In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry. The convolution operation in a convolutional layer involves sliding a small window (called a kernel or filter) across the input data and computing the dot product between the values in the kernel and the input at each position. This process creates a feature map that represents detected features in the input. == Concepts == === Kernel === Kernels, also known as filters, are small matrices of weights that are learned during the training process. Each kernel is responsible for detecting a specific feature in the input data. The size of the kernel is a hyperparameter that affects the network's behavior. === Convolution === For a 2D input x {\displaystyle x} and a 2D kernel w {\displaystyle w} , the 2D convolution operation can be expressed as: y [ i , j ] = ∑ m = 0 k h − 1 ∑ n = 0 k w − 1 x [ i + m , j + n ] ⋅ w [ m , n ] {\displaystyle y[i,j]=\sum _{m=0}^{k_{h}-1}\sum _{n=0}^{k_{w}-1}x[i+m,j+n]\cdot w[m,n]} where k h {\displaystyle k_{h}} and k w {\displaystyle k_{w}} are the height and width of the kernel, respectively. This generalizes immediately to nD convolutions. Commonly used convolutions are 1D (for audio and text), 2D (for images), and 3D (for spatial objects, and videos). === Stride === Stride determines how the kernel moves across the input data. A stride of 1 means the kernel shifts by one pixel at a time, while a larger stride (e.g., 2 or 3) results in less overlap between convolutions and produces smaller output feature maps. === Padding === Padding involves adding extra pixels around the edges of the input data. It serves two main purposes: Preserving spatial dimensions: Without padding, each convolution reduces the size of the feature map. Handling border pixels: Padding ensures that border pixels are given equal importance in the convolution process. Common padding strategies include: No padding/valid padding. This strategy typically causes the output to shrink. Same padding: Any method that ensures the output size same as input size is a same padding strategy. Full padding: Any method that ensures each input entry is convolved over for the same number of times is a full padding strategy. Common padding algorithms include: Zero padding: Add zero entries to the borders of input. Mirror/reflect/symmetric padding: Reflect the input array on the border. Circular padding: Cycle the input array back to the opposite border, like a torus. The exact numbers used in convolutions is complicated, for which we refer to (Dumoulin and Visin, 2018) for details. == Variants == === Standard === The basic form of convolution as described above, where each kernel is applied to the entire input volume. === Depthwise separable === Depthwise separable convolution separates the standard convolution into two steps: depthwise convolution and pointwise convolution. The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel independently and a pointwise convolution ( 1 × 1 {\displaystyle 1\times 1} convolution) that combines the outputs of the depthwise convolution. This factorization significantly reduces computational cost. It was first developed by Laurent Sifre during an internship at Google Brain in 2013 as an architectural variation on AlexNet to improve convergence speed and model size. === Dilated === Dilated convolution, or atrous convolution, introduces gaps between kernel elements, allowing the network to capture a larger receptive field without increasing the kernel size. === Transposed === Transposed convolution, also known as deconvolution, fractionally strided convolution, and upsampling convolution, is a convolution where the output tensor is larger than its input tensor. It's often used in encoder-decoder architectures for upsampling. It's used in image generation, semantic segmentation, and super-resolution tasks. == History == The concept of convolution in neural networks was inspired by the visual cortex in biological brains. Early work by Hubel and Wiesel in the 1960s on the cat's visual system laid the groundwork for artificial convolution networks. An early convolution neural network was developed by Kunihiko Fukushima in 1969. It had mostly hand-designed kernels inspired by convolutions in mammalian vision. In 1979 he improved it to the Neocognitron, which learns all convolutional kernels by unsupervised learning (in his terminology, "self-organized by 'learning without a teacher'"). During the 1988 to 1998 period, a series of CNN were introduced by Yann LeCun et al., ending with LeNet-5 in 1998. It was an early influential CNN architecture for handwritten digit recognition, trained on the MNIST dataset, and was used in ATM. (Olshausen & Field, 1996) discovered that simple cells in the mammalian primary visual cortex implement localized, oriented, bandpass receptive fields, which could be recreated by fitting sparse linear codes for natural scenes. This was later found to also occur in the lowest-level kernels of trained CNNs. The field saw a resurgence in the 2010s with the development of deeper architectures and the availability of large datasets and powerful GPUs. AlexNet, developed by Alex Krizhevsky et al. in 2012, was a catalytic event in modern deep learning. In that year’s ImageNet competition, the AlexNet model achieved a 16% top-five error rate, significantly outperforming the next best entry, which had a 26% error rate. The network used eight trainable layers, approximately 650,000 neurons, and around 60 million parameters, highlighting the impact of deeper architectures and GPU acceleration on image recognition performance. From the 2013 ImageNet competition, most entries adopted deep convolutional neural networks, building on the success of AlexNet. Over the following years, performance steadily improved, with the top-five error rate falling from 16% in 2012 and 12% in 2013 to below 3% by 2017, as networks grew increasingly deep.
