, the gender pay gap increased at a rate of .18% for every 1% increase in robotization of a given industry. == Unassisted RPA == Unassisted RPA, or RPAAI, is the next generation of RPA related technologies. Technological advancements around artificial intelligence allow a process to be run on a computer without needing input from a user. == Hyperautomation == Hyperautomation is the application of advanced technologies like RPA, artificial intelligence, machine learning (ML) and process mining to augment workers and automate processes in ways that are significantly more impactful than traditional automation capabilities. Hyperautomation is the combination of technologies that allow faster application authorship (like low-code and no-code) with automation technologies that coordinate different worker types (i.e. human and artificial) for intelligent and strategic workflow optimization. Gartner's report notes that this trend was kicked off with robotic process automation (RPA). The report notes that, "RPA alone is not hyperautomation. Hyperautomation requires a combination of tools to help support replicating pieces of where the human is involved in a task." == Outsourcing == Back office clerical processes outsourced by large organisations
Electronic lab notebook
An electronic lab notebook or electronic laboratory notebook (ELN) is a computer program designed to replace paper laboratory notebooks. Lab notebooks in general are used by scientists, engineers, and technicians to document research, experiments, and procedures performed in a laboratory. A lab notebook is often maintained to be a legal document and may be used in a court of law as evidence. Similar to an inventor's notebook, the lab notebook is also often referred to in patent prosecution and intellectual property litigation. Electronic lab notebooks offer many benefits to the user as well as organizations; they are easier to search upon, simplify data copying and backups, and support collaboration amongst many users. ELNs can have fine-grained access controls, and can be more secure than their paper counterparts. They also allow the direct incorporation of data from instruments, replacing the practice of printing out data to be stapled into a paper notebook. == Types == ELNs can be divided into two categories: "Specific ELNs" contain features designed to work with specific applications, scientific instrumentation or data types. "Cross-disciplinary ELNs" or "Generic ELNs" are designed to support access to all data and information that needs to be recorded in a lab notebook. Lab Platforms that combine an ELN, LIMS, and scientific data management together, all-in-one configurable software environment. Solutions range from specialized programs designed from the ground up for use as an ELN, to modifications or direct use of more general programs. Examples of using more general software as an ELN include using OpenWetWare, a MediaWiki install (running the same software that Wikipedia uses), WordPress, or the use of general note taking software such as OneNote as an ELN. ELN's come in many different forms. They can be standalone programs, use a client-server model, or be entirely web-based. Some use a lab-notebook approach, others resemble a blog. ELNs are embracing artificial intelligence and LLM technology to provide scientific AI chat assistants. A good many variations on the "ELN" acronym have appeared. Differences between systems with different names are often subtle, with considerable functional overlap between them. Examples include "ERN" (Electronic Research Notebook), "ERMS" (Electronic Resource (or Research or Records) Management System (or Software) and SDMS (Scientific Data (or Document) Management System (or Software). Ultimately, these types of systems all strive to do the same thing: Capture, record, centralize and protect scientific data in a way that is highly searchable, historically accurate, and legally stringent, and which also promotes secure collaboration, greater efficiency, reduced mistakes and lowered total research costs. == Objectives == A good electronic laboratory notebook should offer a secure environment to protect the integrity of both data and process, whilst also affording the flexibility to adopt new processes or changes to existing processes without recourse to further software development. The package architecture should be a modular design, so as to offer the benefit of minimizing validation costs of any subsequent changes that you may wish to make in the future as your needs change. A good electronic laboratory notebook should be an "out of the box" solution that, as standard, has fully configurable forms to comply with the requirements of regulated analytical groups through to a sophisticated ELN for inclusion of structures, spectra, chromatograms, pictures, text, etc. where a preconfigured form is less appropriate. All data within the system may be stored in a database (e.g. MySQL, MS-SQL, Oracle) and be fully searchable. The system should enable data to be collected, stored and retrieved through any combination of forms or ELN that best meets the requirements of the user. The application should enable secure forms to be generated that accept laboratory data input via PCs and/or laptops / palmtops, and should be directly linked to electronic devices such as laboratory balances, pH meters, etc. Networked or wireless communications should be accommodated for by the package which will allow data to be interrogated, tabulated, checked, approved, stored and archived to comply with the latest regulatory guidance and legislation. A system should also include a scheduling option for routine procedures