AI Content Generator

AI Content Generator — hands-on reviews, top picks, pricing, pros and cons and a practical how-to guide on Aizhi.

Tresorit

Tresorit is a Swiss company providing end-to-end encrypted cloud storage and secure content collaboration services. Founded in 2011, the company primarily serves businesses and organizations with elevated data protection and compliance requirements. Since 2021, Tresorit has been part of Swiss Post's digital business services, which, under the name 'Swiss Post Digital' offer secure communication platforms and connectable software solutions for SMEs, public authorities, and the healthcare sector, among others. == History == Tresorit was founded in 2011 by Hungarian software developers Istvan Lam, Szilveszter Szebeni and Gyorgy Szilagyi with the aim of providing a secure alternative to traditional cloud storage solutions. The company developed a cloud collaboration platform based on client-side end-to-end encryption and a zero-knowledge architecture. In its early years, Tresorit gained attention through a public security challenge inviting researchers to attempt to compromise its encryption system. The initiative received coverage in technology and cybersecurity media. The company initially positioned itself as a secure alternative to conventional cloud storage services and gradually expanded its offering toward enterprise-focused collaboration tools. In 2021, Swiss Post Communications Services acquired a majority stake in Tresorit. The company is now part of Swiss Post, and continues to operate independently within Swiss Post’s digital division, while benefiting from the broader infrastructure and institutional framework of its parent organization. Tresorit has offices in Zurich, Munich, and Budapest. == Products and Services == Tresorit provides a cloud-based platform for secure file storage and collaboration. Its services include encrypted file sharing, email encryption, electronic signatures, and encrypted data rooms for managing sensitive documents and workflows. The platform is available on Windows, macOS, Linux, Android, and iOS. == Technology == Tresorit uses client-side end-to-end encryption based on a zero-knowledge model. Files are encrypted on the user’s device before being uploaded to company servers. According to the company, encryption keys remain under user control, meaning that Tresorit and third parties cannot access the content of stored files. == Security challenge == Between 2013 and 2014, Tresorit organized a public challenge inviting security researchers to attempt to compromise the service's encryption implementation. The challenge received coverage in technology and cybersecurity media. == Acquisition by Swiss Post == In 2021, Swiss Post Communications Services acquired a majority stake in Tresorit as part of Swiss Post’s broader digital services strategy. The company is now part of Swiss Post. == Reception == Tresorit has been covered by international technology and business publications in the context of secure cloud storage and encrypted collaboration services. TechCrunch described the company as an early European provider of end-to-end encrypted cloud services, while The New York Times included it in discussions of secure file-sharing tools. Other publications such as TechRadar and ITPro have reviewed Tresorit in the context of enterprise security and confidential data handling.
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Trusted Computing

Trusted Computing (TC) is a technology developed and promoted by the Trusted Computing Group. The term is taken from the field of trusted systems and has a specialized meaning that is distinct from the field of confidential computing. With Trusted Computing, the computer will consistently behave in expected ways, and those behaviors will be enforced by computer hardware and software. Enforcing this behavior is achieved by loading the hardware with a unique encryption key that is inaccessible to the rest of the system and the owner. TC is controversial as the hardware is not only secured for its owner, but also against its owner, leading opponents of the technology like free software activist Richard Stallman to deride it as "treacherous computing", and certain scholarly articles to use scare quotes when referring to the technology. Trusted Computing proponents such as International Data Corporation, the Enterprise Strategy Group and Endpoint Technologies Associates state that the technology will make computers safer, less prone to viruses and malware, and thus more reliable from an end-user perspective. They also state that Trusted Computing will allow computers and servers to offer improved computer security over that which is currently available. Opponents often state that this technology will be used primarily to enforce digital rights management policies (imposed restrictions to the owner) and not to increase computer security. Chip manufacturers Intel and AMD, hardware manufacturers such as HP and Dell, and operating system providers such as Microsoft include Trusted Computing in their products if enabled. The U.S. Army requires that every new PC it purchases comes with a Trusted Platform Module (TPM). As of July 3, 2007, so does virtually the entire United States Department of Defense. == Key concepts == Trusted Computing encompasses six key technology concepts, of which all are required for a fully Trusted system, that is, a system compliant to the TCG specifications: Endorsement key Secure input and output Memory curtaining / protected execution Sealed storage Remote attestation Trusted Third Party (TTP) === Endorsement key === The endorsement key is a 2048-bit RSA public and private key pair that is created randomly on the chip at manufacture time and cannot be changed. The private key never leaves the chip, while the public key is used for attestation and for encryption of sensitive data sent to the chip, as occurs during the TPM_TakeOwnership command. This key is used to allow the execution of secure transactions: every Trusted Platform Module (TPM) is required to be able to sign a random number (in order to allow the owner to show that he has a genuine trusted computer), using a particular protocol created by the Trusted Computing Group (the direct anonymous attestation protocol) in order to ensure its compliance of the TCG standard and to prove its identity; this makes it impossible for a software TPM emulator with an untrusted endorsement key (for example, a self-generated one) to start a secure transaction with a trusted entity. The TPM should be designed to make the extraction of this key by hardware analysis hard, but tamper resistance is not a strong requirement. === Memory curtaining === Memory curtaining extends common memory protection techniques to provide full isolation of sensitive areas of memory—for example, locations containing cryptographic keys. Even the operating system does not have full access to curtained memory. The exact implementation details are vendor specific. === Sealed storage === Sealed storage protects private information by binding it to platform configuration information including the software and hardware being used. This means the data can be released only to a particular combination of software and hardware. Sealed storage can be used for DRM enforcing. For example, users who keep a song on their computer that has not been licensed to be listened will not be able to play it. Currently, a user can locate the song, listen to it, and send it to someone else, play it in the software of their choice, or back it up (and in some cases, use circumvention software to decrypt it). Alternatively, the user may use software to modify the operating system's DRM routines to have it leak the song data once, say, a temporary license was acquired. Using sealed storage, the song is securely encrypted using a key bound to the trusted platform module so that only the unmodified and untampered music player on his or her computer can play it. In this DRM architecture, this might also prevent people from listening to the song after buying a new computer, or upgrading parts of their current one, except after explicit permission of the vendor of the song. === Remote attestation === Remote attestation allows changes to the user's computer to be detected by authorized parties. For example, software companies can identify unauthorized changes to software, including users modifying their software to circumvent commercial digital rights restrictions. It works by having the hardware generate a certificate stating what software is currently running. The computer can then present this certificate to a remote party to show that unaltered software is currently executing. Numerous remote attestation schemes have been proposed for various computer architectures, including Intel, RISC-V, and ARM. Remote attestation is usually combined with public-key encryption so that the information sent can only be read by the programs that requested the attestation, and not by an eavesdropper. To take the song example again, the user's music player software could send the song to other machines, but only if they could attest that they were running an authorized copy of the music player software. Combined with the other technologies, this provides a more restricted path for the music: encrypted I/O prevents the user from recording it as it is transmitted to the audio subsystem, memory locking prevents it from being dumped to regular disk files as it is being worked on, sealed storage curtails unauthorized access to it when saved to the hard drive, and remote attestation prevents unauthorized software from accessing the song even when it is used on other computers. To preserve the privacy of attestation responders, Direct Anonymous Attestation has been proposed as a solution, which uses a group signature scheme to prevent revealing the identity of individual signers. Proof of space (PoS) have been proposed to be used for malware detection, by determining whether the L1 cache of a processor is empty (e.g., has enough space to evaluate the PoSpace routine without cache misses) or contains a routine that resisted being evicted. === Trusted third party === == Known applications == The Microsoft products Windows Vista, Windows 7, Windows 8 and Windows RT make use of a Trusted Platform Module to facilitate BitLocker Drive Encryption. Other known applications with runtime encryption and the use of secure enclaves include the Signal messenger and the e-prescription service ("E-Rezept") by the German government. == Possible applications == === Digital rights management === Trusted Computing would allow companies to create a digital rights management (DRM) system which would be very hard to circumvent, though not impossible. An example is downloading a music file. Sealed storage could be used to prevent the user from opening the file with an unauthorized player or computer. Remote attestation could be used to authorize play only by music players that enforce the record company's rules. The music would be played from curtained memory, which would prevent the user from making an unrestricted copy of the file while it is playing, and secure I/O would prevent capturing what is being sent to the sound system. Circumventing such a system would require either manipulation of the computer's hardware, capturing the analogue (and thus degraded) signal using a recording device or a microphone, or breaking the security of the system. New business models for use of software (services) over Internet may be boosted by the technology. By strengthening the DRM system, one could base a business model on renting programs for a specific time periods or "pay as you go" models. For instance, one could download a music file which could only be played a certain number of times before it becomes unusable, or the music file could be used only within a certain time period. === Preventing cheating in online games === Trusted Computing could be used to combat cheating in online games. Some players modify their game copy in order to gain unfair advantages in the game; remote attestation, secure I/O and memory curtaining could be used to determine that all players connected to a server were running an unmodified copy of the software. === Verification of remote computation for grid computing === Trusted Computing could be used to guarantee participants in a grid computing sys
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List of broadband over power line deployments

