Why does second pre-image resistance imply pre-image resistance? Definitions here:   Pre-image resistance  Given a hash value h it should be difficult to find any message m such that h = hash(m). Second pre-image resistance  Given an input m1 it should be difficult to find different input m2 such that hash(m1) = hash(m2).    says:     These properties form a hierarchy, in that collision resistance implies second pre-image resistance, which in turns implies pre-image resistance, while the converse is not true in general.   Assuming pre-image resistance is broken, we have a function pre(h) which can easily find m such that h = hash(m). How is it helpful in finding a different m2 such that hash(m1) = hash(m2)? What if pre(m1) always returns m1?  Edit. The definition on Wikipedia is not quite formal. A better explanation is .
Why does second pre-image resistance imply pre-image resistance I am studying hash functions. I can understand why collision resistance implies second preimage resistance, but I don't get why second preimage resistance should imply first preimage resistance. Could anybody be help me with this argument from Introduction to Modern Cryptography by Katz &amp; Lindell, please?   Collision resistance: This is the strongest notion and the one we have considered so far.  Second pre-image resistance: Informally speaking, a hash function is second pre-image resistant if given $s$ and $x$ it is infeasible for a probabilistic polynomial-time adversary to find $x' \ne x$ such that $H^s(x') = H^s(s)$.  Pre-image resistance: Informally, a hash function is pre-image resistant if given $s$ and $y = H^s(x)$ (but not $x$ itself) for a randomly chosen $x$, it is infeasible for a probabilistic polynomial-time adversary to find a value $x'$ such that $H^s(x') = y$. (Looking ahead to later chapters in the book, this essentially means that $H^s$ is one-way.)   [...] Likewise, any hash function that is second pre-image resistant is also pre-image resistant. This is due to the fact that if it is possible to invert $y$ and find an $x^\prime$ such that $H^s (x^\prime ) = y$ then it is possible to take $x$, compute $y = H^s (x)$ and invert it again obtaining $x^\prime$. Since the domain of $H$ is infinite, it follows that with good probability $x \neq x^\prime$. We conclude that the above three security requirements form a hierarchy with each definition implying the one below it.
I'm trying to get the subcaptions and captions in sanserif font and Uppercased. According the manual of the caption package this should be possible in the following way.However, this doesnt seem to work. Am I defining something in the wrong way here?  \documentclass{article} \usepackage{floatrow} \usepackage[demo]{graphicx} \usepackage{subfig} \usepackage{caption} \floatsetup[figure]{subcapbesideposition = top}  \captionsetup{labelfont={sf,up}, labelsep=period, format = plain, singlelinecheck = false, textfont=rm, skip = 2pt} \captionsetup[subfloat]{labelfont = {up,sf},format = plain,textfont = rm,labelformat = simple, labelsep = period}  \begin{document}   \begin{figure}[h!]   \ffigbox[\textwidth]     {\begin{subfloatrow}         \sidesubfloat[]{\includegraphics[width = 0.4\textwidth]{A.pdf}}%         \sidesubfloat[]{\includegraphics[width = 0.4\textwidth]{B.pdf}}%       \end{subfloatrow}       \begin{subfloatrow}         \sidesubfloat[]{\includegraphics[width = 0.4\textwidth]{C.pdf}}%         \sidesubfloat[]{\includegraphics[width = 0.4\textwidth]{D.pdf}}%       \end{subfloatrow}}     {\caption{this is a caption}} \end{figure}  \end{document} Calculate limiting distribution of $\frac{\sum_{i=1}^n X_i}{\sum_{i=1}^n Y_i}$ Every irreducible Polynomial is primitive or irreducible constant A formula for the roots of a solvable polynomial Let $F$ be a field and $p(x)\in F[x]$ a separable polynomial, denote $K$ as the splitting field of $p$ and assume that $K/F$ is Galois with a solvable Galois group.  I don't understand if this imply of any formula (in radicals) for the roots of $p$ (however, I do understand how a formula would imply that $p$ is solvable by roots).  Is there some kind of a way to obtain the roots of a solvable polynomial ? "Dummy Output" No sound in Ubuntu 16.04 None of the HDMI output are working, all saying "dummy output", it was working yesterday, but when I use the headphones it became soundless, with or without the headphones.  Thank you already! How do I theme a webform? This question is a bit more subjective, but I'm hoping to get some new perspective.  I'm so used to designing for certain screen size (typically 1024x768) that I find that size to not be a problem.  Expanding the size to 1280x1024 doesn't buy you enough screen real estate to make an appreciable difference, but will give me a little more breathing room.  Basically, I just expand my "grid size" and the same basic design for the slightly smaller screen still works.  However, in the last couple of projects, my clients were all using 1080p (1920x1080) screens and they wanted solutions to use as much of that real estate as possible.  1920 pixels across provides just under twice the width I am used to, and the widescreen makes some of my old go to design approaches not to work as well.  The problem I'm running into is that when presented with so much space, I'm confronted with some major problems.   How many columns should I use?  The wide-format lends itself to a 3 column split with a 2:1:1 split (i.e. the content column bigger than the other two).  However, if I go with three columns what do I do with that extra column? How do I make efficient use of the screen real estate?  There's a temptation to put everything on the screen at once, but too much information actually makes the application harder to use.  White space is important to help make sense of complex information, but too much makes related concepts look too separate. I'm usually working with web applications that have complex data, and visualization and presentation is key to making sense of the raw data.  When your user also has a large screen (at least 24"), some information is out of eyesight and you need to move the pointer a long distance. How do you make sure everything that's needed stays within the visual hot points? Simple sites like blogs actually do better when the width is constrained, which results in a lot of wasted real estate.  