In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d
Statistical relational learning
Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a general manner (universal quantification) and draw upon probabilistic graphical models (such as Bayesian networks or Markov networks) to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s. As is evident from the characterization above, the field is not strictly limited to learning aspects; it is equally concerned with reasoning (specifically probabilistic inference) and knowledge representation. Therefore, alternative terms that reflect the main foci of the field include statistical relational learning and reasoning (emphasizing the importance of reasoning) and first-order probabilistic languages (emphasizing the key properties of the languages with which models are represented). Another term that is sometimes used in the literature is relational machine learning (RML). == Canonical tasks == A number of canonical tasks are associated with statistical relational learning, the most common ones being. collective classification, i.e. the (simultaneous) prediction of the class of several objects given objects' attributes and their relations link prediction, i.e. predicting whether or not two or more objects are related link-based clustering, i.e. the grouping of similar objects, where similarity is determined according to the links of an object, and the related task of collaborative filtering, i.e. the filtering for information that is relevant to an entity (where a piece of information is considered relevant to an entity if it is known to be relevant to a similar entity) social network modelling object identification/entity resolution/record linkage, i.e. the identification of equivalent entries in two or more separate databases/datasets == Representation formalisms == One of the fundamental design goals of the representation formalisms developed in SRL is to abstract away from concrete entities and to represent instead general principles that are intended to be universally applicable. Since there are countless ways in which such principles can be represented, many representation formalisms have been proposed in recent years. In the following, some of the more common ones are listed in alphabetical order: Bayesian logic program BLOG model Markov logic networks Multi-entity Bayesian network Probabilistic logic programs Probabilistic relational model – a Probabilistic Relational Model (PRM) is the counterpart of a Bayesian network in statistical relational learning. Probabilistic soft logic Recursive random field Relational Bayesian network Relational dependency network Relational Markov network Relational Kalman filtering
KLJN Secure Key Exchange
Random-resistor-random-temperature Kirchhoff-law-Johnson-noise key exchange, also known as RRRT-KLJN or simply KLJN, is an approach for distributing cryptographic keys between two parties that claims to offer unconditional security. This claim, which has been contested, is significant, as the only other key exchange approach claiming to offer unconditional security is Quantum key distribution. The KLJN secure key exchange scheme was proposed in 2005 by Laszlo Kish and Granqvist. It has the advantage over quantum key distribution in that it can be performed over a metallic wire with just four resistors, two noise generators, and four voltage measuring devices---equipment that is low-priced and can be readily manufactured. It has the disadvantage that several attacks against KLJN have been identified which must be defended against. "Given that the amount of effort and funding that goes into Quantum Cryptography is substantial (some even mock it as a distraction from the ultimate prize which is quantum computing), it seems to me that the fact that classic thermodynamic resources allow for similar inherent security should give one pause," wrote Henning Dekant, the founder of the Quantum Computing Meetup, in April 2013. The Cybersecurity Curricula 2017, a joint project of the Association for Computing Machinery, the IEEE Computer Society, the Association for Information Systems, and the International Federation for Information Processing Technical Committee on Information Security Education (IFIP WG 11.8) recommends teaching the KLJN Scheme as part of teaching "Advanced concepts" in its knowledge unit on cryptography. == See Also/Further Reading ==
Cryptographic Module Testing Laboratory
Cryptographic Module Testing Laboratory (CMTL) is an information technology (IT) computer security testing laboratory that is accredited to conduct cryptographic module evaluations for conformance to the FIPS 140-2 U.S. Government standard. The National Institute of Standards and Technology (NIST) National Voluntary Laboratory Accreditation Program (NVLAP) accredits CMTLs to meet Cryptographic Module Validation Program (CMVP) standards and procedures. This has been replaced by FIPS 140-2 and the Cryptographic Module Validation Program (CMVP). == CMTL requirements == These laboratories must meet the following requirements: NIST Handbook 150, NVLAP Procedures and General Requirements NIST Handbook 150-17 Information Technology Security Testing - Cryptographic Module Testing NVLAP Specific Operations Checklist for Cryptographic Module Testing == FIPS 140-2 in relation to the Common Criteria == A CMTL can also be a Common Criteria (CC) Testing Laboratory (CCTL). The CC and FIPS 140-2 are different in the abstractness and focus of evaluation. FIPS 