This is a list of broadband over power line deployments. In this sense, "broadband" usually refers to Internet access using power line communication technology. == BPL pilot projects - 1st Gen (UPA) == === Inactive pilot projects === North America: United States: The United Telecom Council publishes the Federal Communications Commission (FCC)-mandated BPL Interference Resolution website, which provides a list of all BPL deployments in the US. Canada: Quebec: As of 2005, PLC communication technology developed by Ariane Controls is being installed inside and outside existing buildings to control lights and other energy-hungry devices. The cheap devices allow energy consumption to be better managed, and so save much energy and bring a clear return on investment. Western Europe: Sweden: Vattenfall is using PLC technology at 1200 baud for automatic meter reading based on an Iskraemeco product. Central and Eastern Europe, and Eurasia: Russian Federation: Electro-com has deployed widely BPL/PLC technology and offers internet access service in Moscow, Nizhny Novgorod, Ryazan, Kaluga and Rostov-on-Don, planning to extend coverage to main Russian cities. Currently the company does not provide other services, though plans to start providing telephone, and television services someday. Base equipment is a DefiDev modem with a DS2 chipset. The company had 35,000 subscribers and an annual growth of 15-20%. The company has, however, halted operations in Moscow in September, 2008, having sold its client network to an IDSL internet provider. Romania: In January, 2006, the Ministry of Communications and Information Technology introduced a PLC trial in the rural locality of Band, Mureș County, offering phone and broadband internet access for €7 per month. The technology was introduced to 50 households. Montenegro: In March, 2002, the Internet Crna Gora biggest internet provider in Montenegro launched a pilot project in town of Cetinje. Serbia: In August 2002, the Star Engineering from Niš launched a pilot project to show a completely new way to access the Internet, which is a new in that time in most countries around the world. Hungary: The first powerline service in Hungary was realized in September, 2003, in the Riverside apartment house in Budapest by 23Vnet Ltd. The PLC equipment was supplied by ASCOM Powerline. After four months the service was counting 100 users from 450 apartment owners. The bandwidth is 4.5 Mbit/s. Asia, Pacific, and Oceania: Indonesia: PT Kejora Gemilang Internusa "KEJORA", under their banner PLANET BROADBAND, is currently rolling out broadband over power line, with over 300,000 homes expected to be enabled by August 2010. PT. Kejora Gemilang Internusa signed an 8-year Joint Venture concession agreement with ICON+ a division of PT. Perusahaan Listrik Negara (Indonesia electricity company). Under the terms of the agreement PLAnet Broadband are to supply BPL/PLC to Jakarta West and West Java. Another company, PT. Broadband Powerline Indonesia, has been developing broadband over power line in apartment buildings since 2006. PT. BPI also produces data couplers to make broadband over powerline possible in three phases (R, S, T) with a single master. India : In India IIIT Allahabad has completed a project in co-operation with Corinex Communications Canada to implement a prototype of BPL for University campus and nearby villages. Africa and the Middle East: Egypt: The Engineering Office for Integrated Projects (EOIP) has deployed PLC technology widely in Alexandria, Fayed, and Tanta. Based on a locally developed system, the company provides AMR for electricity utilities. Currently, the company has about 70,000 subscribers. South Africa: Goal Technology Solutions (GTS) trialled the technology and is offering service in the suburbs of Pretoria, and plans to extend it to other areas. The tests were done with Mitsubishi equipment using a DS2 chipset, and the company claims a maximum throughput of 90 Mbit/s although initially only "512 Kbits/s ADSL equivalent speeds" are available. Now it uses DefiDev's equipment, and according to GTS's website, it will expand available bandwidth up to 5-20 Mbit/s. Ghana: Cactel Communications, Ltd. successfully deployed an MV solution pilot project in the Graphic Communications Group in Accra in June, 2005. A Cactel Remote Energy Management System (REMS) pilot project for the Electricity Company of Ghana (ECG) is running a 40-user pilot project at the University of Ghana in Legon. The current project combines fiber, radio link, Wi-Fi and PLC to provide broadband internet access and telephony. It showcases the interoperability of PLC technology and the company's expertise in emerging market design and deployment. Cactel hopes to deploy nationally, and is in deliberations with the national stakeholders and with Ghana's Ministry of Communications (MoC). AllTerra Communications successfully implemented a pilot test of broadband over power lines in Akosombo. In partnership with VRA, this test involves demonstrating transmission of broadband from medium to low voltage signals. AllTerra is working with VRA to expand the pilot project to include essential grid management utilities that will help balance and manage the current electricity transmission throughout their various substations. Using IT as a catalyst for economic development, AllTerra is expanding into numerous areas throughout Ghana. Vobiss Solutions Ltd successfully implemented a Hybrid Fibre BPL pilot network within EMEFS Hillview Estate in collaboration with ECG. Saudi Arabia: ElectroNet has been working with the Saudi Electric Company since 2005 on a pilot project using broadband over power lines over medium voltage cables and linking into low voltage distribution within a shopping mall. The pilot project also integrates automatic meter readers. Powerlines Communications Co. Ltd. implemented an AMR pilot project for Saudi Electricity Company in 2006. The project was located in the city of Jeddah on the west coast of Saudi Arabia. Digital KWh meters were installed in parallel with analog KWh meters. Readings taken by the Saudi Electricity Company showed variations of less than 1%. A BPL pilot project was included. Saudi Arabian Computer Management Consultants (SACMAC) has signed a deal to become an official system integrator and distributor for Mitsubishi PLC. It is expected to become a great success, because the existing broadband service, monopolized by the Saudi Telecom Company, is expensive and has poor customer service (some clients report that company techs arrive months after ordering). SACMAC has declined to talk about specifics of availability and price but says it will start rolling out the service in a few months (as of May 2006) and its price will be lower than current broadband providers. === Concluded pilot projects === The following pilot projects have ended: Australia, Tasmania: In November 2007, electricity retailer Aurora Energy ended its involvement with BPL and announced it was switching to Optical Fiber. This ended their commercial trial begun in September 2005, offering BPL services to 500 homes in the suburb of Tolmans Hill near Hobart, which had followed a successful technological trial earlier that year. Portugal ended BPL/PLC deployments in the country in October 2006, reportedly for economic reasons., Russian Federation: In September 2008, Russia's only BPL provider Electro-com ended deployments in Moscow for economic reasons. Spain: In May 2007 Iberdrola and Endesa (the main power companies in Spain) ended their projects to deploy PLC. United States: As of July 2010, the City of Manassas, VA has shut down their BPL deployment, which was the largest in the country. As of April 2007, Motorola has shuttered its Powerline LV Access BPL and reportedly plans to re-purpose the technology to a new system called Powerline MU, which is for use within multiple-unit dwellings. Motorola's system uses only residential-side low-voltage power lines for transmission to reduce the antenna effect, and successfully demonstrated frequency-notching for reduced potential for interference over the Amperion Inc. and Current Technologies LLC systems. Motorola invited the American Radio Relay League to participate with these tests, and even installed the Motorola system at their headquarters. Preliminary results were very positive with regard to interference, because the Motorola system does not use BPL on the powerlines leading up to the neighborhood. The BPL carrier is only used for the last leg of the trip from the pole to the house, and gets the signal to the pole via radio. This limits the interference to the area surrounding the last leg to the house. === Dismantled pilot projects === The following other BPL trials in the US are dismantled as of May 2008:
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Data set (IBM mainframe)

