Distributed Evolutionary Algorithms in Python (DEAP) is an evolutionary computation framework for rapid prototyping and testing of ideas. It incorporates the data structures and tools required to implement most common evolutionary computation techniques such as genetic algorithm, genetic programming, evolution strategies, particle swarm optimization, differential evolution, traffic flow and estimation of distribution algorithm. It is developed at Université Laval since 2009. == Example == The following code gives a quick overview how the Onemax problem optimization with genetic algorithm can be implemented with DEAP.
Geometric hashing
In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation, though extensions exist to other object representations and transformations. In an off-line step, the objects are encoded by treating each pair of points as a geometric basis. The remaining points can be represented in an invariant fashion with respect to this basis using two parameters. For each point, its quantized transformed coordinates are stored in the hash table as a key, and indices of the basis points as a value. Then a new pair of basis points is selected, and the process is repeated. In the on-line (recognition) step, randomly selected pairs of data points are considered as candidate bases. For each candidate basis, the remaining data points are encoded according to the basis and possible correspondences from the object are found in the previously constructed table. The candidate basis is accepted if a sufficiently large number of the data points index a consistent object basis. Geometric hashing was originally suggested in computer vision for object recognition in 2D and 3D, but later was applied to different problems such as structural alignment of proteins. == Geometric hashing in computer vision == Geometric hashing is a method used for object recognition. Let’s say that we want to check if a model image can be seen in an input image. This can be accomplished with geometric hashing. The method could be used to recognize one of the multiple objects in a base, in this case the hash table should store not only the pose information but also the index of object model in the base. === Example === For simplicity, this example will not use too many point features and assume that their descriptors are given by their coordinates only (in practice local descriptors such as SIFT could be used for indexing). ==== Training Phase ==== Find the model's feature points. Assume that 5 feature points are found in the model image with the coordinates ( 12 , 17 ) ; {\displaystyle (12,17);} ( 45 , 13 ) ; {\displaystyle (45,13);} ( 40 , 46 ) ; {\displaystyle (40,46);} ( 20 , 35 ) ; {\displaystyle (20,35);} ( 35 , 25 ) {\displaystyle (35,25)} , see the picture. Introduce a basis to describe the locations of the feature points. For 2D space and similarity transformation the basis is defined by a pair of points. The point of origin is placed in the middle of the segment connecting the two points (P2, P4 in our example), the x ′ {\displaystyle x'} axis is directed towards one of them, the y ′ {\displaystyle y'} is orthogonal and goes through the origin. The scale is selected such that absolute value of x ′ {\displaystyle x'} for both basis points is 1. Describe feature locations with respect to that basis, i.e. compute the projections to the new coordinate axes. The coordinates should be discretised to make recognition robust to noise, we take the bin size 0.25. We thus get the coordinates ( − 0.75 , − 1.25 ) ; {\displaystyle (-0.75,-1.25);} ( 1.00 , 0.00 ) ; {\displaystyle (1.00,0.00);} ( − 0.50 , 1.25 ) ; {\displaystyle (-0.50,1.25);} ( − 1.00 , 0.00 ) ; {\displaystyle (-1.00,0.00);} ( 0.00 , 0.25 ) {\displaystyle (0.00,0.25)} Store the basis in a hash table indexed by the features (only transformed coordinates in this case). If there were more objects to match with, we should also store the object number along with the basis pair. Repeat the process for a different basis pair (Step 2). It is needed to handle occlusions. Ideally, all the non-colinear pairs should be enumerated. We provide the hash table after two iterations, the pair (P1, P3) is selected for the second one. Hash Table: Most hash tables cannot have identical keys mapped to different values. So in real life one won’t encode basis keys (1.0, 0.0) and (-1.0, 0.0) in a hash table. ==== Recognition Phase ==== Find interesting feature points in the input image. Choose an arbitrary basis. If there isn't a suitable arbitrary basis, then it is likely that the input image does not contain the target object. Describe coordinates of the feature points in the new basis. Quantize obtained coordinates as it was done before. Compare all the transformed point features in the input image with the hash table. If the point features are identical or similar, then increase the count for the corresponding basis (and the type of object, if any). For each basis such that the count exceeds a certain threshold, verify the hypothesis that it corresponds to an image basis chosen in Step 2. Transfer the image coordinate system to the model one (for the supposed object) and try to match them. If successful, the object is found. Otherwise, go back to Step 2. === Finding mirrored pattern === It seems that this method is only capable of handling scaling, translation, and rotation. However, the input image may contain the object in mirror transform. Therefore, geometric hashing should be able to find the object, too. There are two ways to detect mirrored objects. For the vector graph, make the left side positive, and the right side negative. Multiplying the x position by -1 will give the same result. Use 3 points for the basis. This allows detecting mirror images (or objects). Actually, using 3 points for the basis is another approach for geometric hashing. === Geometric hashing in higher-dimensions === Similar to the example above, hashing applies to higher-dimensional data. For three-dimensional data points, three points are also needed for the basis. The first two points define the x-axis, and the third point defines the y-axis (with the first point). The z-axis is perpendicular to the created axis using the right-hand rule. Notice that the order of the points affects the resulting basis