140-2 testing is against a defined cryptographic module and provides a suite of conformance tests to four FIPS 140 security levels. FIPS 140-2 describes the requirements for cryptographic modules and includes such areas as physical security, key management, self tests, roles and services, etc. The standard was initially developed in 1994 - prior to the development of the CC. The CC is an evaluation against a Protection Profile (PP), or security target (ST). Typically, a PP covers a broad range of products. A CC evaluation does not supersede or replace a validation to either FIPS 140-1, FIPS140-2 or FIPS 140-3. The four security levels in FIPS 140-1 and FIPS 140-2 do not map directly to specific CC EALs or to CC functional requirements. A CC certificate cannot be a substitute for a FIPS 140-1 or FIPS 140-2 certificate. If the operational environment is a modifiable operational environment, the operating system requirements of the Common Criteria are applicable at FIPS Security Levels 2 and above. FIPS 140-1 required evaluated operating systems that referenced the Trusted Computer System Evaluation Criteria (TCSEC) classes C2, B1 and B2. However, TCSEC is no longer in use and has been replaced by the Common Criteria. Consequently, FIPS 140-2 now references the Common Criteria. FIPS 140-2 or FIPS 140-3 validation efforts can be in some parts reused in Common Criteria evaluations, specifically in areas related to entropy source and cryptographic algorithms.
Social media measurement
Social media measurement, also called social media controlling, is the management practice of evaluating successful social media communications of brands, companies, or other organizations. Key performance indicators may be measured by extracting information from social media channels, such as blogs, wikis, micro-blogs such as Twitter, social networking sites, or video/photo sharing websites, forums from time to time. It is also used by companies to gauge current trends in the industry. The process first gathers data from different websites and then performs analysis based on different metrics like time spent on the page, click through rate, content share, comments, text analytics to identify positive or negative emotions about the brand. Some other social media metrics include share of voice, owned mentions, and earned mentions. The social media measurement process starts with defining a goal that needs to be achieved and defining the expected outcome of the process. The expected outcome varies per the goal and is usually measured by a variety of metrics. This is followed by defining possible social strategies to be used to achieve the goal. Then the next step is designing strategies to be used and setting up configuration tools that ease the process of collecting the data. In the next step, strategies and tools are deployed in real-time. This step involves conducting Quality Assurance tests of the methods deployed to collect the data. And in the final step, data collected from the system is analyzed and if the need arises, it is refined on the run time to enhance the methodologies used. The last step ensures that the result obtained is more aligned with the goal defined in the first step. == Data Acquisition == Acquiring data from social media is in demand of an exploring the user participation and population with the purpose of retrieving and collecting so many kinds of data(ex: comments, downloads etc.). There are several prevalent techniques to acquire data such as Network traffic analysis, Ad-hoc application and Crawling Network Traffic Analysis - Network traffic analysis is the process of capturing network traffic and observing it closely to determine what is happening in the network. It is primarily done to improve the performance, security and other general management of the network. However concerned about the potential tort of privacy on the Internet, network traffic analysis is always restricted by the government. Furthermore, high-speed links are not adaptable to traffic analysis because of the possible overload problem according to the packet sniffing mechanism Ad-hoc Application - Ad-hoc application is a kind of application that provides services and games to social network users by developing the APIs offered by social network companies (Facebook Developer Platform). The infrastructure of Ad-hoc application allows the user to interact with the interface layer instead of the application servers. The API provides a path for application to access information after the user login. Moreover, the size of the data set collected vary with the popularity of the social media platform i.e. social media platforms having high number of users will have more data than platforms having less user base. Scraping is a process in which the APIs collect online data from social media. The data collected from Scraping is in raw format. However, having access to these types of data is a bit difficult because of its commercial value. Crawling - Crawling is a process in which a web crawler creates indexes of all the words in a web-page, stores them, then follows all the hyperlinks and indexes on that page and again stores them. It is the most popular technique for data acquisition and is also well known for its easy operation based on prevalent Object-Orientated Programming Language (Java or Python etc.). And most important, social network companies (YouTube, Flicker, Facebook, Instagram, etc.) are friendly to crawling techniques by