In the context of IBM mainframe computers in the IBM System/360 line and its successors, a data set (IBM preferred) or dataset is a computer file having a record organization. Use of this term began with, e.g., DOS/360 and OS/360, and is still used by their successors, including the current VSE and z/OS. Documentation for these systems historically preferred this term rather than file. A data set is typically stored on a direct access storage device (DASD) or magnetic tape, however unit record devices, such as punch card readers, card punches, line printers and page printers can provide input/output (I/O) for a data set (file). Data sets are not unstructured streams of bytes, but rather are organized in various logical record and block structures determined by the DSORG (data set organization), RECFM (record format), and other parameters. These parameters are specified at the time of the data set allocation (creation), for example with Job Control Language DD statements. Within a running program they are stored in the Data Control Block (DCB) or Access Control Block (ACB), which are data structures used to access data sets using access methods. Records in a data set may be fixed, variable, or “undefined” length. == Data set organization == For OS/360, the DCB's DSORG parameter specifies how the data set is organized. It may be CQ Queued Telecommunications Access Method (QTAM) in Message Control Program (MCP) CX Communications line group DA Basic Direct Access Method (BDAM) GS Graphics device for Graphics Access Method(GAM) IS Indexed Sequential Access Method (ISAM) MQ QTAM message queue in application PO Partitioned Organization PS Physical Sequential among others. Data sets on tape may only be DSORG=PS. The choice of organization depends on how the data is to be accessed, and in particular, how it is to be updated. Programmers utilize various access methods (such as QSAM or VSAM) in programs for reading and writing data sets. Access method depends on the given data set organization. == Record format (RECFM) == Regardless of organization, the physical structure of each record is essentially the same, and is uniform throughout the data set. This is specified in the DCB RECFM parameter. RECFM=F means that the records are of fixed length, specified via the LRECL parameter. RECFM=V specifies a variable-length record. V records when stored on media are prefixed by a Record Descriptor Word (RDW) containing the integer length of the record in bytes and flag bits. With RECFM=FB and RECFM=VB, multiple logical records are grouped together into a single physical block on tape or DASD. FB and VB are fixed-blocked, and variable-blocked, respectively. RECFM=U (undefined) is also variable length, but the length of the record is determined by the length of the block rather than by a control field. The BLKSIZE parameter specifies the maximum length of the block. RECFM=FBS could be also specified, meaning fixed-blocked standard, meaning all the blocks except the last one were required to be in full BLKSIZE length. RECFM=VBS, or variable-blocked spanned, means a logical record could be spanned across two or more blocks, with flags in the RDW indicating whether a record segment is continued into the next block and/or was continued from the previous one. This mechanism eliminates the need for using any "delimiter" byte value to separate records. Thus data can be of any type, including binary integers, floating-point, or characters, without introducing a false end-of-record condition. The data set is an abstraction of a collection of records, in contrast to files as unstructured streams of bytes. == Partitioned data set == A partitioned data set (PDS) is a data set containing multiple members, each of which holds a separate sub-data set, similar to a directory in other types of file systems. This type of data set is often used to hold load modules (old format bound executable programs), source program libraries (especially Assembler macro definitions), ISPF screen definitions, and Job Control Language. A PDS may be compared to a Zip file or COM Structured Storage. A Partitioned Data Set can only be allocated on a single volume and have a maximum size of 65,535 tracks. Besides members, a PDS contains also a directory. Each member can be accessed indirectly via the directory structure. Once a member is located, the data stored in that member are handled in the same manner as a PS (sequential) data set. Whenever a member is deleted, the space it occupied is unusable for storing other data. Likewise, if a member is re-written, it is stored in a new spot at the back of the PDS and leaves wasted “dead” space in the middle. The only way to recover “dead” space is to perform file compression. Compression, which is done using the IEBCOPY utility, moves all members to the front of the data space and leaves free usable space at the back. (Note that in modern parlance, this kind of operation might be called defragmentation or garbage collection; data compression nowadays refers to a different, more complicated concept.) PDS files can only reside on DASD, not on magnetic tape, in order to use the directory structure to access individual members. Partitioned data sets are most often used for storing multiple job control language files, utility control statements, and executable modules. An improvement of this scheme is a Partitioned Data Set Extended (PDSE or PDS/E, sometimes just libraries) introduced with DFSMSdfp for MVS/XA and MVS/ESA systems. A PDS/E library can store program objects or other types of members, but not both. BPAM cannot process a PDS/E containing program objects. PDS/E structure is similar to PDS and is used to store the same types of data. However, PDS/E files have a better directory structure which does not require pre-allocation of directory blocks when the PDS/E is defined (and therefore does not run out of directory blocks if not enough were specified). Also, PDS/E automatically stores members in such a way that compression operation is not needed to reclaim "dead" space. PDS/E files can only reside on DASD in order to use the directory structure to access individual members. == Generation Data Group == A Generation Data Group (GDG) is a group of non-VSAM data sets that are successive generations of historically-related data stored on an IBM mainframe (running OS/360 and its successors or DOS/360 and its successors). A GDG is usually cataloged. An individual member of the GDG collection is called a "Generation Data Set." The latter may be identified by an absolute number, ACCTG.OURGDG(1234), or a relative number: (-1) for the previous generation, (0) for the current one, and (+1) the next generation. A GDG specifies how many generations of a data set are to be kept and at what age a generation will be deleted. Whenever a new generation is created, the system checks whether one or more obsolete generations are to be deleted. The purpose of GDGs is to automate archival, using the command language JCL, the data set name given is generic. When DSN appears, the GDG data set appears along with the history number, where (0) is the most recent version (-1), (-2), ... are previous generations (+1) a new generation (see DD) Another use of GDGs is to be able to address all generations simultaneously within a JCL script without having to know the number of currently available generations. To do this, you have to omit the parentheses and the generation number in the JCL when specifying the dataset. === GDG JCL & features === Generation Data Groups are defined using either the BLDG statement of the IEHPROGM utility or the DEFINE GENERATIONGROUP statement of the newer IDCAMS utility, which allows setting various parameters. LIMIT(10) would limit the number of generations limit to 10. SCRATCH FOR (91) would retain each member, up to the limited#generations, at least 91 days. IDCAMS can also delete (and optionally uncatalog) a GDG. ==== Example ==== Creation of a standard GDG for five safety scopes, each at least 35 days old: Delete a standard GDG:
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Availability zone