iWARP is a computer networking protocol that implements remote direct memory access (RDMA) for efficient data transfer over Internet Protocol networks. Contrary to some accounts, iWARP is not an acronym. Because iWARP is layered on Internet Engineering Task Force (IETF)-standard congestion-aware protocols such as Transmission Control Protocol (TCP) and Stream Control Transmission Protocol (SCTP), it makes few requirements on the network, and can be successfully deployed in a broad range of environments. == History == In 2007, the IETF published five Request for Comments (RFCs) that define iWARP: RFC 5040 A Remote Direct Memory Access Protocol Specification is layered over Direct Data Placement Protocol (DDP). It defines how RDMA Send, Read, and Write operations are encoded using DDP into headers on the network. RFC 5041 Direct Data Placement over Reliable Transports is layered over MPA/TCP or SCTP. It defines how received data can be directly placed into an upper layer protocols receive buffer without intermediate buffers. RFC 5042 Direct Data Placement Protocol (DDP) / Remote Direct Memory Access Protocol (RDMAP) Security analyzes security issues related to iWARP DDP and RDMAP protocol layers. RFC 5043 Stream Control Transmission Protocol (SCTP) Direct Data Placement (DDP) Adaptation defines an adaptation layer that enables DDP over SCTP. RFC 5044 Marker PDU Aligned Framing for TCP Specification defines an adaptation layer that enables preservation of DDP-level protocol record boundaries layered over the TCP reliable connected byte stream. These RFCs are based on the RDMA Consortium's specifications for RDMA over TCP. The RDMA Consortium's specifications are influenced by earlier RDMA standards, including Virtual Interface Architecture (VIA) and InfiniBand (IB). Since 2007, the IETF has published three additional RFCs that maintain and extend iWARP: RFC 6580 IANA Registries for the Remote Direct Data Placement (RDDP) Protocols published in 2012 defines IANA registries for Remote Direct Data Placement (RDDP) error codes, operation codes, and function codes. RFC 6581 Enhanced Remote Direct Memory Access (RDMA) Connection Establishment published in 2011 fixes shortcomings with iWARP connection setup. RFC 7306 Remote Direct Memory Access (RDMA) Protocol Extensions published in 2014 extends RFC 5040 with atomic operations and RDMA Write with Immediate Data. == Protocol == The main component in the iWARP protocol is the Direct Data Placement Protocol (DDP), which permits the actual zero-copy transmission. DDP itself does not perform the transmission; the underlying protocol (TCP or SCTP) does. However, TCP does not respect message boundaries; it sends data as a sequence of bytes without regard to protocol data units (PDU). In this regard, DDP itself may be better suited for SCTP, and indeed the IETF proposed a standard RDMA over SCTP. To run DDP over TCP requires a tweak known as marker PDU aligned (MPA) framing to guarantee boundaries of messages. Furthermore, DDP is not intended to be accessed directly. Instead, a separate RDMA protocol (RDMAP) provides the services to read and write data. Therefore, the entire RDMA over TCP specification is really RDMAP over DDP over either MPA/TCP or SCTP. All of these protocols can be implemented in hardware. Unlike IB, iWARP only has reliable connected communication, as this is the only service that TCP and SCTP provide. The iWARP specification omits other features of IB, such as Send with Immediate Data operations. With RFC 7306, the IETF is working to reduce these omissions. == Implementation == Because a kernel implementation of the TCP stack can be seen as a bottleneck, the protocol is typically implemented in hardware RDMA network interface controllers (rNICs). As simple data losses are rare in tightly coupled network environments, the error-correction mechanisms of TCP may be performed by software while the more frequently performed communications are handled strictly by logic embedded on the rNIC. Similarly, connections are often established entirely by software and then handed off to the hardware. Furthermore, the handling of iWARP specific protocol details is typically isolated from the TCP implementation, allowing rNICs to be used for both as RDMA offload and TCP offload (in support of traditional sockets based TCP/IP applications). The portion of the hardware implementation used for implementing the TCP protocol is known as the TCP Offload Engine (TOE). TOE itself does not prevent copying on the reception side, and must be combined with RDMA hardware for zero-copy results. The RDMA / TCP specification is a set of different wire protocols intended to be implemented in hardware (though it seems feasible to emulate it in software for compatibility but without the performance benefits). == Interfaces == iWARP is a protocol, not an implementation, but defines protocol behavior in terms of the operations that are legal for the protocol, known as Verbs. As such, iWARP does not have any single standard programming interface. However, programming interfaces tend to very closely correspond to the Verbs. Several programmatic interfaces have been proposed, including OpenFabrics Verbs, Network Direct, uDAPL, kDAPL, IT-API, and RNICPI. Implementations of some of these interfaces are available for different platforms, including Windows and Linux. == Services available == Networking services implemented over iWARP include those offered in the OpenFabrics Enterprise Distribution (OFED) by the OpenFabrics Alliance for Linux operating systems, and by Microsoft Windows via Network Direct. NVMe over Fabrics (NVMEoF) iSCSI Extensions for RDMA (iSER) Server Message Block Direct (SMB Direct) Sockets Direct Protocol (SDP) SCSI RDMA Protocol (SRP) Network File System over RDMA (NFS over RDMA) GPUDirect