providing public APIs == Applications == === For branding === Monitoring social media allows researchers to find insights into a brand's overall visibility on social media, to measure the impact of campaigns, to identify opportunities for engagement, to assess competitor activity and share of voice, and to detect impending crises. It can also provide valuable information about emerging trends and what consumers and clients think about specific topics, brands or products. This is the work of a cross-section of groups that include market researchers, PR staff, marketing teams, social-engagement, and community staff, agencies and sales teams. Several different providers have developed tools to facilitate the monitoring of a variety of social media channels - from blogging to internet video to internet forums. This allows companies to track what consumers say about their brands and actions. Companies can then react to these conversations and interact with consumers through social media platforms. === In government === Apart from commercial applications, social media monitoring has become a pervasive technique applied by public organizations and governments. Monitoring is a tradition within the public sector, and social-media monitoring provides a real-time approach to detecting and responding to social developments. Governments have come to realize the need for strategies to cope with surprises from the rapid expansion of public issues. Sobkowicz introduced a framework with three blocks of social-media opinion tracking, simulating and forecasting. It includes: real-time detection of emotions, topics and opinions information-flow modelling and agent-based simulation modeling of opinion networks Bekkers introduced the application of social media monitoring in the Netherlands. Public organizations in the Netherlands (such as the Tax Agency and the Education Ministry) have started to use social media monitoring to obtain better insights into the sentiments of target groups. On the one hand, the public sector will be enabled to provide timely and efficient answers to the public by using social media monitoring techniques, but on the other hand, they also have to deal with concerns about ethical issues such as transparency and privacy. == Quantifying social media == Social media management software (SMMS) is an application program or software that facilitates an organization's ability to successfully engage in social media across different communication channels. SMMS is used to monitor inbound and outbound conversations, support customer interaction, audit or document social marketing initiatives and evaluate the usefulness of a social media presence. It can be difficult to measure all social media conversations. Due to privacy settings and other issues, not all social media conversations can be found and reported by monitoring tools. However, whilst social media monitoring cannot give absolute figures, it can be extremely useful for identifying trends and for benchmarking, in addition to the uses mentioned above. These findings can, in turn, influence and shape future business decisions. In order to access social media data (posts, Tweets, and meta-data) and to analyze and monitor social media, many companies use software technologies built for business. These range from in-platform analytics dashboards to dedicated third-party platforms, which offer more advanced capabilities including cross-platform audience intelligence, sentiment analysis, and trend detection at scale. == Location-based == Most social media networks allow users to add a location to their posts (reference all of our feeds). The location can be classified as either 'at-the-location' or 'about-the-location'. "'At-the-location' services can be defined as services where location-based content is created at the geographic location. 'About-the-location' services can be defined as services which are referring to a particular location but the content is not necessarily created in this particular physical place." The added information available from geotagged (link to Geotagging article) posts means that they can be displayed on a map. This means that a location can be used as the start of a social media search rather than a keyword or hashtag. This has major implications for disaster relief, event monitoring, safety and security professionals since a large portion of their job is related to tracking and monitoring specific locations. == Technologies used == Various monitoring platforms use different technologies for social media monitoring and measurement. These technology providers may connect to the API provided by social platforms that are created for 3rd party developers to develop their own applications and services that access data. Facebook's Graph API is one such API that social media monitoring solution products would connect to pull data from. Some social media monitoring and analytics companies use calls to data providers each time an end-user d
Cooperative storage cloud