In cloud computing, an availability region is a group of data centres that are located in the same geographical region. Availability regions comprise multiple availability zones, which are groups of data centres that are located far enough from each other to prevent large-scale outages in the event of failure of a single zone, whilst still being close enough to each other to enable low-latency connections. Distributed systems spanning multiple availability zones allow for high availability, even in the event of catastrophic failure, such as natural disasters. Services offering distinct availability zones include Amazon Web Services, Microsoft Azure and Google Cloud.
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Feistel cipher

In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering research while working for IBM; it is also commonly known as a Feistel network. A large number of block ciphers use the scheme, including the US Data Encryption Standard, the Soviet/Russian GOST (aka Magma) and the more recent Blowfish and Twofish ciphers. In a Feistel cipher, encryption and decryption are very similar operations, and both consist of iteratively running a function called a "round function" a fixed number of times. == History == Many modern symmetric block ciphers are based on Feistel networks. Feistel networks were first seen commercially in IBM's Lucifer cipher, designed by Horst Feistel and Don Coppersmith in 1973. Feistel networks gained respectability when the U.S. Federal Government adopted the DES (a cipher based on Lucifer, with changes made by the NSA) in 1976. Like other components of the DES, the iterative nature of the Feistel construction makes implementing the cryptosystem in hardware easier (particularly on the hardware available at the time of DES's design). == Design == A Feistel network uses a round function, a function which takes two inputs – a data block and a subkey – and returns one output of the same size as the data block. In each round, the round function is run on half of the data to be encrypted, and its output is XORed with the other half of the data. This is repeated a fixed number of times, and the final output is the encrypted data. An important advantage of Feistel networks compared to other cipher designs such as substitution–permutation networks (SP-networks) is that the entire operation is guaranteed to be invertible (that is, encrypted data can be decrypted), even if the round function is not itself invertible. The round function can be made arbitrarily complicated, since it does not need to be designed to be invertible. Furthermore, the encryption and decryption operations are very similar, even identical in some cases, requiring only a reversal of the key schedule. Therefore, the size of the code or circuitry required to implement such a cipher is nearly halved. Unlike SP-networks, Feistel networks also do not depend on a substitution box that could cause timing side-channels in software implementations. == Theoretical work == The structure and properties of Feistel ciphers have been extensively analyzed by cryptographers. Michael Luby and Charles Rackoff analyzed the Feistel cipher construction and proved that if the round function is a cryptographically secure pseudorandom function, with Ki used as the seed, then 3 rounds are sufficient to make the block cipher a pseudorandom permutation, while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom even to an adversary who gets oracle access to its inverse permutation). Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called Luby–Rackoff block ciphers. Further theoretical work has generalized the construction somewhat and given more precise bounds for security. == Construction details == Let F {\displaystyle \mathrm {F} } be the round function and let K 0 , K 1 , … , K n {\displaystyle K_{0},K_{1},\ldots ,K_{n}} be the sub-keys for the rounds 0 , 1 , … , n {\displaystyle 0,1,\ldots ,n} respectively. Then the basic operation is as follows: Split the plaintext block into two equal pieces: ( L 0 {\displaystyle L_{0}} , R 0 {\displaystyle R_{0}} ). For each round i = 0 , 1 , … , n {\displaystyle i=0,1,\dots ,n} , compute L i + 1 = R i , {\displaystyle L_{i+1}=R_{i},} R i + 1 = L i ⊕ F ( R i , K i ) , {\displaystyle R_{i+1}=L_{i}\oplus \mathrm {F} (R_{i},K_{i}),} where ⊕ {\displaystyle \oplus } means XOR. Then the ciphertext is ( R n + 1 , L n + 1 ) {\displaystyle (R_{n+1},L_{n+1})} . Decryption of a ciphertext ( R n + 1 , L n + 1 ) {\displaystyle (R_{n+1},L_{n+1})} is accomplished by computing for i = n , n − 1 , … , 0 {\displaystyle i=n,n-1,\ldots ,0} R i = L i + 1 , {\displaystyle R_{i}=L_{i+1},} L i = R i + 1 ⊕ F ⁡ ( L i + 1 , K i ) . {\displaystyle L_{i}=R_{i+1}\oplus \operatorname {F} (L_{i+1},K_{i}).} Then ( L 0 , R 0 ) {\displaystyle (L_{0},R_{0})} is the plaintext again. The diagram illustrates both encryption and decryption. Note the reversal of the subkey order for decryption; this is the only difference between encryption and decryption. === Unbalanced Feistel cipher === Unbalanced Feistel ciphers use a modified structure where L 0 {\displaystyle L_{0}} and R 0 {\displaystyle R_{0}} are not of equal lengths. The Skipjack cipher is an example of such a cipher. The Texas Instruments digital signature transponder uses a proprietary unbalanced Feistel cipher to perform challenge–response authentication. The Thorp shuffle is an extreme case of an unbalanced Feistel cipher in which one side is a single bit. This has better provable security than a balanced Feistel cipher but requires more rounds. There exists Type-1, Type-2, and Type-3 Feistel networks, where the Feistel function is one fourth the size of the block but operates a varying number of times within one round. === Other uses === The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the optimal asymmetric encryption padding (OAEP) scheme uses a simple Feistel network to randomize ciphertexts in certain asymmetric-key encryption schemes. A generalized Feistel algorithm can be used to create strong permutations on small domains of size not a power of two (see format-preserving encryption). === Feistel networks as a design component === Whether the entire cipher is a Feistel cipher or not, Feistel-like networks can be used as a component of a cipher's design. For example, MISTY1 is a Feistel cipher using a three-round Feistel network in its round function, Skipjack is a modified Feistel cipher using a Feistel network in its G permutation, and Threefish (part of Skein) is a non-Feistel block cipher that uses a Feistel-like MIX function. == List of Feistel ciphers == Feistel or modified Feistel: Generalised Feistel: CAST-256 CLEFIA MacGuffin RC2 RC6 Skipjack SMS4
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Memory-hard function