Social media marketing
Social media marketing is the use of social media platforms and websites to promote a product or service. Although the terms e-marketing and digital marketing are still dominant in academia, social media marketing is becoming more popular for practitioners and researchers. Social media platforms such as Facebook, LinkedIn, Instagram, and Twitter, among others, have built-in data analytics tools that companies can use to track the progress, success, and engagement of social media marketing campaigns. Companies address a range of stakeholders through social media marketing, including current and potential customers, current and potential employees, journalists, bloggers, and the general public. On a strategic level, social media marketing includes the management of a marketing campaign, governance, setting the scope (e.g. more active or passive use) and the establishment of a firm's desired social media "culture" and "tone". Firms that use social media marketing can allow customers and Internet users to post user-generated content (e.g., online comments, product reviews, etc.), also known as "earned media", rather than use marketer-prepared advertising copy. == Purposes and tactics == Social media may be employed in marketing as a communications tool that makes companies accessible to those who are interested in their product and visible to those who are not familiar with their products. It is used by companies to create buzz, learn from customers, and target them. Of the top 10 factors that correlate with a strong Google organic search, seven are social media-dependent. This means that if brands with little to no social media presence tend to show up less on Google searches. While platforms such as Twitter, Facebook and—in the past—Google+ have a larger number of monthly users, the visual media-sharing-based mobile platforms garner a higher interaction rate in comparison, and have registered the fastest growth, and have changed the ways in which consumers engage with brand content. Instagram has an interaction rate of 1.46% with an average of 130 million users monthly as opposed to Twitter, which has a .03% interaction rate with an average of 210 million monthly users. Unlike traditional media that are often cost-prohibitive to many companies, a social media strategy does not require significant financial investment. To this end, companies make use of platforms such as Facebook, Twitter, YouTube, TikTok and Instagram to reach audiences much wider than through traditional print, television, or radio advertisements alone at a fraction of the cost, as most social networking sites can be used at little or no cost (however, some websites charge companies for premium services). This has changed the ways that companies approach and interact with customers, as a substantial percentage of consumer interactions are now being carried out over online platforms with much higher visibility. Customers can post reviews of products and services, rate customer service, and ask questions or voice concerns directly to companies through social media platforms. According to Measuring Success, over 80% of consumers use the web to research products and services. Thus social media marketing is also used by businesses in order to build relationships of trust with consumers. To this aim, companies may hire personnel to specifically handle these social media interactions, who usually report under the title of online community managers. Handling these interactions in a satisfactory manner can result in an increase of consumer trust. To both this aim and to fix the public's perception of a company, three steps are taken in order to address consumer concerns: Identifying the extent of the social chatter Engaging the influencers to help Developing a proportional response == Strategies == === Passive approach === Social media can be a useful source of market information and a way to hear customers' perspectives. Blogs, content communities, and forums are platforms where individuals share their reviews and recommendations of brands, products, and services. Businesses are able to tap into and analyze customer voices and feedback generated in social media for marketing purposes. In this sense, social media is a relatively inexpensive source of market intelligence which can be used by marketers and managers to track and respond to consumer-identified problems and detect market opportunities. === Active approach === Social media can be used as a public relations tool, a direct marketing tool, and a communication channel to target very specific audiences, with social media influencers and social media personalities as effective customer engagement tools. This tactic is widely known as influencer marketing, which gives brands the opportunity to reach their target audience via a group of selected influencers advertising their product or service. Brands were projected to spend up to $15 billion on influencer marketing by 2022, per Business Insider Intelligence estimates, based on Mediakix data. The use of customer influencers, such as popular bloggers, can be an efficient and cost-effective method to launch new products or services. == Engagement == Engagement with the social web means that customers and stakeholders are active participants rather than passive spectators. An example of these are consumer advocacy groups and groups that criticize companies (e.g., lobby groups or advocacy organizations). The use of Social media in a