such as equipment qualification and study related timelines. It should include configurable qualification requirements to automatically verify that instruments have been cleaned and calibrated within a specified time period, that reagents have been quality-checked and have not expired, and that workers are trained and authorized to use the equipment and perform the procedures. == Regulatory and legal aspects == The laboratory accreditation criteria found in the ISO 17025 standard needs to be considered for the protection and computer backup of electronic records. These criteria can be found specifically in clause 4.13.1.4 of the standard. Electronic lab notebooks used for development or research in regulated industries, such as medical devices or pharmaceuticals, are expected to comply with FDA regulations related to software validation. The purpose of the regulations is to ensure the integrity of the entries in terms of time, authorship, and content. Unlike ELNs for patent protection, FDA is not concerned with patent interference proceedings, but is concerned with avoidance of falsification. Typical provisions related to software validation are included in the medical device regulations at 21 CFR 820 (et seq.) and Title 21 CFR Part 11. Essentially, the requirements are that the software has been designed and implemented to be suitable for its intended purposes. Evidence to show that this is the case is often provided by a Software Requirements Specification (SRS) setting forth the intended uses and the needs that the ELN will meet; one or more testing protocols that, when followed, demonstrate that the ELN meets the requirements of the specification and that the requirements are satisfied under worst-case conditions. Security, audit trails, prevention of unauthorized changes without substantial collusion of otherwise independent personnel (i.e., those having no interest in the content of the ELN such as independent quality unit personnel) and similar tests are fundamental. Finally, one or more reports demonstrating the results of the testing in accordance with the predefined protocols are required prior to release of the ELN software for use. If the reports show that the software failed to satisfy any of the SRS requirements, then corrective and preventive action ("CAPA") must be undertaken and documented. Such CAPA may extend to minor software revisions, or changes in architecture or major revisions. CAPA activities need to be documented as well. Aside from the requirements to follow such steps for regulated industry, such an approach is generally a good practice in terms of development and release of any software to assure its quality and fitness for use. There are standards related to software development and testing that can be applied (see ref.).
Personal web page
Personal web pages are World Wide Web pages created by an individual to contain content of a personal nature rather than content pertaining to a company, organization or institution. Personal web pages are primarily used for informative or entertainment purposes but can also be used for personal career marketing (by containing a list of the individual's skills, experience and a CV), social networking with other people with shared interests, or as a space for personal expression. These terms do not usually refer to just a single "page" or HTML file, but to a website—a collection of webpages and related files under a common URL or Web address. In strictly technical terms, a site's actual home page (index page) often only contains sparse content with some catchy introductory material and serves mostly as a pointer or table of contents to the more content-rich pages inside, such as résumés, family, hobbies, family genealogy, a web log/diary ("blog"), opinions, online journals and diaries or other writing, examples of written work, digital audio sound clips, digital video clips, digital photos, or information about a user's other interests. Many personal pages only include information of interest to friends and family of the author. However, some webpages set up by hobbyists or enthusiasts of certain subject areas can be valuable topical web directories. == History == In the 1990s, most Internet service providers (ISPs) provided a free small personal, user-created webpage along with free Usenet News service. These were all considered part of full Internet service. Also several free web hosting services such as GeoCities provided free web space for personal web pages. These free web hosting services would typically include web-based site management and a few pre-configured scripts to easily integrate an input form or guestbook script into the user's site. Early personal web pages were often called "home pages" and were intended to be set as a default page in a web browser's preferences, usually by their owner. These pages would often contain links, to-do lists, and other information their author found useful. In the days when search engines were in their infancy, these pages (and the links they contained) could be an important resource in navigating the web. Since the early 2000s, the rise of blogging and the development of user friendly web page designing software made it easier for amateur users who did not have computer programming or website designer training to create personal web pages. Some website design websites provided free ready-made blogging scripts, where all the user had to do was input their content into a template. At the same time, a personal web presence became easier with the increased popularity of social networking services, some with blogging platforms such as LiveJournal and Blogger. These