In cryptography, a memory-hard function (MHF) is a function that costs a significant amount of memory to efficiently evaluate. It differs from a memory-bound function, which incurs cost by slowing down computation through memory latency. MHFs have found use in key stretching and proof of work as their increased memory requirements significantly reduce the computational efficiency advantage of custom hardware over general-purpose hardware compared to non-MHFs. == Introduction == MHFs are designed to consume large amounts of memory on a computer in order to reduce the effectiveness of parallel computing. In order to evaluate the function using less memory, a significant time penalty is incurred. As each MHF computation requires a large amount of memory, the number of function computations that can occur simultaneously is limited by the amount of available memory. This reduces the efficiency of specialised hardware, such as application-specific integrated circuits and graphics processing units, which utilise parallelisation, in computing a MHF for a large number of inputs, such as when brute-forcing password hashes or mining cryptocurrency. == Motivation and examples == Bitcoin's proof-of-work uses repeated evaluation of the SHA-256 function, but modern general-purpose processors, such as off-the-shelf CPUs, are inefficient when computing a fixed function many times over. Specialized hardware, such as application-specific integrated circuits (ASICs) designed for Bitcoin mining, can use 30,000 times less energy per hash than x86 CPUs whilst having much greater hash rates. This led to concerns about the centralization of mining for Bitcoin and other cryptocurrencies. Because of this inequality between miners using ASICs and miners using CPUs or off-the shelf hardware, designers of later proof-of-work systems utilised hash functions for which it was difficult to construct ASICs that could evaluate the hash function significantly faster than a CPU. As memory cost is platform-independent, MHFs have found use in cryptocurrency mining, such as for Litecoin, which uses scrypt as its hash function. They are also useful in password hashing because they significantly increase the cost of trying many possible passwords against a leaked database of hashed passwords without significantly increasing the computation time for legitimate users. == Measuring memory hardness == There are various ways to measure the memory hardness of a function. One commonly seen measure is cumulative memory complexity (CMC). In a parallel model, CMC is the sum of the memory required to compute a function over every time step of the computation. Other viable measures include integrating memory usage against time and measuring memory bandwidth consumption on a memory bus. Functions requiring high memory bandwidth are sometimes referred to as "bandwidth-hard functions". == Variants == MHFs can be categorized into two different groups based on their evaluation patterns: data-dependent memory-hard functions (dMHF) and data-independent memory-hard functions (iMHF). As opposed to iMHFs, the memory access pattern of a dMHF depends on the function input, such as the password provided to a key derivation function. Examples of dMHFs are scrypt and Argon2d, while examples of iMHFs are Argon2i and catena. Many of these MHFs have been designed to be used as password hashing functions because of their memory hardness. A notable problem with dMHFs is that they are prone to side-channel attacks such as cache timing. This has resulted in a preference for using iMHFs when hashing passwords. However, iMHFs have been mathematically proven to have weaker memory hardness properties than dMHFs.
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Link encryption

Link encryption is an approach to communications security that encrypts and decrypts all network traffic at each network routing point (e.g. network switch, or node through which it passes) until arrival at its final destination. This repeated decryption and encryption is necessary to allow the routing information contained in each transmission to be read and employed further to direct the transmission toward its destination, before which it is re-encrypted. This contrasts with end-to-end encryption where internal information, but not the header/routing information, is encrypted by the sender at the point of origin and only decrypted by the intended recipient. Link encryption offers two main advantages: encryption is automatic so there is less opportunity for human error. if the communications link operates continuously and carries an unvarying level of traffic, link encryption defeats traffic analysis. On the other hand, end-to-end encryption ensures only the intended recipient has access to the plaintext. Link encryption can be used with end-to-end systems by superencrypting the messages. Bulk encryption refers to encrypting a large number of circuits at once, after they have been multiplexed.
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Smart speaker industry in South Korea

Smart speakers, or AI speakers, have been developed by multiple domestic electronics and telecommunications firms in South Korea. Since their introduction to the local market in 2016, they have been used by millions of people in the country. == Brands == === Google === In September 2018, Google Home (including the Google Home Mini) launched in South Korea. Running Google Assistant, it featured simultaneous recognition of two languages among a total of seven, including Korean. At launch, it could play music from Bugs!, in addition to YouTube. === Kakao === In November 2017, Kakao launched the Kakao Mini, featuring integrated KakaoTalk functionality. === KT === KT launched the GiGA Genie smart speaker in January 2017, using a Harman Kardon speaker. In November 2017, KT announced GiGA Genie LTE, a portable AI speaker with LTE support. They also released a mini speaker called GiGA Genie Buddy. In 2018, KT created a special version of GiGa Genie with a screen for use in hotels. On 29 April 2019, KT announced the GiGA Genie Table TV, a consumer-oriented smart speaker with a display. It featured paid TV access through Wi-Fi. Based on usage data from the hotel model, KT decided not to add a touchscreen. The Table TV also featured a limited-access "personalized-text-to-speech technology" which could use parents' voice recording inputs to read children books. In February 2022, KT began rolling out Amazon Alexa integration into its speakers for English support. === Naver === In August 2017, Naver announced the Wave smart speaker, operating on Clova. In October 2017, Naver launched the Friends smart speaker, which were designed based on Line characters. ==== LG Uplus ==== In December 2017, LG Uplus launched the Friends+ speaker with Naver, operating on U+ Home AI. === Samsung === In August 2018, Samsung announced the Samsung Galaxy Home in partnership with Spotify. The original size was delayed, while the Galaxy Home Mini appeared briefly as a bonus for Samsung Galaxy S20 preorders in South Korea in February 2020. === SK Telecom === SK Telecom launched the Nugu smart speaker in September 2016, using an Astell & Kern audio system. In August 2017, SKT released a portable speaker named Nugu mini. In July 2018, SKT launched the Nugu Candle, featuring expanded mood lighting. The first-generation Nugu was subsequently discontinued. On 18 April 2019, SKT released the NUGU Nemo AI, which featured a display and JBL stereo speaker. In August 2019, SKT collaborated with SM Entertainment, incorporating functions related to the agency's artists into Nugu. In January 2022, SKT showcased the NUGU Candle SE, introducing Alexa support. == Usage == In 2018, approximately 3 million people in South Korea used smart speakers. According to data from KT in 2018, the most common commands to its speakers were for controlling televisions. Based on a broader survey in 2017, music was selected as the most frequent use case. By 2018, smart speaker companies were partnering with reading and other education services, adding potential use-cases for children. By 2022, smart speakers were being utilized by the South Korean government. SKT, in partnership with 70 regional governments, distributed smart speakers to 12,000 senior citizens living alone. The government paid for monthly subscriptions to help seniors stay mentally engaged. Naver made an agreement with the Seoul Metropolitan Government to provide Clova CareCall, an automated health checkup program to hundreds of senior citizens living alone. KT's AI care service included an emergency dispatch call function and medication notifications. == Criticism == === Communication === In a survey of 300 users in 2017, approximately half reported having some type of communication issue with their smart speakers. === Privacy === South Korean smart speakers sparked privacy concerns when they were found to be collecting and documenting user audio data in 2019. The speaker companies responded that only a minority of data was collected and that it was anonymized. They stated that such recordings were collected for performance improvements.
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Cryptographic nonce