business or political context allows people to express and share opinions about a company's products, services or business practices, or a government's actions. On social media, each participant becomes part of the marketing department (or a challenge to the marketing effort) as other customers read their comments or reviews. The effectiveness of social media marketing campaigns is dependent on the promotion of online engagement. With the advent of social media marketing, it has become increasingly important to gain customer interest in products and services, which can eventually be translated into buying behavior, or voting and donating behavior in a political context. New online marketing concepts of engagement and loyalty have emerged which aim to build customer participation and brand reputation. Engagement in social media for the purpose of a social media strategy is divided into two parts. The first is proactive, regular posting of new online content, which can be seen through digital photos, digital videos, text, and conversations. It is also represented through sharing of content and information from others via weblinks. The second part is reactive conversations, with social media users responding to those who reach out to others' social media profiles through comments or messages. == Campaigns == === Local businesses === Small businesses use social networking sites as a promotional technique. Businesses can follow individuals' social media usage in their local area and advertise specials and deals, which can be exclusive and in the form of "get a free drink with a copy of this tweet". This type of message encourages other locals to follow the business on their official websites in order to obtain the promotional deal. The business's brand visibility is enhanced in the process. Social networking sites are also used by small businesses to develop their own market research on new products and services. By encouraging their customers to give feedback on new product ideas, businesses can gain insights on whether or not a product may be accepted by their target market enough to merit full production. In addition, customers will feel the company has engaged them in the process of co-creation—the process in which the business uses customer feedback to create or modify a product or service to fill a need of the target market. Such feedback can be presented in various forms, such as surveys, contests, and polls. Social networking sites such as LinkedIn, also provide opportunities for small businesses to find candidates to fill staff positions. Review sites such as Yelp help small businesses build their reputation beyond brand visibility. Positive customer peer reviews help influence new prospects to purchase goods and services more than company advertising. == Benefits == Social Media Marketing allows companies to promote themselves to large, diverse audiences that could not be reached through traditional marketing such as phone and email-based advertising. Marketing on most social media platforms also comes at little to no cost, making it accessible to virtually any size business. Social Media Marketing accommodates personalized and direct marketing that targets specific demographics and markets. Companies can engage with customers directly, allowing them to obtain feedback and resolve issues almost immediately. Another advantage of social media marketing is that it's an ideal environment for a company to conduct market research. It can be used
SocialIQ
Social IQ (formerly Soovox Inc.) was a San Diego-based influencer marketing platform that measured users' online social influence and connected them with brands for word-of-mouth marketing campaigns. The company was founded in 2009 by Akram Benmbarek and was headquartered in San Diego, California. == History == Akram Benmbarek, who had previously worked in technology finance at Advanced Equities Financial Corp and in wealth management at Morgan Stanley, Merrill Lynch, and UBS, founded the company in mid-2009 under the name Soovox. In October 2011, Benmbarek rebranded the company as SocialIQ. At that time, the company was seeking a Series A round of venture capital, having raised under $1 million in angel seed funding. == Similar metrics == Klout PeerIndex
Tokenization (data security)
Tokenization, when applied to data security, is the process of substituting a sensitive data element with a non-sensitive equivalent, referred to as a token, that has no intrinsic or exploitable meaning or value. The token is a reference (i.e. identifier) that maps back to the sensitive data through a tokenization system. The mapping from original data to a token uses methods that render tokens infeasible to reverse in the absence of the tokenization system, for example using tokens created from random numbers. A one-way cryptographic function is used to convert the original data into tokens, making it difficult to recreate the original data without obtaining entry to the tokenization system's resources. To deliver such services, the system maintains a vault database of tokens that are connected to the corresponding sensitive data. Protecting the system vault is vital to the system, and improved processes must be put in place to offer database integrity and physical security. The tokenization system must be secured and validated using security best practices applicable to sensitive data protection, secure storage, audit, authentication and authorization. The tokenization system provides data processing applications with the authority and interfaces to request tokens, or detokenize back to sensitive data. The security and risk reduction benefits of tokenization require that the tokenization system is logically isolated and segmented from data processing systems and applications that previously processed or stored sensitive data replaced by tokens. Only the tokenization system can