A social film is a type of interactive film that is presented through the lens of social media. A social film is distributed digitally and integrates with a social networking service, such as Facebook or YouTube. It combines features of web video, social network games and social media. == Key elements == Social films are a more recent phenomenon, and, in turn, there are few precedents for their format. Although there are not many examples of this genre of film, the medium has certain identifiable elements: Casual entertainment Social media User-generated content Game mechanics Using just one of these factors or a combination of them, a social film engages viewers to interact directly with the work. This can be done through usual social media functionality like comments and ranking or adding directly to the narrative itself. Just as with memes, social film distribution relies on the viral spread enabled by social media. This is based on the viral expansion loops model, in which a viewer benefits from sharing the application with friends, exponentially creating new viewers compelled to share the application. == History == One of the first social films to be created was from the YouTube channel lonelygirl15. This social film started in 2006 and was created by Miles Beckett , Mesh Flinders, and Greg Goodfried. They used YouTube posts to create an interactive video series about a fictional character who showcased her life in a vlog format. As the videos went on, more bizarre things would keep happening to the main character, Bree, before she just stopped uploading. This channel was not only the first viral social film, but went on to be one of the first viral YouTube channels to be created. It did take a few years to see any more films in this genre, but 2011 saw many people start to try their hand at making these films. The first social film in this year was a film called Him, Her and Them which was produced and released by Murmur in April 2011. It was distributed exclusively through Facebook and promoted as the first “Facebook film.” The film is composed of short video clips and interactive slideshows, integrating Facebook's Social Graph API. Users participate via text-based additions to the story, which are viewable only by friends within their social network. In May 2011, Canon and Ron Howard teamed up to create Project Imagin8ion, which was a photo contest where photographers submitted photos and the top 8 photos would be the inspiration for a short film. This short film was called "When You Find Me" and could be found exclusively on YouTube. In July 2011, Intel and Toshiba partnered together to create Hollywood's first Social Film experience, a thriller called Inside, directed by D.J. Caruso and starring Emmy Rossum. The project is broken up into several segments across multiple social media platforms including Facebook, YouTube, and Twitter. In this instance, the audience is challenged to help Emmy Rossum's character, Christina, safely make it out of the room she's been trapped in. This particular form of social film is a major undertaking in that it combines social media activity with A-list acting talent to create a user experience that all happens in real time. Although not quite the same idea, Hollywood also started experimenting with the idea of interactive and crowd-sourced films. One of the first examples of this was a short film called "Life In A Day" directed by Kevin Macdonald and produced by Ridley Scott. Kevin asked people from all over the world to submit videos onto YouTube of what they were doing on July 24th, 2010. They combined all of the best videos that were submitted together to create one film of people doing different things all around the world, no matter how boring or simple those things seemed. They took this short to film festivals before releasing it to the public on YouTube in 2011. In August 2012, Intel and Toshiba partnered again to create The Beauty Inside, directed by Drake Doremus, starring Mary Elizabeth Winstead and Topher Grace. It's Hollywood's first social film that gives everyone in the audience a chance to play Alex, the lead role. The experience will be broken up into six filmed episodes interspersed with real-time interactive storytelling that all takes place on Alex's Facebook timeline. In August 2013, Intel and Toshiba released their third entry into the category, The Power Inside, directed by Will Speck and Josh Gordon and starring Harvey Keitel, Analeigh Tipton, and Craig Roberts. It's Hollywood's first social film that asks the audience to audition to help save or destroy the world. The experience is broken up into six filmed episodes interspersed with user-generated content and interactive storytelling on the main character's Facebook timeline. In 2015, Intel partnered with Dell for their fourth entry, What Lives Inside directed by Robert Stromberg and starring Colin Hanks, Catherine O'Hara, and J. K. Simmons. The first of four episodes was released on Hulu on March 25, 2015.
Developed at UC Berkeley, "Opinion Space" (also known as The Collective Discovery Engine) is a social media technology designed to help communities generate and exchange ideas about important issues and policies. Version 1.0 was launched on April 4, 2009, at UC Berkeley, and explored the question "Do you think legalizing marijuana is a good idea?" It has since undergone 4 different iterations, and been used in partnership with various organizations including The Occupy movement (Version 4.0, 5/24/2013) and the African Robots Network (Version 4.0, 5/25/2013). Opinion Space has also been used in collaboration with the United States State Department and the University of California's Berkeley Center for New Media (Version 2.0, 12/1/2009 and Version 3.0, 2/25/2012) to gain public perspective on foreign policy issues. Then U.S. Secretary of State Hillary Rodham Clinton explained, "Opinion Space will harness the power of connection technologies to provide a unique forum for international dialogue. This is...an opportunity to extend our engagement beyond the halls of government directly to the people of the world" (2010). The website uses data visualization and statistical analysis to present and develop public opinion and ideas. Opinion Space is a self-organizing system that uses an intuitive graphical "map" that displays patterns, trends, and insights as they emerge and employs the wisdom of crowds to identify and highlight the most insightful ideas. The system uses a game model that incorporates techniques from deliberative polling, collaborative filtering, and multidimensional visualization.