websites provided an attractive and easy-to-use content management system for regular users. Most of the early personal websites were Web 1.0 style, in which a static display of text and images or photos was displayed to individuals who came to the page. About the only interaction that was possible on these early websites was signing the virtual "guestbook". With the collapse of the dot-com bubble in the late 1990s, the ISP industry consolidated, and the focus of web hosting services shifted away from the surviving ISP companies to independent Internet hosting services and to ones with other affiliations. For example, many university departments provided personal pages for professors and television broadcasters provided them for their on-air personalities. These free webpages served as a perquisite ("perk") for staff, while at the same time boosting the Web visibility of the parent organization. Web hosting companies either charge a monthly fee, or provide service that is "free" (advertising based) for personal web pages. These are priced or limited according to the total size of all files in bytes on the host's hard drive, or by bandwidth, (traffic), or by some combination of both. For those customers who continue to use their ISP for these services, national ISPs commonly continue to provide both disk space and help including ready-made drop-in scripts. With the rise of Web 2.0-style websites, both professional websites and user-created, amateur websites tended to contain interactive features, such as "clickable" links to online newspaper articles or favourite websites, the option to comment on content displayed on the website, the option to "tag" images, videos or links on the site, the option of "clicking" on an image to enlarge it or find out more information, the option of user participation for website guests to evaluate or review the pages, or even the option to create new user-generated content for others to see. A key difference between Web 1.0 personal webpages and Web 2.0 personal pages was while the former tended to be created by hackers, computer programmers and computer hobbyists, the latter were created by a much wider variety of users, including individuals whose main interests lay in hobbies or topics outside of computers (e.g., indie music fans, political activists, and social entrepreneurs). == Motivations == In a study done by Zinkhan, participants had four main reasons to create personal web pages. First, people use personal web pages as a portrayal of self, in a sense marketing themselves, since creators have the freedom to portray their own identities. Second, personal web pages are a way to interact with people who have similar interests as the creator, possible employers, or colleagues. Third, personal web pages can gain social acceptance with groups that the creator is interested in depending on the information that the creator reveals about themselves. Fourth, personal web pages can give creators a sense of connection to the world since these web pages are public and a way to introduce oneself to other people around the globe. People may maintain personal web pages to serve as a showcase for their skills in professional life, creative skills or self promotion of their business, charity or band. The use of personal web pages to display an individual's professional life has become more common in the 21st century. Mary Madden, an expert researcher on privacy and technology, did a study that found a tenth of American jobs require Personal web pages that advertise an individual online. Personal web pages have become a source of initial impression of possible employees used by employers. It can also be used to express opinions on issues ranging from news and politics to movies. Others may use their personal web page as a communication method. For example, an aspiring artist might give out business cards with their personal web page, and invite people to visit their page and see their artwork, "like" their page or sign their guestbook. A personal web page gives the owner generally more control on presence in search results and how they wish to be viewed online. It also allows more freedom in types and quantity of content than a social network profile offers, and can link various social media profiles with each other. It can be used to correct the record on something, or clear up potential confusion between you and someone with the same name. In the 2010s, some amateur writers, bands and filmmakers release digital versions of their stories, songs and short films online, with the aim of gaining an audience and becoming more well-known. While the huge number of aspiring artists posting their work online makes it unlikely for individuals and groups to become popular via the Internet, there are a small number of YouTube stars who were unknown until their online performances garnered them a huge audience. == Sites of academics == Academic professionals (especially at the college and university level), including professors and researchers, are often given online space for creating and storing personal web documents, including personal web pages, CVs and a list of their books, academic papers and conference presentations, on the websites of their employers. This goes back to the early decade of the World Wide Web and its original purpose of providing a quick and easy way for academics to share research papers and data. Researchers may have a personal website to share more information about themselves, about their academic activities and for sharing (unpublished) results of their research. This has been noted as part of the success of open-access repositories such as arXiv.