tokenize data to create tokens, or detokenize back to redeem sensitive data under strict security controls. The token generation method must be proven to have the property that there is no feasible means through direct attack, cryptanalysis, side channel analysis, token mapping table exposure or brute force techniques to reverse tokens back to live data. Replacing live data with tokens in systems is intended to minimize exposure of sensitive data to those applications, stores, people and processes, reducing risk of compromise or accidental exposure and unauthorized access to sensitive data. Applications can operate using tokens instead of live data, with the exception of a small number of trusted applications explicitly permitted to detokenize when strictly necessary for an approved business purpose. Tokenization systems may be operated in-house within a secure isolated segment of the data center, or as a service from a secure service provider. Tokenization may be used to safeguard sensitive data involving, for example, bank accounts, financial statements, medical records, criminal records, driver's licenses, loan applications, stock trades, voter registrations, and other types of personally identifiable information (PII). Tokenization is often used in credit card processing. The PCI Council defines tokenization as "a process by which the primary account number (PAN) is replaced with a surrogate value called a token. A PAN may be linked to a reference number through the tokenization process. In this case, the merchant simply has to retain the token and a reliable third party controls the relationship and holds the PAN. The token may be created independently of the PAN, or the PAN can be used as part of the data input to the tokenization technique. The communication between the merchant and the third-party supplier must be secure to prevent an attacker from intercepting to gain the PAN and the token. De-tokenization is the reverse process of redeeming a token for its associated PAN value. The security of an individual token relies predominantly on the infeasibility of determining the original PAN knowing only the surrogate value". The choice of tokenization as an alternative to other techniques such as encryption will depend on varying regulatory requirements, interpretation, and acceptance by respective auditing or assessment entities. This is in addition to any technical, architectural or operational constraint that tokenization imposes in practical use. == Concepts and origins == The concept of tokenization, as adopted by the industry today, has existed since the first currency systems emerged centuries ago as a means to reduce risk in handling high value financial instruments by replacing them with surrogate equivalents. In the physical world, coin tokens have a long history of use replacing the financial instrument of minted coins and banknotes. In more recent history, subway tokens and casino chips found adoption for their respective systems to replace physical currency and cash handling risks such as theft. Exonumia and scrip are terms synonymous with such tokens. In the digital world, similar substitution techniques have been used since the 1970s as a means to isolate real data elements from exposure to other data systems. In databases for example, surrogate key values have been used since 1976 to isolate data associated with the internal mechanisms of databases and their external equivalents for a variety of uses in data processing. More recently, these concepts have been extended to consider this isolation tactic to provide a security mechanism for the purposes of data protection. In the payment card industry, tokenization is one means of protecting sensitive cardholder data in order to comply with industry standards and government regulations. Tokenization was applied to payment card data by Shift4 Corporation and released to the public during an industry Security Summit in Las Vegas, Nevada in 2005. The technology is meant to prevent the theft of the credit card information in storage. Shift4 defines tokenization as: "The concept of using a non-decryptable piece of data to represent, by reference, sensitive or secret data. In payment card industry (PCI) context, tokens are used to reference cardholder data that is managed in a tokenization system, application or off-site secure facility." To protect data over its full lifecycle, tokenization is often combined with end-to-end encryption to secure data in transit to the tokenization system or service, with a token replacing the original data on return. For example, to avoid the risks of malware stealing data from low-trust systems such as point of sale (POS) systems, as in the Target breach of 2013, cardholder data encryption must take place prior to card data entering the POS and not after. Encryption takes place within the confines of a security hardened and validated card reading device and data remains encrypted until received by the processing host, an approach pioneered by Heartland Payment Systems as a means to secure payment data from advanced threats, now widely adopted by industry payment processing companies and technology companies. The PCI Council has also specified end-to-end encryption (certified point-to-point encryption—P2PE) for various service implementations in various PCI Council Point-to-point Encryption documents. == The tokenization process == The process of tokenization consists of the following steps: The application sends the tokenization data and authentication information to the tokenization system. It is stopped if authentication fails and the data is delivered to an event management system. As a result, administrators can discover problems and effectively manage the system. The system moves on to the next phase if authentication is successful. Using one-way cryptographic or random generation techniques, a token is generated