Circular thresholding is an algorithm for automatic image threshold selection in image processing. Most threshold selection algorithms assume that the values (e.g. intensities) lie on a linear scale. However, some quantities such as hue and orientation are a circular quantity, and therefore require circular thresholding algorithms. The example shows that the standard linear version of Otsu's method when applied to the hue channel of an image of blood cells fails to correctly segment the large white blood cells (leukocytes). In contrast the white blood cells are correctly segmented by the circular version of Otsu's method. == Methods == There are a relatively small number of circular image threshold selection algorithms. The following examples are all based on Otsu's method for linear histograms: (Tseng, Li and Tung 1995) smooth the circular histogram, and apply Otsu's method. The histogram is cyclically rotated so that the selected threshold is shifted to zero. Otsu's method and histogram rotation are applied iteratively until several heuristics involving class size, threshold location, and class variance are satisfied. (Wu et al. 2006) smooth the circular histogram until it contains only two peaks. The histogram is cyclically rotated so that the midpoint between the peaks is shifted to zero. Otsu's method and histogram rotation are applied iteratively until convergence of the threshold. (Lai and Rosin 2014) applied Otsu's method to the circular histogram. For the two class circular thresholding task they showed that, for a histogram with an even number of bins, the optimal solution for Otsu's criterion of within-class variance is obtained when the histogram is split into two halves. Therefore the optimal solution can be efficiently obtained in linear rather than quadratic time. == References and further reading == D.-C. Tseng, Y.-F. Li, and C.-T. Tung, Circular histogram thresholding for color image segmentation in Proc. Int. Conf. Document Anal. Recognit., 1995, pp. 673–676. J. Wu, P. Zeng, Y. Zhou, and C. Olivier, A novel color image segmentation method and its application to white blood cell image analysis in Proc. Int. Conf. Signal Process., vol. 2. 2006, pp. 16–20. Y.K. Lai, P.L. Rosin, Efficient Circular Thresholding, IEEE Trans. on Image Processing 23(3), 992–1001 (2014). doi:10.1109/TIP.2013.2297014
Content engineering is a term applied to an engineering specialty dealing with the complexities around the use of content in computer-facilitated environments. Content authoring and production, content management, content modeling, content conversion, and content use and repurposing are all areas involving this practice. It is not a specialty with wide industry recognition and is often performed on an ad hoc basis by members of software development or content production or marketing staff, but is beginning to be recognized as a necessary function in any complex content-centric project involving both content production as well as software system development mainly involving content management systems (CMS) or digital experience platforms (DXP). Content engineering tends to bridge the gap between groups involved in the production of content (publishing and editorial staff, marketing, sales, human resources) and more technologically oriented departments such as software development, or IT that put this content to use in web or other software-based environments, and requires an understanding of the issues and processes of both sides. Typically, content engineering involves extensive use of embedded XML technologies, XML being the most widespread language for representing structured content. Content management systems are a key technology often used in the practice of content engineering. == Definition == Content engineering is the practice of organizing the shape and structure of content by deploying content and metadata models, in authoring and publishing processes in a manner that meets the requirements of an organization's Content Strategy, and its implementation through the use of technology such as CMS, XML, schema markup, artificial intelligence, APIs and others. == Purpose and goal == In very general terms, content engineering practices aim to maximize the ROI of content through content reuse and improving efficiency of content marketing, content operations, content strategy. Content engineering can help address content challenges that fairly typical organizations face: Siloed content supply chains Duplicate content in a myriad of formats Inefficient content authoring workflows Chunky, unstructured content Outdated technology Technology in place does not match needs Inability to reuse content across channels (multi-channel content) Metadata and schema are not used Lack of standards for metadata Lack of findability of content for internal and external use Poor SEO performance Inability to implement personalization == Key skills == Content engineering draws on a combination of technical, strategic, and editorial competencies. Practitioners typically require proficiency across several domains: === Content modeling and information architecture === Content engineers design structured content models that define how content is created, stored, and distributed. This includes building taxonomies, ontologies, and metadata schemas that enable content reuse across channels and platforms. === Structured content and markup languages === Proficiency in XML, JSON, HTML, and schema.org markup is