In cryptography, a nonce is an arbitrary number that can be used just once in a cryptographic communication. It is often a random or pseudo-random number issued in an authentication protocol to ensure that each communication session is unique, and therefore that old communications cannot be reused in replay attacks. Nonces can also be useful as initialization vectors and in cryptographic hash functions. == Definition == A nonce is an arbitrary number used only once in a cryptographic communication, in the spirit of a nonce word. They are often random or pseudo-random numbers. Many nonces also include a timestamp to ensure exact timeliness, though this requires clock synchronisation between organisations. The addition of a client nonce ("cnonce") helps to improve the security in some ways as implemented in digest access authentication. To ensure that a nonce is used only once, it should be time-variant (including a suitably fine-grained timestamp in its value), or generated with enough random bits to ensure an insignificantly low chance of repeating a previously generated value. Some authors define pseudo-randomness (or unpredictability) as a requirement for a nonce. Nonce is a word dating back to Middle English for something only used once or temporarily (often with the construction "for the nonce"). It descends from the construction "then anes" ("the one [purpose]"). A false etymology claiming it to stand for "number used once" or similar is incorrect. == Usage == === Authentication === Authentication protocols may use nonces to ensure that old communications cannot be reused in replay attacks. For instance, nonces are used in HTTP digest access authentication to calculate an MD5 digest of the password. The nonces are different each time the 401 authentication challenge response code is presented, thus making replay attacks virtually impossible. The scenario of ordering products over the Internet can provide an example of the usefulness of nonces in replay attacks. An attacker could take the encrypted information and—without needing to decrypt—could continue to send a particular order to the supplier, thereby ordering products over and over again under the same name and purchase information. The nonce is used to give 'originality' to a given message so that if the company receives any other orders from the same person with the same nonce, it will discard those as invalid orders. A nonce may be used to ensure security for a stream cipher. Where the same key is used for more than one message and then a different nonce is used to ensure that the keystream is different for different messages encrypted with that key; often the message number is used. Secret nonce values are used by the Lamport signature scheme as a signer-side secret which can be selectively revealed for comparison to public hashes for signature creation and verification. === Hashing === Nonces are used in proof-of-work systems to vary the input to a cryptographic hash function so as to obtain a hash for a certain input that fulfils certain arbitrary conditions. In doing so, it becomes far more difficult to create a "desirable" hash than to verify it, shifting the burden of work onto one side of a transaction or system. For example, proof of work, using hash functions, was considered as a means to combat email spam by forcing email senders to find a hash value for the email (which included a timestamp to prevent pre-computation of useful hashes for later use) that had an arbitrary number of leading zeroes, by hashing the same input with a large number of values until a "desirable" hash was obtained. Similarly, the Bitcoin blockchain hashing algorithm can be tuned to an arbitrary difficulty by changing the required minimum/maximum value of the hash so that the number of bitcoins awarded for new blocks does not increase linearly with increased network computation power as new users join. This is likewise achieved by forcing Bitcoin miners to add nonce values to the value being hashed to change the hash algorithm output. As cryptographic hash algorithms cannot easily be predicted based on their inputs, this makes the act of blockchain hashing and the possibility of being awarded bitcoins something of a lottery, where the first "miner" to find a nonce that delivers a desirable hash is awarded bitcoins.
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Death of Molly Russell

In November 2017, Molly Russell, a fourteen-year-old British schoolgirl from Harrow, London, was found dead in her bedroom by her parents. In an inquest, the coroner stated that she had died from an act of self-harm following depression and the results of social media consumption, including material on Instagram and Pinterest. She also had a Twitter account in which she documented her growing depression. == Life == Russell had been a pupil at Hatch End High School. At the inquest, the school's head teacher expressed shock that she was able to access distressing online content. Her parents stated that she had never shown any previous signs of struggle and was doing very well in school. It was revealed at the inquest that in the six months prior to her death, 2,100 of 16,300 pieces of content she had interacted with on Instagram were on topics such as self-harm, depression, and suicide. It was also noted that throughout her experience on social media, there were never any warning signs about the information she viewed on these platforms. == Subsequent events == Dr. Navin Venugopal, the child psychiatrist assigned to the case investigating her death, called the material she viewed "disturbing and distressing" and said he was unable to sleep well for weeks after viewing it. The coroner Andrew Walker concluded that Molly's death was "an act of self harm suffering from depression and the negative effects of online content". He issued a prevention of future deaths report regarding her death, in which he made a number of recommendations for operators of online platforms, including: separating platforms for adults and children age verification changes in policy on filtering of age-specific content adding features for parental supervision and control data retention of material viewed by children He suggested that this could be accomplished by either legislation or self-regulation. The lawyer representing her family at the inquest stated that the findings "captured all of the elements of why this material is so harmful." The case has been cited as a motivator for the passage of the Online Safety Act. A charity, the Molly Rose Foundation, was set up in her memory, with the goal of suicide prevention for young people. Meta and Pinterest are believed to have made substantial donations to the charity.
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Vans challenge

The Vans challenge is a viral internet challenge that began in March 2019 where people show their Vans shoes landing right-side up after tossing them in the air. The viral sensation reportedly started after a Twitter user shared a video of the occurrence, which was captioned: “Did you know it doesn’t matter how you throw your Vans they will land facing up.” Since then, multiple people on social media posted similar videos of them throwing their Vans in the air and landing right-side up, along with Crocs, UGG boots, and other popular shoes. This theory proved false, as these shoes have not always landed facing up after tossing them.
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Richardson–Lucy deconvolution