A cooperative storage cloud is a decentralized model of networked online storage where data is stored on multiple computers (nodes), hosted by the participants cooperating in the cloud. For the cooperative scheme to be viable, the total storage contributed in aggregate must be at least equal to the amount of storage needed by end users. However, some nodes may contribute less storage and some may contribute more. There may be reward models to compensate the nodes contributing more. Unlike a traditional storage cloud, a cooperative does not directly employ dedicated servers for the actual storage of the data, thereby eliminating the need for a significant dedicated hardware investment. Each node in the cooperative runs specialized software which communicates with a centralized control and orchestration server, thereby allowing the node to both consume and contribute storage space to the cloud. The centralized control and orchestration server requires several orders of magnitude less resources (storage, computing power, and bandwidth) to operate, relative to the overall capacity of the cooperative. == Data security == Files hosted in the cloud are fragmented and encrypted before leaving the local machine. They are then distributed randomly using a load balancing and geo-distribution algorithm to other nodes in the cooperative. Users can add an additional layer of security and reduce storage space by compressing and encrypting files before they are copied to the cloud. == Data redundancy == In order to maintain data integrity and high availability across a relatively unreliable set of computers over a wide area network like the Internet, the source node will add some level of redundancy to each data block. This allows the system to recreate the entire block even if some nodes are temporarily unavailable (due to loss of network connectivity, the machine being powered off or a hardware failure). The most storage and bandwidth efficient forms of redundancy use erasure coding techniques like Reed–Solomon. A simple, less CPU intensive but more expensive form of redundancy is duplicate copies. == Flexible contribution == Due to bandwidth or hardware constraints some nodes may not be able to contribute as much space as they consume in the cloud. On the other hand, nodes with large storage space and limited or no bandwidth constraints may contribute more than they consume, thereby the cooperative can stay in balance.
Sex differences in social media use
Men and women use social media in different ways and with different frequencies. In general, several researchers have found that women tend to use social network services (SNSs) more than men and primiarly to socialize. == Differences == === Predilection for usage === Many studies have found that women are more likely to use either specific SNSs such as Facebook or MySpace or SNSs in general. In 2015, 73% of online men and 80% of online women used social networking sites. The gap in gender differences has become less apparent in LinkedIn. In 2015 about 26 percent of online men and 25% of online women used the business-and employee-oriented networking site. Researchers who have examined the gender of users of multiple SNSs have found contradictory results. Hargittai's groundbreaking 2007 study examining race, gender, and other differences between undergraduate college student users of SNSs found that women were not only more likely to have used SNSes than men but that they were also more likely to have used many different services, including Facebook, MySpace, and Friendster; these differences persisted in several models and analyses. Although she only surveyed students at one institution – the University of Illinois at Chicago – Hargittai selected that institution intentionally as "an ideal location for studies of how different kinds of people use online sites and services." In contrast, data collected by the Pew Internet & American Life Project found that men were more likely to have multiple SNS profiles. Although the sample sizes of the two surveys are comparable – 1,650 Internet users in the Pew survey compared with 1,060 in Hargittai's survey – the data from the Pew survey are newer and arguably more representative of the entire adult United States population. Pinterest, Facebook, and Instagram attract more females. Picture sharing sites overall are very popular among women. Pinterest alone attracts three times as many female users than male. However, use of Pinterest by men has increased from 5% in 2012. Facebook attracts about 77% of women online. Instagram is also more likely to attract women. Men are more likely to participate in online forums like Reddit, Digg or Slashdot. One in five men claim to be a part of an online forum. === Uses === In general, women seem to use SNSs more to explicitly foster social connections. A study conducted by Pew research centers found that women were more avid users of social media. In November 2010, the gap between men and women was as high as 15%. Female participants in a multi-stage study conducted in 2007 to discover the motivations of Facebook users scored higher on scales for social connection and posting of photographs. Studies have also been conducted on the differences between females and males with regards to blogging. The Pew Research Center found that younger females are more likely to blog than males their own age, even males that are older than them. Similarly, in a study of blogs maintained in MySpace, women were found to be more likely to not only write blogs but also write about family, romantic relationships, friendships, and health in those blogs. A study of Swedish SNS users found that women were more likely to have expressions of friendship, specifically in the areas of (a) publishing photos of their friends, (b) specifically naming their best friends, and (c) writing poems to and about their friends. Women were also more likely to have expressions related to family