fundamental. Content engineers use these languages to structure content for machine readability, search engine optimization, and interoperability between systems. === Content management systems and platforms === Content engineers require working knowledge of content management systems (CMS), digital experience platforms (DXP), and headless CMS architectures. This includes configuring content types, workflows, and publishing pipelines within these systems. === Workflow design and automation === Designing and implementing content workflows - from authoring through review, approval, and distribution - is a core function. Increasingly, this involves configuring AI-assisted and agentic workflows that automate research, drafting, repurposing, and distribution tasks at scale. === Content strategy and editorial understanding === Unlike purely technical roles, content engineering requires a working understanding of content strategy, brand management, editorial standards, and audience analysis. Content engineers must translate strategic objectives into technical content structures and system configurations. === API integration and data interoperability === Content engineers work with APIs to connect content systems, analytics platforms, distribution channels, and third-party services. Understanding how content flows between systems is essential for enabling multi-channel publishing and content personalization. === Analytics and performance measurement === Measuring content effectiveness through web analytics, SEO performance data, and engagement metrics informs how content engineers refine structures, metadata, and distribution workflows. == The role of a content engineer == Content engineers bridge the divide between content strategists and producers and the developers and content managers who publish and distribute content. But rather than simply wedging themselves between these players, content engineers help define and facilitate the content structure during the entire content strategy, production and distribution cycle from beginning to end. As the role has evolved, content engineers are increasingly expected to build and manage AI-powered content systems, moving beyond traditional CMS configuration into agentic workflows that automate content research, production, and distribution. By integrating skills in business and technology, content engineers do not see content as static or finished. Rather, they look at the value of the content and how it can best be adapted and personalized to serve customers and emerging content platforms, technologies, and opportunities. === Create customer experience === Content marketing suffers from two fundamental limitations that constrain the true power and potential that a great content marketing plan can bring to a business' bottom line: Content relevance: how to make content more relevant and personalized to their audiences. The marketer and content strategist direct the customer experience itself, and the content engineer makes it happen with content structure, schema, metadata, microdata, taxonomy, and CMS topology. Content agility: Marketers who are burdened with one-size-fits-all content remain stuck managing their content rather than their customers' experience. Content engineers give marketers the "super powers" to move content-powered experiences across interfaces and personalization variants. === Break down barriers === Empower content strategists: Content engineers work with content strategists by helping them connect content not as a fixed message, but as a modular construct which can be channeled and manipulated. Enable content producers: A content engineer will work with a content producer by helping to find new sources of content and ways the content can be combined and presented. Guide and free developers: The content engineer helps translate marketing strategy into clear technical needs and functions developers can build into content management systems Enhance content management: Develop content structures that make it easier for content writers and content managers to author to a single, very usable, interface for even complex content types that might contain dozens of elements. Engineer content for success: Content engineers help all members of a marketing team work more smoothly, with the support and structures needed to get the most out of the content they produce. === Salary benchmarks === Content engineering roles command significantly higher salaries than traditional content marketing positions. In the United States, IC-level content engineers earn between $120,000 and $165,000 annually, while senior roles reach $160,000 to $220,000. Head of content engineering positions range from $200,000 to $280,000, and VP-level roles can exceed $375,000. The emergence of dedicated content engineer job postings from companies such as Exit Five reflects the growing recognition of the role as a distinct function within marketing organizations.