The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy, who described it independently. == Description == When an image is produced using an optical system and detected using photographic film, a charge-coupled device or a CMOS sensor, for example, it is inevitably blurred, with an ideal point source not appearing as a point but being spread out into what is known as the point spread function. Extended sources can be decomposed into the sum of many individual point sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: d i = ∑ j p i , j u j , {\displaystyle d_{i}=\sum _{j}p_{i,j}u_{j},} where u j {\displaystyle u_{j}} is the intensity of the underlying image at pixel j {\displaystyle j} , and d i {\displaystyle d_{i}} is the detected intensity at pixel i {\displaystyle i} . In general, a matrix whose elements are p i , j {\displaystyle p_{i,j}} describes the portion of light from source pixel j that is detected in pixel i. In most good optical systems (or in general, linear systems that are described as shift-invariant) the transfer function p can be expressed simply in terms of the spatial offset between the source pixel j and the observation pixel i: p i , j = P ( i − j ) , {\displaystyle p_{i,j}=P(i-j),} where P ( Δ i ) {\displaystyle P(\Delta i)} is called a point spread function. In that case the above equation becomes a convolution. This has been written for one spatial dimension, but most imaging systems are two-dimensional, with the source, detected image, and point spread function all having two indices. So a two-dimensional detected image is a convolution of the underlying image with a two-dimensional point spread function P ( Δ x , Δ y ) {\displaystyle P(\Delta x,\Delta y)} plus added detection noise. In order to estimate u j {\displaystyle u_{j}} given the observed d i {\displaystyle d_{i}} and a known P ( Δ i x , Δ j y ) {\displaystyle P(\Delta i_{x},\Delta j_{y})} , the following iterative procedure is employed in which the estimate of u j {\displaystyle u_{j}} (called u ^ j ( t ) {\displaystyle {\hat {u}}_{j}^{(t)}} ) for iteration number t is updated as follows: u ^ j ( t + 1 ) = u ^ j ( t ) ∑ i d i c i p i j , {\displaystyle {\hat {u}}_{j}^{(t+1)}={\hat {u}}_{j}^{(t)}\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij},} where c i = ∑ j p i j u ^ j ( t ) , {\displaystyle c_{i}=\sum _{j}p_{ij}{\hat {u}}_{j}^{(t)},} and ∑ j p i j = 1 {\displaystyle \sum _{j}p_{ij}=1} is assumed. It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for u j {\displaystyle u_{j}} . Writing this more generally for two (or more) dimensions in terms of convolution with a point spread function P: u ^ ( t + 1 ) = u ^ ( t ) ⋅ ( d u ^ ( t ) ⊗ P ⊗ P ∗ ) , {\displaystyle {\hat {u}}^{(t+1)}={\hat {u}}^{(t)}\cdot \left({\frac {d}{{\hat {u}}^{(t)}\otimes P}}\otimes P^{}\right),} where the division and multiplication are element-wise, ⊗ {\displaystyle \otimes } indicates a 2D convolution, and P ∗ {\displaystyle P^{}} is the mirrored point spread function, or the inverse Fourier transform of the Hermitian transpose of the optical transfer function. In problems where the point spread function p i j {\displaystyle p_{ij}} is not known a priori, a modification of the Richardson–Lucy algorithm has been proposed, in order to accomplish blind deconvolution. == Derivation == In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m = [ m 0 , … , m K ] {\displaystyle \mathbf {m} =[m_{0},\dots ,m_{K}]} for expected values E = [ E 0 , … , E K ] {\displaystyle \mathbf {E} =[E_{0},\dots ,E_{K}]} for a detector with K + 1 {\displaystyle K+1} pixels is given by P ( m ∣ E ) = ∏ i K Poisson ⁡ ( E i ) = ∏ i K E i m i e − E i m i ! . {\displaystyle P(\mathbf {m} \mid \mathbf {E} )=\prod _{i}^{K}\operatorname {Poisson} (E_{i})=\prod _{i}^{K}{\frac {E_{i}^{m_{i}}e^{-E_{i}}}{m_{i}!}}.} Since in the context of maximum-likelihood estimation the aim is to locate the maximum of the likelihood function without concern for its absolute value, it is convenient to work with ln ⁡ ( P ) {\displaystyle \ln(P)} : ln ⁡ P ( m ∣ E ) = ∑ i K [ ( m i ln ⁡ E i − E i ) − ln ⁡ ( m i ! ) ] . {\displaystyle \ln P(\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[(m_{i}\ln E_{i}-E_{i})-\ln(m_{i}!)].} Moreover, since ln ⁡ ( m i ! ) {\displaystyle \ln(m_{i}!)} is a constant, it does not give any additional information regarding the position of the maximum, so consider α ( m ∣ E ) = ∑ i K [ m i ln ⁡ E i − E i ] , {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}],} where α {\displaystyle \alpha } is something that shares the same maximum position as P ( m ∣ E ) {\displaystyle P(\mathbf {m} \mid \mathbf {E} )} . Now consider that E {\displaystyle \mathbf {E} } comes from a ground truth x {\displaystyle \mathbf {x} } and a measurement H {\displaystyle \mathbf {H} } which is assumed to be linear. Then E = H x , {\displaystyle \mathbf {E} =\mathbf {H} \mathbf {x} ,} where a matrix multiplication is implied. This can also be written in the form E m = ∑ n K H m n x n , {\displaystyle E_{m}=\sum _{n}^{K}H_{mn}x_{n},} where it can be seen how H {\displaystyle H} mixes or blurs the ground truth. It can also be shown that the derivative of an element of E {\displaystyle \mathbf {E} } , ( E i ) {\displaystyle (E_{i})} with respect to some other element of x j {\displaystyle x_{j}} can be written as It is easy to see this by writing a matrix H {\displaystyle \mathbf {H} } of, say, 5 × 5 and two arrays E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } of 5 elements and check it. This last equation can be interpreted as how much one element of x {\displaystyle \mathbf {x} } , say element i {\displaystyle i} , influences the other elements j ≠ i {\displaystyle j\neq i} (and of course the case i = j {\displaystyle i=j} is also taken into account). For example, in a typical case an element of the ground truth x {\displaystyle \mathbf {x} } will influence nearby elements in E {\displaystyle \mathbf {E} } but not the very distant ones (a value of 0 {\displaystyle 0} is expected on those matrix elements). Now, the key and arbitrary step: x {\displaystyle \mathbf {x} } is not known but may be estimated by x ^ {\displaystyle {\hat {\mathbf {x} }}} . Let's call x ^ old {\displaystyle {\hat {\mathbf {x} }}_{\text{old}}} and x ^ new {\displaystyle {\hat {\mathbf {x} }}_{\text{new}}} the estimated ground truths while using the RL algorithm, where the hat symbol is used to distinguish ground truth from estimator of the ground truth where ∂ ∂ x {\displaystyle {\frac {\partial }{\partial \mathbf {x} }}} stands for a K {\displaystyle K} -dimensional gradient. Performing the partial derivative of α ( m ∣ E ( x ) ) {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))} yields the following expression: ∂ α ( m ∣ E ( x ) ) ∂ x j = ∂ ∂ x j ∑ i K [ m i ln ⁡ E i − E i ] = ∑ i K [ m i E i ∂ ∂ x j E i − ∂ ∂ x j E i ] = ∑ i K ∂ E i ∂ x j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}]=\sum _{i}^{K}\left[{\frac {m_{i}}{E_{i}}}{\frac {\partial }{\partial x_{j}}}E_{i}-{\frac {\partial }{\partial x_{j}}}E_{i}\right]=\sum _{i}^{K}{\frac {\partial E_{i}}{\partial x_{j}}}\left[{\frac {m_{i}}{E_{i}}}-1\right].} By substituting (1), it follows that ∂ α ( m ∣ E ( x ) ) ∂ x j = ∑ i K H i j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}=\sum _{i}^{K}H_{ij}\left[{\frac {m_{i}}{E_{i}}}-1\right].} Note that H j i T = H i j {\displaystyle H_{ji}^{T}=H_{ij}} by the definition of a matrix transpose. And hence Since this equation is true for all j {\displaystyle j} spanning all the elements from 1 {\displaystyle 1} to K {\displaystyle K} , these K {\displaystyle K} equations may be compactly rewritten as a single vectorial equation ∂ α ( m ∣ E ( x ) ) ∂ x = H T [ m E − 1 ] , {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial \mathbf {x} }}=\mathbf {H} ^{T}\left[{\frac {\mathbf {m} }{\mathbf {E} }}-\mathbf {1} \right],} where H T {\displaystyle \mathbf {H} ^{T}} is a matrix, and m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and 1 {\displaystyle \mathbf {1} } are vectors. Now, as a seemingly arbitrary but key step, let where 1 {\displaystyle \mathbf {1} } is a vector of ones of size K {\displaystyle K} (same as m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } ), and the d
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Story (social media)

