# groups Published articles for groups. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Two's Complement and Group Theory DevFeed: [Two's Complement and Group Theory]() Original publisher: [Read original article]() Published: 2023-07-10T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [math](), [Mathematics](), [Computer science](), [Programming]() Tags: [abelian-groups](), [arithmetic](), [bits](), [boolean](), [circuits](), [computer-science](), [group-actions](), [groups](), [math](), [mathematics](), [programming](), [quotients](), [symmetry](), [twos-complement]() ### AI overview The article explains two's-complement signed integer arithmetic using group theory. It presents signed and unsigned n-bit integers as representations of the quotient group of integers modulo 2^n, clarifying why the same arithmetic circuits can operate on both. ### Source excerpt Before I discovered math, I was a first year undergrad computer science student taking Electrical Engineering 101. The first topic I learned was what bits and boolean gates are, and the second was the two's complement representation of a negative n-bit integer. At the time two's complement seemed to me like a bizarre quirk of computer programming, with minutiae you just had to memorize. If the leading bit is 1, it's negative, and otherwise it's positive. ## Group Actions and Hashing Unordered Multisets DevFeed: [Group Actions and Hashing Unordered Multisets]() Original publisher: [Read original article]() Published: 2021-10-14T08:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [hashing](), [Programming]() Tags: [abelian-groups](), [group-actions](), [group-theory](), [groups](), [hashing](), [mathematics](), [multiset](), [multisets](), [practical](), [programming](), [xor]() ### AI overview The article introduces a result by Kevin Ventullo that applies group actions to hash functions for unordered sets and multisets. It explains why incremental, order-independent hashing is useful and describes collision-related weaknesses of addition and XOR approaches. ### Source excerpt I learned of a neat result due to Kevin Ventullo that uses group actions to study the structure of hash functions for unordered sets and multisets. This piqued my interest because a while back a colleague asked me if I could think of any applications of "pure" group theory to practical computer programming that were not cryptographic in nature. He meant, not including rings, fields, or vector spaces whose definitions happen to be groups when you forget the extra structure. ## Scaling Threat Modeling Training DevFeed: [Scaling Threat Modeling Training]() Original publisher: [Read original article]() Author: Adam Published: 2019-01-02T00:00:00Z Content type: article Language: en Sources: [Shostack & Friends Blog]() Topics: [Learning](), [Security]() Tags: [classes](), [free](), [groups](), [introduction](), [linkedin](), [training]() ### AI overview The author discusses the limitations of scaling in-person threat modeling training and announces a free 42-minute Introduction to Threat Modeling for Security Professionals course on LinkedIn Learning. The article contrasts the benefits of in-person interaction with short online video lessons. ### Source excerpt For the last few years, I've been delivering in-person threat modeling training. I've trained groups ranging from 2 to 100 people at a time, and I've done classes as short as a few hours and as long as a week. ## Threat Modeling: Citizens Versus Systems DevFeed: [Threat Modeling: Citizens Versus Systems]() Original publisher: [Read original article]() Author: Adam Published: 2018-03-08T00:00:00Z Content type: opinion Language: en Sources: [Shostack & Friends Blog]() Topics: [systems](), [data]() Tags: [data](), [government](), [groups](), [privacy](), [risk](), [systems]() ### AI overview This commentary examines threat modeling centered on citizens and communities rather than only on the technologies they use. It discusses cataloging data collection, the difficulty of tracing secondary data flows, limited disclosure by organizations, and the need to account for different risk profiles, including those of immigrants and victims of intimate partner violence. ### Source excerpt [no description provided] ## (Finite) Fields -- A Primer DevFeed: [(Finite) Fields -- A Primer]() Original publisher: [Read original article]() Published: 2014-02-26T10:00:01Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic]() Tags: [complex-numbers](), [cryptography](), [euclidean-domains](), [field](), [field-characteristic](), [finite-fields](), [groups](), [ideals](), [mathematics](), [monoids](), [operations](), [polynomial-ring](), [vector-spaces]() ### AI overview This primer introduces fields as commutative rings with 0 and 1 in which every nonzero element has a multiplicative inverse. It defines the field axioms, places fields within related algebraic structures, and raises the question of finite fields. ### Source excerpt So far on this blog we've given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they're just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We'll give a list of all of the properties that go into this "simple" definition in a moment, but an even more simple way to describe a field is as