Malleability is a property of some cryptographic algorithms. An encryption algorithm is said to be malleable if it is possible to transform a ciphertext into another ciphertext which decrypts to a related plaintext. That is, given an encryption of a plaintext m {\displaystyle m} , it is possible to generate another ciphertext which decrypts to f ( m ) {\displaystyle f(m)} , for a known function f {\displaystyle f} , without necessarily knowing or learning m {\displaystyle m} . Malleability is often an undesirable property in a general-purpose cryptosystem, since it allows an attacker to modify the contents of a message. For example, suppose that a bank uses a stream cipher to hide its financial information, and a user sends an encrypted message containing, say, "TRANSFER $0000100.00 TO ACCOUNT #199." If an attacker can modify the message on the wire, and can guess the format of the unencrypted message, the attacker could change the amount of the transaction, or the recipient of the funds, e.g. "TRANSFER $0100000.00 TO ACCOUNT #227". Malleability does not refer to the attacker's ability to read the encrypted message. Both before and after tampering, the attacker cannot read the encrypted message. On the other hand, some cryptosystems are malleable by design. In other words, in some circumstances it may be viewed as a feature that anyone can transform an encryption of m {\displaystyle m} into a valid encryption of f ( m ) {\displaystyle f(m)} (for some restricted class of functions f {\displaystyle f} ) without necessarily learning m {\displaystyle m} . Such schemes are known as homomorphic encryption schemes. A cryptosystem may be semantically secure against chosen-plaintext attacks or even non-adaptive chosen-ciphertext attacks (CCA1) while still being malleable. However, security against adaptive chosen-ciphertext attacks (CCA2) is equivalent to non-malleability. == Example malleable cryptosystems == In a stream cipher, the ciphertext is produced by taking the exclusive or of the plaintext and a pseudorandom stream based on a secret key k {\displaystyle k} , as E ( m ) = m ⊕ S ( k ) {\displaystyle E(m)=m\oplus S(k)} . An adversary can construct an encryption of m ⊕ t {\displaystyle m\oplus t} for any t {\displaystyle t} , as E ( m ) ⊕ t = m ⊕ t ⊕ S ( k ) = E ( m ⊕ t ) {\displaystyle E(m)\oplus t=m\oplus t\oplus S(k)=E(m\oplus t)} . In the RSA cryptosystem, a plaintext m {\displaystyle m} is encrypted as E ( m ) = m e mod n {\displaystyle E(m)=m^{e}{\bmod {n}}} , where ( e , n ) {\displaystyle (e,n)} is the public key. Given such a ciphertext, an adversary can construct an encryption of m t {\displaystyle mt} for any t {\displaystyle t} , as E ( m ) ⋅ t e mod n = ( m t ) e mod n = E ( m t ) {\textstyle E(m)\cdot t^{e}{\bmod {n}}=(mt)^{e}{\bmod {n}}=E(mt)} . For this reason, RSA is commonly used together with padding methods such as OAEP or PKCS1. In the ElGamal cryptosystem, a plaintext m {\displaystyle m} is encrypted as E ( m ) = ( g b , m A b ) {\displaystyle E(m)=(g^{b},mA^{b})} , where ( g , A ) {\displaystyle (g,A)} is the public key. Given such a ciphertext ( c 1 , c 2 ) {\displaystyle (c_{1},c_{2})} , an adversary can compute ( c 1 , t ⋅ c 2 ) {\displaystyle (c_{1},t\cdot c_{2})} , which is a valid encryption of t m {\displaystyle tm} , for any t {\displaystyle t} . In contrast, the Cramer-Shoup system (which is based on ElGamal) is not malleable. In the Paillier, ElGamal, and RSA cryptosystems, it is also possible to combine several ciphertexts together in a useful way to produce a related ciphertext. In Paillier, given only the public key and an encryption of m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} , one can compute a valid encryption of their sum m 1 + m 2 {\displaystyle m_{1}+m_{2}} . In ElGamal and in RSA, one can combine encryptions of m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} to obtain a valid encryption of their product m 1 m 2 {\displaystyle m_{1}m_{2}} . Block ciphers in the cipher block chaining mode of operation, for example, are partly malleable: flipping a bit in a ciphertext block will completely mangle the plaintext it decrypts to, but will result in the same bit being flipped in the plaintext of the next block. This allows an attacker to 'sacrifice' one block of plaintext in order to change some data in the next one, possibly managing to maliciously alter the message. This is essentially the core idea of the padding oracle attack on CBC, which allows the attacker to decrypt almost an entire ciphertext without knowing the key. For this and many other reasons, a message authentication code is required to guard against any method of tampering. == Complete non-malleability == Fischlin, in 2005, defined the notion of complete non-malleability as the ability of the system to remain non-malleable while giving the adversary additional power to choose a new public key which could be a function of the original public key. In other words, the adversary shouldn't be able to come up with a ciphertext whose underlying plaintext is related to the original message through a relation that also takes public keys into account.
Cryptographic bill of materials (CBOM—also cryptography bill of materials) is a structured inventory of all cryptographic assets present in a software, firmware, device, or system. It enumerates algorithms (and parameters such as key sizes and modes), cryptographic libraries or modules, digital certificates, keys and related material, and protocols in use, and maps their relationships to the components that implement or invoke them. CBOMs are used to improve security analysis, compliance, and cryptographic agility, and are increasingly referenced in guidance for post‑quantum cryptography (PQC) migration. == Definition and scope == A CBOM inventories cryptographic primitives and materials—such as encryption and signature algorithms (with specific variants and modes), key sizes, cryptographic libraries/modules, digital certificates (e.g., X.509), keys