relationships and romantic relationships. One of the key findings of this research is that those men who do have expressions of romantic relationships in their profile had expressions just as strong as the women. However, the researcher speculated that this may be in part due to a desire to publicly express heterosexual behaviors and mannerisms instead of merely expressing romantic feelings. A large-scale study of gender differences in MySpace found that both men and women tended to have a majority of female Friends, and both men and women tended to have a majority of female "Top" Friends in the site. A later study found women to author disproportionately many (public) comments in MySpace, but an investigation into the role of emotion in public MySpace comments found that women both give and receive stronger positive emotion. It was hypothesised that women are simply more effective at using social networking sites because they are better able to harness positive emotion. A study focused on the influence of gender and personality on individuals' use of online social networking websites such as Facebook, reported that men use social networking sites with the intention of forming new relationships, whereas, women use them more for relationship maintenance. In addition to this, women are more likely to use Facebook or MySpace to compare themselves to others and also to search for information. Men, however, are more likely to look at other people's profiles with in the intention to find friends. Women were less successful at actually finding new friends, but more successful at "maintaining existing relationships, making new relationships, using for academic purposes and following specific agenda". Similarly, men also self-reported this motivation "while women reported using them more for relationship maintenance". === Personality === OCEAN personality traits are known to systematically vary between human males and females. In one study, the same women were more extraverted and agreeable, such as less neurotic while on social media than offline. Other studies associated neuroticism with female use of social media. === Privacy === Privacy has been the primary topic of many studies of SNS users, and many of these studies have found differences between male and female SNS users, although some studies have found results contradictory to those found in other studies. Some researchers have found that women are more protective of their personal information and more likely to have private profiles. Other researchers have found that women are less likely to post some types of information. Acquisti and Gross found that women in their sample were less likely to reveal their sexual orientation, personal address, or cell phone number. This is similar to Pew Internet & American Life research of children users of SNSs that found that boys and girls presented different views of privacy and behaviors, with girls being more concerned about and restrictive of information such as city, town, last name, and cell phone number that could be used to locate them. At least one group of researchers has found that women are less likely to share information that "identifies them directly – last name, cell phone number, and address or home phone number," linking that resistance to women's greater concerns about "cyberstalking", "cyberbullying", and security problems. Despite these concerns about privacy, researchers have found that women are more likely to maintain up-to-date photos of themselves. Further, Kolek and Saunders found in their sample of college student Facebook users that women were more likely to not only post a photograph of themselves in their profile but that they were more likely to have a publicly viewable Facebook account (a contradictory finding compared to many other studies), post photos, and post photo albums. Women were more likely to have: (a) a publicly viewable Facebook account, (b) more photo albums, (c) more photos, (d) a photo of themselves as their profile picture, (e) positive references to alcohol, partying, or drugs, and (f) more positive references to or about the institution or institution-related activities. In general, women were more likely to disclose information about themselves in their Facebook profile, with the primary exception of sharing their telephone number. Similarly, female respondents to Strano's study were more likely to keep their profile photo recent and choose a photo that made them appear attractive, happy, and fun-loving. Citing several examples, Strano opined that there may also be a difference in how men and women Facebook users display and interpret profile photos depicting relationships. Privacy has also been a concern for the SnapChat app, which allows you to send messages either text or photo or video which then disappear. One study has shown that security is not a major concern for the majority of users and that most do not use Snapchat to send sensitive content (although up to 25% may do so experimentally). As part of their research almost no statistically significant gender differences were found. === Cyberbullying === Past research carried out to investigate if there are any gender differences in cyber-bullying has found that boys commit more cyber verbal bullying, cyber forgery and more violence based on hidden identity or presenting themselves as other person. === Mansplaining === A 2021 article found that mansplaining could be seen more prominent online rather than offl