a place where "arithmetic makes sense. ## Elliptic Curves as Python Objects DevFeed: [Elliptic Curves as Python Objects]() Original publisher: [Read original article]() Published: 2014-02-24T10:00:28Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Python](), [Algorithm](), [Code](), [Programming](), [classes](), [object](), [constructor](), [test](), [unit test]() Tags: [algorithm](), [classes](), [code](), [constructor](), [elliptic-curves](), [groups](), [object](), [programming](), [python](), [test](), [unit-test]() ### AI overview This tutorial translates elliptic-curve point addition from its geometric and formal description into Python code. It introduces curve and point classes, associates each point with its curve, implements relevant operators, and includes checks that points lie on smooth curves. ### Source excerpt Last time we saw a geometric version of the algorithm to add points on elliptic curves. We went quite deep into the formal setting for it (projective space $ \mathbb{P}^2$), and we spent a lot of time talking about the right way to define the "zero" object in our elliptic curve so that our issues with vertical lines would disappear. With that understanding in mind we now finally turn to code, and write classes for curves and points and implement the addition algorithm. ## Using Individual Emails to Improve Feedback and Measure Response DevFeed: [Using Individual Emails to Improve Feedback and Measure Response]() Original publisher: [Read original article]() Author: Map Published: 2014-02-07T20:55:56Z Content type: opinion Language: en Sources: [Craig Kerstiens]() Topics: [email](), [Messaging]() Tags: [communication](), [email](), [engagement](), [groups](), [productivity]() ### AI overview The article argues that individually addressed emails can produce more and more detailed responses than sending one message to a large mailing list. It recommends tailoring the number and audience of requests as feedback is refined. ### Source excerpt In a conversation with @alexbaldwin yesterday the topic of email came up, with each of us quickly diving into various observations, how its both awesome and a great form of communication/engagement, how most people still do it really bad. Alex has some good experience with it with hack design having over 100,000 subscribers. A tangent in an entirely unrelated meeting with @mschoening and others it was suggested instead of emailing a list to send out a ton of individual emails instead. Both of these reminded me that email is incredibly powerful, but taking advantage of its power has to be intentional. This is not about ways to get to inbox 0 or better manage your inflow of emails. Rather its about how to get the maximum output out of emails that you send, or minimum output depending on what you prefer. 1 email to 100 vs. 100 emails to 1 This is perhaps my favorite approach to get more efficient feedback and also know how broad an impact something has. Most smaller companies or groups within a company have a mailing list thats all@yourcompany.com or ourgroup@mycompany.com. When people want to communicate out to the entire list its a great mechanism, however when you want feedback from the entire company its not a great mechanism. The reason being is that most people will know how many are on that list and assume that someone else will pick it up. This concept is fairly common in physical settings known as the bystander effect, stating that individuals often do not offer up help to a victim when there are other bystanders preset. Finally in certain situations you'll want to hear the same thing 100 times. Hearing something once doesn't represent how much others echo that. You'll only see so many +1s on a thread, getting 100 individual responses ensure you get not only the breadth of responses but amplitude of them. FWIW, I ran a test of this sending an email to essentially all@heroku, then an individualized email in a similar form. The one directly addressed to people r ## Groups -- A Primer DevFeed: [Groups -- A Primer]() Original publisher: [Read original article]() Published: 2012-12-08T23:42:10Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [structure](), [Math and Logic](), [Cryptography]() Tags: [applications](), [group-actions](), [groups](), [lagrange](), [mathematics](), [public-key](), [set-theory](), [structure](), [symmetry](), [theory]() ### AI overview This primer introduces group theory as the study of algebraic structures that can describe operations beyond ordinary numbers. It motivates the subject through examples involving symmetry, squares, and Rubik's Cube, and notes applications including public-key cryptography, error detection, crystal structures, particle physics, and mathematical biology. ### Source excerpt The study of groups is often one's first foray into advanced mathematics. In the naivete of set theory one develops tools for describing basic objects, and through a first run at analysis one develops a certain dexterity for manipulating symbols and definitions. But it is not until the study of groups that one must step back and inspect the larger picture. The main point of that picture (and indeed the main point of a group) is that algebraic structure can be found in the most unalgebraic of settings.