and other related cryptographic material, and security protocols (e.g., TLS, IPsec). It also documents dependencies (for example, an application uses an algorithm provided by a library; a protocol uses several algorithms) and can capture certificate lifecycles, cryptographic module certifications (e.g., FIPS 140‑3), and policy conformance metadata. In common practice, a CBOM may be embedded within an SBOM format (such as CycloneDX) or exported as a separate, linked artifact. === Typical CBOM fields === The exact schema varies by implementation, but common fields are summarized below (see CycloneDX CBOM guide and NIST SP 1800‑38B). == Relation to SBOM == A CBOM is complementary to, but distinct from, a software bill of materials (SBOM). Whereas an SBOM lists software components and their versions, a CBOM focuses specifically on the cryptography present and how it is configured and used. For example, an SBOM might enumerate inclusion of a library such as OpenSSL, while the CBOM would identify which algorithms and parameters that library enables (e.g., RSA‑2048, ECDH P‑256, AES‑GCM) and list relevant keys and certificates. The pairing enables both supply‑chain transparency and cryptographic transparency. == History == The term and practice emerged in the early–mid 2020s alongside software‑supply‑chain transparency and PQC planning. The OWASP CycloneDX standard introduced native CBOM support (v1.6 and later), modeling algorithms, keys, certificates, and protocols as first‑class “cryptographic assets” and providing dependency semantics (uses/implements) between software and cryptography. Open tooling from industry and researchers (e.g., IBM's CBOMkit and related generators/viewers) appeared to automate discovery and representation of cryptographic use in the CycloneDX CBOM schema. == Regulatory and policy context == In the United States, policy has emphasized cryptographic inventories as a prerequisite to PQC migration. The White House's National Security Memorandum 10 (2022) directed a government‑wide transition to quantum‑resistant cryptography; the Office of Management and Budget's M‑23‑02 (November 2022) operationalized this by requiring agencies to submit a prioritized inventory of cryptographic systems (with algorithm and key details) by 4 May 2023 and annually thereafter, and tasked CISA/NSA/NIST to develop automated discovery and inventory strategies. A 2024 Office of the National Cyber Director report reiterated that a “comprehensive cryptographic inventory” is the baseline for PQC planning and must be maintained iteratively with both automated and manual discovery. NIST's NCCoE practice guide (SP 1800‑38B, preliminary draft) provides concrete methods for cryptographic discovery and documentation across enterprises, aligning with CBOM‑style representations. CISA later published a strategy to migrate federal agencies to automated cryptography discovery and inventory tools to support continuous reporting. Separately, NSA, CISA, and NIST issued joint guidance encouraging all organisations to prepare cryptographic inventories and roadmaps for PQC, beyond government environments. == Role in quantum readiness and cryptographic agility == Because large‑scale quantum computing threatens widely used public‑key algorithms (e.g., RSA, ECC), organisations are planning multi‑year transitions to post-quantum cryptography. CBOMs enable that planning by identifying where quantum‑vulnerable algorithms appear, prioritising high‑impact systems, and tracking replacements over time. A machine‑readable CBOM also supports cryptographic agility and incident response: if an algorithm, library, or certificate lifecycle becomes non‑compliant or vulnerable, the CBOM indicates which products and systems are affected and where mitigations must be applied first. == Standards and tooling == CycloneDX (OWASP): Native CBOM modelling (v1.6+) for algorithms, certificates, keys/related material, and protocols, with dependency semantics and examples. The project publishes a CBOM guide and use‑case profiles (e.g., certificate and algorithm inventories). NIST NCCoE SP 1800‑38 series: Practice guides for PQC migration include enterprise cryptographic discovery methods that produce CBOM‑like inventories and integrate multiple discovery tools. Government automation initiatives: Following M‑23‑02, CISA issued a strategy to migrate to automated cryptography discovery and inventory tools to support agency reporting and continuous inventory management. Open‑source and vendor tools: IBM's CBOMkit and related components generate, analyse, and visualise CBOMs; the IBM CBOM specification work was upstreamed into CycloneDX 1.6. === Data model and interchange (example) === CycloneDX provides machine‑readable encodings (JSON/XML) for CBOM content. The example below (subset) shows an application depending on a crypto library that provides the AES‑256‑GCM algorithm, and the application also depends on a leaf X.509 certificate. See the CycloneDX CBOM guide, JSON reference, and the “Implementation details” use‑case for the semantics of `dependsOn` and `provides`. == Relationship to cybersecurity supply chain initiatives == CBOMs complement SBOM‑focused supply‑chain transparency introduced by U.S. Executive Order 14028 and NTIA/NIST SBOM work. SBOMs document software components; CBOMs add detail on embedded cryptography to support risk management, policy compliance (e.g., disallowing deprecated algorithms), and PQC transition planning.