and kept in a highly secure data vault. The new token is provided to the application for further use, replacing the sensitive data for processing and storage. Tokenization systems share several components according to established standards. Token generation is the process of producing a token using any means, such as one-way nonreversible cryptographic functions (e.g., a hash function with a strong, secret salt) or assignment via a randomly generated number. Random number generator (RNG) techniques are often the best choice for generating token values. Token mapping – this is the process of assigning the created token value to its original value. To enable permitted look-ups of the original value using the token as the index, a secure cross-reference database must be constructed. Token data store – this is a central repository for the token mapping process that holds the original sensitive values and their related token values. Sensitive data and token values must be securely kept in an encrypted format. Management of cryptographic keys. Strong key management procedures are required for sensitive data encryption on token data stores. == Difference from encryption == Tokenization and "classic" encryption effectively protect data if implemented properly, and a computer security system may use both. While similar in certain regards, tokenization and classic encryption differ in a few key aspects. Both are cryptographic data security methods and the
PNGOUT
PNGOUT is a freeware command line optimizer for PNG images written by Ken Silverman. The transformation is lossless, meaning that the resulting image is visually identical to the source image. According to its author, this program can often get higher compression than other optimizers by 5–10%. It is possible to compress some inflated PNGs to a size below 1% of the original file. PNGOUT was also available as a plug-in for the freeware image viewer IrfanView and can be enabled as an option when saving files. It allows editing of various PNGOUT settings via a dialog box. PNGOUT integration was removed in IrfanView version 4.58 in favour of OptiPNG. In 2006, a commercial version of PNGOUT with a graphical user interface, known as PNGOUTWin, was released by Ardfry Imaging, a small company Silverman co-founded in 2005. There is also a freeware GUI frontend to PNGOUT available, known as PNGGauntlet. == Main operation == The main function of PNGOUT is to reduce the size of image data contained in the IDAT chunk. This chunk is compressed using the deflate algorithm. Deflate algorithms can vary in speed and compression ratio, with higher compression ratios generally implying lower speed. Ken Silverman wrote a deflate compressor for PNGOUT that is slower than the ones used in most graphics software, but produces smaller files. PNGOUT also performs automatic bit depth, color, and palette reduction where appropriate.
Hardware random number generator
In computing, a hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator is a device that generates random numbers from a physical process capable of producing entropy, unlike a pseudorandom number generator (PRNG) that utilizes a deterministic algorithm and non-physical nondeterministic random bit generators that do not include hardware dedicated to generation of entropy. Many natural phenomena generate low-level, statistically random "noise" signals, including thermal and shot noise, jitter and metastability of electronic circuits, Brownian motion, and atmospheric noise. Researchers also used the photoelectric effect, involving a beam splitter, other quantum phenomena, and even nuclear decay (due to practical considerations the latter, as well as the atmospheric noise, is not viable except for fairly restricted applications or online distribution services). While "classical" (non-quantum) phenomena are not truly random, an unpredictable physical system is usually acceptable as a source of randomness, so the qualifiers "true" and "physical" are used interchangeably. A hardware random number generator is expected to output near-perfect random numbers ("full entropy"). A physical process usually does not have this property, and a practical TRNG typically includes a few blocks: a noise source that implements the physical process producing the entropy. Usually this process is analog, so a digitizer is used to convert the output of the analog source into a binary representation; a conditioner (randomness extractor) that improves the quality of the random bits; health tests. TRNGs are mostly used in cryptographical algorithms that get completely broken if the random numbers have low entropy, so the testing functionality is usually included. Hardware random number generators generally produce only a limited number of random bits per second. In order to increase the available output data rate, they are often used to generate the "seed" for a faster PRNG. PRNG also helps with the noise source "anonymization" (whitening out the noise source identifying characteristics) and entropy extraction. With a proper PRNG algorithm selected (cryptographically secure pseudorandom number generator, CSPRNG), the combination can satisfy the requirements of Federal Information Processing Standards and Common Criteria standards. == Uses == Hardware random number generators can be used in any application that needs randomness. However, in many scientific applications additional cost and complexity of a TRNG (when compared with pseudo random number generators) provide no meaningful benefits. TRNGs have additional drawbacks for data science and statistical applications: impossibility to re-run a series of numbers unless they are stored, reliance on an analog physical entity can obscure the failure of the source. The TRNGs therefore are primarily used in the applications where their unpredictability and the impossibility to re-run the sequence of numbers