Trace zero cryptography
First proposed by Gerhard Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose. Trace zero varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive. Trace zero varieties feature a better scalar multiplication performance than elliptic curves. This allows fast arithmetic in these groups, which can speed up the calculations with a factor 3 compared with elliptic curves and hence speed up the cryptosystem. Another advantage is that for groups of cryptographically relevant size, the order of the group can simply be calculated using the characteristic polynomial of the Frobenius endomorphism. This is not the case, for example, in elliptic curve cryptography when the group of points of an elliptic curve over a prime field is used for cryptographic purpose. However, to represent an element of the trace zero variety more bits are needed compared with elements of elliptic or hyperelliptic curves. Another disadvantage is the fact that it is possible to reduce the security of the TZV of 1/6th of the bit length using cover attack. == Mathematical background == A hyperelliptic curve C of genus g over a prime field F q {\displaystyle \mathbb {F} _{q}} where q = pn (p prime) of odd characteristic is defined as C : y 2 + h ( x ) y = f ( x ) , {\displaystyle C:~y^{2}+h(x)y=f(x),} where f monic, deg(f) = 2g + 1 and deg(h) ≤ g. The curve has at least one F q {\displaystyle \mathbb {F} _{q}} -rational Weierstraßpoint. The Jacobian variety J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C is for all finite extension F q n {\displaystyle \mathbb {F} _{q^{n}}} isomorphic to the ideal class group Cl ( C / F q n ) {\displaystyle \operatorname {Cl} (C/\mathbb {F} _{q^{n}})} . With the Mumford's representation it is possible to represent the elements of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} with a pair of polynomials [u, v], where u, v ∈ F q n [ x ] {\displaystyle \mathbb {F} _{q^{n}}[x]} . The Frobenius endomorphism σ is used on an element [u, v] of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} to raise the power of each coefficient of that element to q: σ([u, v]) = [uq(x), vq(x)]. The characteristic polynomial of this endomorphism has the following form: χ ( T ) = T 2 g + a 1 T 2 g − 1 + ⋯ + a g T g + ⋯ + a 1 q g − 1 T + q g , {\displaystyle \chi (T)=T^{2g}+a_{1}T^{2g-1}+\cdots +a_{g}T^{g}+\cdots +a_{1}q^{g-1}T+q^{g},} where ai in Z {\displaystyle \mathbb {Z} } With the Hasse–Weil theorem it is possible to receive the group order of any extension field F q n {\displaystyle \mathbb {F} _{q^{n}}} by using the complex roots τi of χ(T): | J C ( F q n ) | = ∏ i = 1 2 g ( 1 − τ i n ) {\displaystyle |J_{C}(\mathbb {F} _{q^{n}})|=\prod _{i=1}^{2g}(1-\tau _{i}^{n})} Let D be an element of the J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C, then it is possible to define an endomorphism of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , the so-called trace of D: Tr ( D ) = ∑ i = 0 n − 1 σ i ( D ) = D + σ ( D ) + ⋯ + σ n − 1 ( D ) {\displaystyle \operatorname {Tr} (D)=\sum _{i=0}^{n-1}\sigma ^{i}(D)=D+\sigma (D)+\cdots +\sigma ^{n-1}(D)} Based on this endomorphism one can reduce the Jacobian variety to a subgroup G with the property, that every element is of trace zero: G = { D ∈ J C ( F q n ) | Tr ( D ) = 0 } , ( 0 neutral element in J C ( F q n ) {\displaystyle G=\{D\in J_{C}(\mathbb {F} _{q^{n}})~|~{\text{Tr}}(D)={\textbf {0}}\},~~~({\textbf {0}}{\text{ neutral element in }}J_{C}(\mathbb {F} _{q^{n}})} G is the kernel of the trace endomorphism and thus G is a group, the so-called trace zero (sub)variety (TZV) of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} . The intersection of G and J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} is produced by the n-torsion elements of J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} . If the greatest common divisor gcd ( n , | J C ( F q ) | ) = 1 {\displaystyle \gcd(n,|J_{C}(\mathbb {F} _{q})|)=1} the intersection is empty and one can compute the group order of G: | G | = | J C ( F q n ) | | J C ( F q ) | = ∏ i = 1 2 g ( 1 − τ i n ) ∏ i = 1 2 g ( 1 − τ i ) {\displaystyle |G|={\dfrac {|J_{C}(\mathbb {F} _{q^{n}})|}{|J_{C}(\mathbb {F} _{q})|}}={\dfrac {\prod _{i=1}^{2g}(1-\tau _{i}^{n})}{\prod _{i=1}^{2g}(1-\tau _{i})}}} The actual group used in cryptographic applications is a subgroup G0 of G of a large prime order l. This group may be G itself. There exist three different cases of cryptographical relevance for TZV: g = 1, n = 3 g = 1, n = 5 g = 2, n = 3 == Arithmetic == The arithmetic used in the TZV group G0 based on the arithmetic for the whole group J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , But it is possible to use the Frobenius endomorphism σ to speed up the scalar multiplication. This can be archived if G0 is generated by D of order l then σ(D) = sD, for some integers s. For the given cases of TZV s can be computed as follows, where ai come from the characteristic polynomial of the Frobenius endomorphism : For g = 1, n = 3: s = q − 1 1 − a 1 mod ℓ {\displaystyle s={\dfrac {q-1}{1-a_{1}}}{\bmod {\ell }}} For g = 1, n = 5: s = q 2 − q − a 1 2 q + a 1 q + 1 q − 2 a 1 q + a 1 3 − a 1 2 + a 1 − 1 mod ℓ {\displaystyle s={\dfrac {q^{2}-q-a_{1}^{2}q+a_{1}q+1}{q-2a_{1}q+a_{1}^{3}-a_{1}^{2}+a_{1}-1}}{\bmod {\ell }}} For g = 2, n = 3: s = − q 2 − a 2 + a 1 a 1 q − a 2 + 1 mod ℓ {\displaystyle s=-{\dfrac {q^{2}-a_{2}+a_{1}}{a_{1}q-a_{2}+1}}{\bmod {\ell }}} Knowing this, it is possible to replace any scalar multiplication mD (|m| ≤ l/2) with: m 0 D + m 1 σ ( D ) + ⋯ + m n − 1 σ n − 1 ( D ) , where m i = O ( ℓ 1 / ( n − 1 ) ) = O ( q g ) {\displaystyle m_{0}D+m_{1}\sigma (D)+\cdots +m_{n-1}\sigma ^{n-1}(D),~~~~{\text{where }}m_{i}=O(\ell ^{1/(n-1)})=O(q^{g})} With this trick the multiple scalar product can be reduced to about 1/(n − 1)th of doublings necessary for calculating mD, if the implied constants are small enough. == Security == The security of cryptographic systems based on trace zero subvarieties according to the results of the papers comparable to the security of hyper-elliptic curves of low genus g' over F p ′ {\displaystyle \mathbb {F} _{p'}} , where p' ~ (n − 1)(g/g' ) for |G| ~128 bits. For the cases where n = 3, g = 2 and n = 5, g = 1 it is possible to reduce the security for at most 6 bits, where |G| ~ 2256, because one can not be sure that G is contained in a Jacobian of a curve of genus 6. The security of curves of genus 4 for similar fields are far less secure. == Cover attack on a trace zero crypto-system == The attack published in shows, that the DLP in trace zero groups of genus 2 over finite fields of characteristic diverse than 2 or 3 and a field extension of degree 3 can be transformed into a DLP in a class group of degree 0 with genus of at most 6 over the base field. In this new class group the DLP can be attacked with the index calculus methods. This leads to a reduction of the bit length 1/6th.