1DayLater was a free, web-based software that was focused on professional invoicing. The company was formed in 2009 and closed in October 2013. The main function of 1DayLater was to help users create invoices for clients. It could also be used to track time and other expenses, work to budgets, and to track projects. Multiple users could simultaneously work on the same projects together. PC Magazine (PCMag) voted 1DayLater as one of the 'Best Free Software of 2010'. == History == The software was developed by two brothers, Paul and David King; after they experienced similar frustrations while working freelance, the brothers wanted to create a product that would let them track time, expenses and business miles in a single online location. == Media coverage == 1DayLater had the following press coverage: BBC Webscape (July 2010) - Kate Russell gives her latest selection of the best sites on the World Wide Web PCMag (March 2010) - The best free software of 2010 Lifehacker (February 2010) - "A worthy addition to our 'Top Ten Tips and Tools for Freelancers'" Gigaom (February 2010) - Taking a closer look with 1DayLater The Journal (May 2009) - "Top Ten Brands of the North East" (UK) Techcrunch (January 2009) - "A 'feisty time tracking solution from the North East of England'"
A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key's security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange. == Scope == The key is what is used to encrypt data from plaintext to ciphertext. There are different methods for utilizing keys and encryption. === Symmetric cryptography === Symmetric cryptography refers to the practice of the same key being used for both encryption and decryption. === Asymmetric cryptography === Asymmetric cryptography has separate keys for encrypting and decrypting. These keys are known as the public and private keys, respectively. == Purpose == Since the key protects the confidentiality and integrity of the system, it is important to be kept secret from unauthorized parties. With public key cryptography, only the private key must be kept secret, but with symmetric cryptography, it is important to maintain the confidentiality of the key. Kerckhoff's principle states that the entire security of the cryptographic system relies on the secrecy of the key. == Key sizes == Key size is the number of bits in the key defined by the algorithm. This size defines the upper bound of the cryptographic algorithm's security. The larger the key size, the longer it will take before the key is compromised by a brute force attack. Since perfect secrecy is not feasible for key algorithms, researches are now more focused on computational security. In the past, keys were required to be a minimum of 40 bits in length, however, as technology advanced, these keys were being broken quicker and quicker. As a response, restrictions on symmetric keys were enhanced to be greater in size. Currently, 2048 bit RSA is commonly used, which is sufficient for current systems. However, current RSA key sizes would all be cracked quickly with a powerful quantum computer. "The keys used in public key cryptography have some mathematical structure. For example, public keys used in the RSA system are the product of two prime numbers. Thus public key systems require longer key lengths than symmetric systems for an equivalent level of security. 3072 bits is the suggested key length for systems based on factoring and integer discrete logarithms which aim to have security equivalent to a 128 bit symmetric cipher." == Key generation == To prevent a key from being guessed, keys need to be generated randomly and contain sufficient entropy. The problem of how to safely generate random keys is difficult and has been addressed in many ways by various cryptographic systems. A key can directly be generated by using the output of a Random Bit Generator (RBG), a system that generates a sequence of unpredictable and unbiased bits. A RBG can be used to directly produce either a symmetric key or the random output for an asymmetric key pair generation. Alternatively, a key can also be indirectly created during a key-agreement transaction, from another key or from a password. Some operating systems include tools for "collecting" entropy from the timing of unpredictable operations such as disk drive head movements. For the production of small amounts of keying material, ordinary dice provide a good source of high-quality randomness. == Establishment scheme == The security of a key is dependent on how a key is exchanged between parties. Establishing a secured communication channel is necessary so that outsiders cannot obtain the key. A key establishment scheme (or key exchange) is used to transfer an encryption key among entities. Key agreement and key transport are the two types of a key exchange scheme that are used to be remotely exchanged between entities . In a key agreement scheme, a secret key, which is used between the sender and the receiver to encrypt and decrypt information, is set up to be sent indirectly. All parties exchange information (the shared secret) that permits each party to derive the secret key material. In a key transport scheme, encrypted keying material that is chosen by the sender is transported to the receiver. Either symmetric key or asymmetric key techniques can be used in both schemes. The Diffie–Hellman key exchange and Rivest-Shamir-Adleman (RSA) are the most two widely used key exchange algorithms. In 1976, Whitfield Diffie and Martin Hellman constructed the Diffie–Hellman algorithm, which was the first public key algorithm. The Diffie–Hellman key exchange protocol allows key exchange over an insecure channel by electronically generating a shared key between two parties. On the other hand, RSA is a form of the asymmetric key system which consists of three steps: key generation, encryption, and decryption. Key confirmation delivers an assurance between the key confirmation recipient and provider that the shared keying materials are correct and established. The National Institute of Standards and Technology recommends key confirmation to be integrated into a key establishment scheme to validate its implementations. == Management == Key management concerns the generation, establishment, storage, usage and replacement of cryptographic keys. A key management system (KMS) typically includes three steps of establishing, storing and using keys. The base of security for the generation, storage, distribution, use and destruction of keys depends on successful key management protocols. == Key vs password == A password is a memorized series of characters including letters, digits, and other special symbols that are used to verify identity. It is often produced by a human user or a password management software to protect personal and sensitive information or generate cryptographic keys. Passwords are often created to be memorized by users and may contain non-random information such as dictionary words. On the other hand, a key can help strengthen password protection by implementing a cryptographic algorithm which is difficult to guess or replace the password altogether. A key is generated based on random or pseudo-random data and can often be unreadable to humans. A password is less safe than a cryptographic key due to its low entropy, randomness, and human-readable properties. However, the password may be the only secret data that is accessible to the cryptographic algorithm for information security in some applications such as securing information in storage devices. Thus, a deterministic algorithm called a key derivation function (KDF) uses a password to generate the secure cryptographic keying material to compensate for the password's weakness. Various methods such as adding a salt or key stretching may be used in the generation.
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
In cryptography, a critical security parameter (CSP) is information that is either user or system defined and is used to operate a cryptography module in processing encryption functions including cryptographic keys and authentication data, such as passwords, the disclosure or modification of which can compromise the security of a cryptographic module or the security of the information protected by the module.