are crucial to the success of the implementation: in cryptography and gambling machines. === Cryptography === The major use for hardware random number generators is in the field of data encryption, for example to create random cryptographic keys and nonces needed to encrypt and sign data. In addition to randomness, there are at least two additional requirements imposed by the cryptographic applications: forward secrecy guarantees that the knowledge of the past output and internal state of the device should not enable the attacker to predict future data; backward secrecy protects the "opposite direction": knowledge of the output and internal state in the future should not divulge the preceding data. A typical way to fulfill these requirements is to use a TRNG to seed a cryptographically secure pseudorandom number generator. == History == Physical devices were used to generate random numbers for thousands of years, primarily for gambling. Dice in particular have been known for more than 5000 years (found on locations in modern Iraq and Iran), and flipping a coin (thus producing a random bit) dates at least to the times of ancient Rome. The first documented use of a physical random number generator for scientific purposes was by Francis Galton (1890). He devised a way to sample a probability distribution using a common gambling die. In addition to the top digit, Galton also looked at the face of a die closest to him, thus creating 64 = 24 outcomes (about 4.6 bits of randomness). Kendall and Babington-Smith (1938) used a fast-rotating 10-sector disk that was illuminated by periodic bursts of light. The sampling was done by a human who wrote the number under the light beam onto a pad. The device was utilized to produce a 100,000-digit random number table (at the time such tables were used for statistical experiments, like PRNG nowadays). On 29 April 1947, the RAND Corporation began generating random digits with an "electronic roulette wheel", consisting of a random frequency pulse source of about 100,000 pulses per second gated once per second with a constant frequency pulse and fed into a five-bit binary counter. Douglas Aircraft built the equipment, implementing Cecil Hasting's suggestion (RAND P-113) for a noise source (most likely the well known behavior of the 6D4 miniature gas thyratron tube, when placed in a magnetic field). Twenty of the 32 possible counter values were mapped onto the 10 decimal digits and the other 12 counter values were discarded. The results of a long run from the RAND machine, filtered and tested, were converted into a table, which originally existed only as a deck of punched cards, but was later published in 1955 as a book, 50 rows of 50 digits on each page (A Million Random Digits with 100,000 Normal Deviates). The RAND table was a significant breakthrough in delivering random numbers because such a large and carefully prepared table had never before been available. It has been a useful source for simulations, modeling, and for deriving the arbitrary constants in cryptographic algorithms to demonstrate that the constants had not been selected maliciously ("nothing up my sleeve numbers"). Since the early 1950s, research into TRNGs has been highly active, with thousands of research works published and about 2000 patents granted by 2017. == Physical phenomena with random properties == Multiple different TRNG designs were proposed over time with a large variety of noise sources and digitization techniques ("harvesting"). However, practical considerations (size, power, cost, performance, robustness) dictate the following desirable traits: use of a commonly available inexpensive silicon process; exclusive use of digital design techniques. This allows an easier system-on-chip integration and enables the use of FPGAs; compact and low-power design. This discourages use of analog components (e.g., amplifiers); mathematical justification of the entropy collection mechanisms. Stipčević & Koç in 2014 classified the physical phenomena used to implement TRNG into four groups: electrical noise; free-running oscillators; chaos; quantum effects. === Electrical noise-based RNG === Noise-based RNGs generally follow the same outline: the source of a noise generator is fed into a comparator. If the voltage is above threshold, the comparator output is 1, otherwise 0. The random bit value is latched using a flip-flop. Sources of noise vary and include: Johnson–Nyquist noise ("thermal noise"); Zener noise; avalanche breakdown. The drawbacks of using noise sources for an RNG design are: noise levels are hard to control, they vary with environmental changes and device-to-device; calibration processes needed to ensure a guaranteed amount of entropy are time-consuming; noise levels are typically low, thus the design requires power-hungry amplifiers. The sensitivity of amplifier inputs enables manipulation by an attacker; circuitry located nearby generates a lot of non-random noise thus lowering the entropy; a proof of randomness is near-impossible as multiple interacting physical processes are involved. === Chaos-based RNG === The idea of chaos-based noise stems from the use of a complex system that is hard to characterize by observing its behavior over time. For example, lasers can be put into (undesirable in other applications) chaos mode with chaotically fluctuating power, with power detected using a photodiode and sampled by a comparator. The design can be quite small, as all photonics elements can be integrated on-chip. Stipčević & Koç characterize this technique as "most objectionable", mostly due to the fact that chaotic behavior is usually controlled by a differential equation and no new randomness is introduced, thus there is a possibility of the chaos-based TRNG producing a limited subset of possible output strings. === Free-running oscillators-based RNG === The TRNGs based on a free-running oscilla