In social media, a story is a function in which the user tells a narrative or provides status messages and information in the form of short, time-limited clips in an automatically running sequence. == Definition == A story is a short sequence of images, videos, or other social media content, which can be accompanied by backgrounds, music, text, stickers, animations, filters or emojis. Social media platforms typically advance through the sequence automatically when presenting a story to a viewer. Although the sequential nature of stories can be used to tell a narrative, the pieces of a story can also be unrelated. Social media platforms that offer stories will typically have a primary story for each user which consists of everything the user posted to their story over a certain period of time, usually the most recent 24 hours. Most stories cannot be changed afterwards and are only available for a short time. Stories are almost exclusively created on a mobile device such as a smartphone or tablet computer and are usually displayed vertically. == History == In October 2013, Snapchat first introduced the story function as a series of Snaps that can together tell a narrative through a chronological order, with each Snap being viewable by all of the poster's friends and deleted after 24 hours. Stories soon surpassed private Snaps to become Snapchat's most-viewed type of post. After 2015, Snapchat introduced a feature allowing users to post private stories viewable by a chosen subset of their friends. Later other apps would copy this feature. In August 2016, Instagram introduced a stories function that deletes the content after 24 hours. Various commenters have accused the site of copying Snapchat. In February 2017, the instant messenger WhatsApp introduced the Now Status stories function in beta, which was later renamed Status. In March 2017, a story function was introduced in Facebook Messenger. In February 2018, Google launched AMP Stories, bringing a story-style format to certain Google search results on mobile devices. In August 2018, YouTube introduced a stories function that initially was limited to pictures, but was later expanded to support short video clips. The feature was shut down in June 2023. In August 2018, the GIF website Giphy introduced a story function. In March 2022, TikTok added a story feature which allowed users to create 15 second long videos that delete after 24 hours. In June 2023, Telegram CEO Pavel Durov announced stories for Telegram would be released in July 2023. In July 2023, the feature was released for premium users, and in August 2023 it was rolled out for all users. == User motivations == In 2022, a study performed by Jia-Dai (Evelyn) Lu and Jhih-Syuan (Elaine) Lin examined the various motivations for updating stories on Instagram. The researchers found a new configuration of motivations for using Instagram Stories: exploration, self-enhancement, perceived functionality, entertainment, social sharing, relationship building, novelty, and surveillance. The findings also highlighted that contribution and creation activities are likely to result in positive emotions, while creation alone predicts negative emotions while updating stories on Instagram. == Usage statistics == In 2019, around 1.5 billion people worldwide every day on average used the stories function in a social network or messenger. Younger people in particular use this function. More than 20% of people aged 18 to 24 use Instagram stories, while it is just under 2% of those over 55. In a Facebook survey of 18,000 participants from 12 countries, 68% said they used the stories function at least once a month. Stories in the areas of fashion and tourism are particularly popular. The website Fanpage Karma analyzed several Instagram accounts and determined the average reach of posts and stories per follower, concluding that posts have a higher reach than stories, which often have less than half the reach.
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Undeniable signature

An undeniable signature is a digital signature scheme which allows the signer to be selective to whom they allow to verify signatures. The scheme adds explicit signature repudiation, preventing a signer later refusing to verify a signature by omission; a situation that would devalue the signature in the eyes of the verifier. It was invented by David Chaum and Hans van Antwerpen in 1989. == Overview == In this scheme, a signer possessing a private key can publish a signature of a message. However, the signature reveals nothing to a recipient/verifier of the message and signature without taking part in either of two interactive protocols: Confirmation protocol, which confirms that a candidate is a valid signature of the message issued by the signer, identified by the public key. Disavowal protocol, which confirms that a candidate is not a valid signature of the message issued by the signer. The motivation for the scheme is to allow the signer to choose to whom signatures are verified. However, that the signer might claim the signature is invalid at any later point, by refusing to take part in verification, would devalue signatures to verifiers. The disavowal protocol distinguishes these cases removing the signer's plausible deniability. It is important that the confirmation and disavowal exchanges are not transferable. They achieve this by having the property of zero-knowledge; both parties can create transcripts of both confirmation and disavowal that are indistinguishable, to a third-party, of correct exchanges. The designated verifier signature scheme improves upon deniable signatures by allowing, for each signature, the interactive portion of the scheme to be offloaded onto another party, a designated verifier, reducing the burden on the signer. == Zero-knowledge protocol == The following protocol was suggested by David Chaum. A group, G, is chosen in which the discrete logarithm problem is intractable, and all operation in the scheme take place in this group. Commonly, this will be the finite cyclic group of order p contained in Z/nZ, with p being a large prime number; this group is equipped with the group operation of integer multiplication modulo n. An arbitrary primitive element (or generator), g, of G is chosen; computed powers of g then combine obeying fixed axioms. Alice generates a key pair, randomly chooses a private key, x, and then derives and publishes the public key, y = gx. === Message signing === Alice signs the message, m, by computing and publishing the signature, z = mx. === Confirmation (i.e., avowal) protocol === Bob wishes to verify the signature, z, of m by Alice under the key, y. Bob picks two random numbers: a and b, and uses them to blind the message, sending to Alice: c = magb. Alice picks a random number, q, uses it to blind, c, and then signing this using her private key, x, sending to Bob: s1 = cgq ands2 = s1x. Note that s1x = (cgq)x = (magb)xgqx = (mx)a(gx)b+q = zayb+q. Bob reveals a and b. Alice verifies that a and b are the correct blind values, then, if so, reveals q. Revealing these blinds makes the exchange zero knowledge. Bob verifies s1 = cgq, proving q has not been chosen dishonestly, and s2 = zayb+q, proving z is valid signature issued by Alice's key. Note that zayb+q = (mx)a(gx)b+q. Alice can cheat at step 2 by attempting to randomly guess s2. === Disavowal protocol === Alice wishes to convince Bob that z is not a valid signature of m under the key, gx; i.e., z ≠ mx. Alice and Bob have agreed an integer, k, which sets the computational burden on Alice and the likelihood that she should succeed by chance. Bob picks random values, s ∈ {0, 1, ..., k} and a, and sends: v1 = msga and v2 = zsya, where exponentiating by a is used to blind the sent values. Note that v2 = zsya = (mx)s(gx)a = v1x. Alice, using her private key, computes v1x and then the quotient, v1xv2−1 = (msga)x(zsgxa)−1 = msxz−s = (mxz−1)s. Thus, v1xv2−1 = 1, unless z ≠ mx. Alice then tests v1xv2−1 for equality against the values: (mxz−1)i for i ∈ {0, 1, …, k}; which are calculated by repeated multiplication of mxz−1 (rather than exponentiating for each i). If the test succeeds, Alice conjectures the relevant i to be s; otherwise, she conjectures random value. Where z = mx, (mxz−1)i = v1xv2−1 = 1 for all i, s is unrecoverable. Alice commits to i: she picks a random r and sends hash(r, i) to Bob. Bob reveals a. Alice confirms that a is the correct blind (i.e., v1 and v2 can be generated using it), then, if so, reveals r. Revealing these blinds makes the exchange zero knowledge. Bob checks hash(r, i) = hash(r, s), proving Alice knows s, hence z ≠ mx. If Alice attempts to cheat at step 3 by guessing s at random, the probability of succeeding is 1/(k + 1). So, if k = 1023 and the protocol is conducted ten times, her chances are 1 to 2100.
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