I kind of wonder if having the text box and the text preview side by side would be a big benefit for the admin side of that type of screen? (1:1 two-column split).   For your answers, I know almost everything in the design is "it depends".  What I'm looking for is:   General principles you use How your approach to design has changed   I'm finding that I have to retrain myself how to work with this different format.  Every bump in the resolution I've worked through to date has been about 25%: 640 to 800 (25% increase), 800 to 1024 (28% increase), and 1024 to 1280 (25% increase).  However, the jump from 1280 to 1920 is a good 50% increase in space--the equivalent from jumping from 640 straight to 1024.  There was no commonly used middle size to help learn lessons more gradually.    To help focus the question a little bit, I had a project that was somewhat similar to Atlassian JIRA, an issue management system.  There were about six different types of records the client wanted to keep, all of them could potentially be related to each other.  Gathering data wasn't the core problem, although it did play a part.  The more important side of the problem was creating a system which would suggest potential relationships between the records and helped the analysts recognize patterns in the reported incidents.  There were different types of analysts that focused on the different problem domains, and due to the nature of their exploratory type of work, they didn't know what they wanted.  They just knew they had to make sense of a lot of data, draw correlations, and characterize classes of issues.    (Originally asked here: , but told that this might be more appropriate)    For the bounty: Stretch your minds a bit.  The pat answer "Make everything bigger" has a limit to how useful the answer is.  We are talking about users who have to make sense of a lot of data and find relationships between records.  If I simply bump up the size on everything they are going to be very limited in what they can see on the screen--particularly because the vertical is so constrained. Proteins are synthesized on ribosomes from mRNA copies of regions of the DNA. But ribosomes themselves are made up of proteins (and RNA). So how could the first ribosomes have arisen? Was there previously some other way of making proteins other than by ribosomes and mRNA? The title says it all. I'd like to know how I can install software - an example is the Chromium web browser. Stack Exchange's heavy reliance on external scripts Story about a future with races Regular cast vs. static_cast vs. dynamic_cast Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it. Is Iron Man stronger than the Hulk? In Avengers: Endgame, when Hulk initially uses the new Infinity Gauntlet, it takes a tremendous effort from him (in addition to almost burning his entire arm), in order to snap his fingers and restore the world as we knew it. Yet at the end of the movie, when Iron Man uses the Gauntlet, it seems very easy for him to snap his fingers.  How was Tony able to wield the stones with such ease when Hulk was clearly struggling with it? This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How do I start writing my first unit test?  How do I unit test this code?  I need help writing this unit test.   Salesforce Stack Exchange looks for detailed, specific questions that the community can help you with, and can't write tests on your behalf. We feel that working with the resources below can help you get started, and we encourage you to make an attempt to write your test and return to SFSE with your specific questions when you encounter challenges you can't resolve. I got the brand new Custodian badge today for reviewing posts. Inspired by that, I reviewed some more suggested edits. Now I ran into a limit:     You have no more suggested edit votes today; come back in x hours.   How is that limit calculated? I made 61 reviews today which seems to be some calculated limit.  I searched for an answer on meta but found nothing helpful. I thought it was The Tommyknockers by Stephen King, but after a check with Wikipedia, it appears that's not the case.  What I remember about the story (a TV movie I think, but definitely based on a book) was that the world is created anew every night, and that the old, used up, Earth was eaten nightly by some scary creatures.  The major plot point involved some protagonists not getting onto the new world at midnight, and having to escape from the monsters that were eating up yesterday's planet.  Does this ring a bell for anyone? I'm finding it very hard to Google for. I have an HP ProBook 450 G2. Every time I shut down the computer and turn it back on after a day, the battery level decreases by about 5%. I'm sure that the computer is shut down, not in sleep or hibernate. I removed the battery from laptop and after inserting it, the battery percentage does not change. I tried updating the BIOS, disabling wake on LAN in BIOS options, and calibrating the battery several times.  Is this drain normal? If not, is it a hardware failure or can I fix it with software? A friend of mine has some very old photos where the deterioration process seems to have increased in the past few years, and the owner is worried about the preservation of these old memories.  They have been stored inside an album within plastic sleeves. The owner is not aware of the display method prior to that.   I have been informed by the owner that since being in their possession, they seem to be looking worse than when first viewed and seem to be falling apart.   He is looking for the best way to preserve these photos inside an album, but not really sure what would be the best method. I have suggested for the albums as a whole to be stored in vacuum sealed bags for now, but I'm not even sure if that is good!  I am looking for any suggestions or personal experiences from anyone who has had to deal with such photos and what they did to preserve their memories. I recently bought a new laptop with following configuration   CPU: Intel i5 2450 RAM: 8 GB DDR3 GPU: NVIDIA GeForce GTX 520 1GB   I've setup a virtual machine using VirtualBox with Windows 7 as guest. I want to use my (host's) graphics card in it but the virtual machine is only showing 128 MB of video memory.  I am using Bumblebee and start the virtual machine using   $ optirun VBoxManage startvm "Windows 7"   Please suggest me how should I use my graphics card for 3D acceleration in virtual machine.