Phase congruency
Phase congruency is a measure of feature significance in computer images, a method of edge detection that is particularly robust against changes in illumination and contrast. == Foundations == Phase congruency reflects the behaviour of the image in the frequency domain. It has been noted that edgelike features have many of their frequency components in the same phase. The concept is similar to coherence, except that it applies to functions of different wavelength. For example, the Fourier decomposition of a square wave consists of sine functions, whose frequencies are odd multiples of the fundamental frequency. At the rising edges of the square wave, each sinusoidal component has a rising phase; the phases have maximal congruency at the edges. This corresponds to the human-perceived edges in an image where there are sharp changes between light and dark. == Definition == Phase congruency compares the weighted alignment of the Fourier components of a signal A n {\displaystyle A_{\rm {n}}} with the sum of the Fourier components. P C ( t ) = max ϕ ¯ ∑ n A n cos ( ϕ n ( t ) − ϕ ¯ ) ∑ n A n {\displaystyle PC(t)=\max _{\bar {\phi }}{\frac {\sum _{\rm {n}}A_{\rm {n}}\cos(\phi _{\rm {n}}(t)-{\bar {\phi }})}{\sum _{\rm {n}}A_{n}}}} where ϕ n {\displaystyle \phi _{\rm {n}}} is the local or instantaneous phase as can be calculated using the Hilbert transform and A n {\displaystyle A_{\rm {n}}} are the local amplitude, or energy, of the signal. When all the phases are aligned, this is equal to 1. Several ways of implementing phase congruency have been developed, of which two versions are available in open source, one written for MATLAB and the other written in Java as a plugin for the ImageJ software. Given the different notations used for its formulation, a unified version has been recently presented, where a methodology for the parameter tuning is also presented. == Advantages == The square-wave example is naive in that most edge detection methods deal with it equally well. For example, the first derivative has a maximal magnitude at the edges. However, there are cases where the perceived edge does not have a sharp step or a large derivative. The method of phase congruency applies to many cases where other methods fail. A notable example is an image feature consisting of a single line, such as the letter "l". Many edge-detection algorithms will pick up two adjacent edges: the transitions from white to black, and black to white. On the other hand, the phase congruency map has a single line. A simple Fourier analogy of this case is a triangle wave. In each of its crests there is a congruency of crests from different sinusoidal functions. == Disadvantages == Calculating the phase congruency map of an image is very computationally intensive, and sensitive to image noise. Techniques of noise reduction are usually applied prior to the calculation.
Cypherpunks (book)
Cypherpunks: Freedom and the Future of the Internet is a 2012 book by Julian Assange, in discussion with Internet activists and cypherpunks Jacob Appelbaum, Andy Müller-Maguhn and Jérémie Zimmermann. Its primary topic is society's relationship with information security. In the book, the authors warn that the Internet has become a tool of the police state, and that the world is inadvertently heading toward a form of totalitarianism. They promote the use of cryptography to protect against state surveillance. In the introduction, Assange says that the book is "not a manifesto [...] [but] a warning". He told Guardian journalist Decca Aitkenhead: A well-defined mathematical algorithm can encrypt something quickly, but to decrypt it would take billions of years – or trillions of dollars' worth of electricity to drive the computer. So cryptography is the essential building block of independence for organisations on the Internet, just like armies are the essential building blocks of states, because otherwise one state just takes over another. There is no other way for our intellectual life to gain proper independence from the security guards of the world, the people who control physical reality. Assange later wrote in The Guardian: "Strong cryptography is a vital tool in fighting state oppression." saying that was the message of his book, Cypherpunks. Cypherpunks is published by OR Books. It is primarily a transcript of World Tomorrow episode eight, a two-part interview between Assange, Jacob Appelbaum, Andy Müller-Maguhn, and Jérémie Zimmermann. In the foreword, Assange said, "the Internet, our greatest tool for emancipation, has been transformed into the most dangerous facilitator of totalitarianism we have ever seen".