Is that proved that breaking ECDSA (Elliptic Curve Digital Signature Algorithm) as hard as solving ECDLP(Elliptic Curve Discrete Logarithm Problem)?
Is there proof that the DSA construction, also used by ECDSA, is secure assuming that discrete logarithms in the relevant group representation are difficult?
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?) I have three different 1024-bit public keys with common exponent $e$ but different moduli. A message $m$ is encrypted (without padding) using the three keys, which results in three different encrypted messages.  Given the three pairs of public keys $(N_i,e)$ and the encrypted messages $c_i=m^e\bmod N_i$ , how do I decipher the original message $m$ ? Setting DIV width and height in JavaScript Iterating through columns in table using ModelBuilder? I am unable to find any info on how to use ModelBuilder to run a certain spatial analysis function on each column in a table.  I have a table to sample locations and at each location there are a series of measures (e.g. temperature, flow rate, number of certain species).  For each of those attributes (columns in the table), I was to run the IDW function from the surface tools.  This would be easy if I had each attribute in a separate shp/feature class, but not very efficient.  I tried Iterate Feature Selection, but was unable to pass the field name as the Z value in the IDW function.  This is for ArcGIS 10.1 (Basic and Spatial Analyst license) For the following pretty straightforward task: query a list of products from a DB and present it on a webpage, consider 2 setups:  Setup1: PHP script queries. All content is built on the server and the entire page is served back to the client.  Setup2: Static HTML "page skeleton" requesting content using AJAX. Received content is parsed on the client side using Javascript and rendered using innerHTML or similar.  Of course the second setup only makes sense when you have pages, categories and tags for the client user to choose from.  I need to compare these two, at least by means of:   time it will take content to be served user experience (setup1 is delivered as a whole, setup2 is delivered in "two parts") scalability - how do the setups compare when I have 100,000 queries daily   Any thoughts on the issue will be much appreciated. solve $T(n)=T(n-1)+T(\frac{n}{2})+n$ Using the recursion tree i tried solving this: $T(n)=T(n-1)+T(\frac{n}{2})+n$; the tree has two parts (branches) one that of $T(n-1)$ and other branch is of $T(\frac{n}{2})$. But as the term T(n-1) reach higher depth, I solved that part of the tree. Finally it resulted in O$(2^n)$ is it correct or is it $O(n^2)$? How can we solve it by substitution method? One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus.  Now Schrödinger describes the electron as a wave function. His theory is able to describe all atoms (in contrast to Bohr's model), but how is the radiation problem solved? I understand that the wave has not an exact position in the time anymore. But the electron still "moves", so it has an acceleration anyway (because of vibrations or so).   Why is in this theory the electron not radiating anymore? And if it is, why doesn't the atom collapse? why is my screen black after rdp connection? After connecting from my home via remote desktop, both my screens are black when I arrive at work. The only thing I can see is a mouse pointer on one of the screens. I then seem to have only two choices: rebooting or working from a remote desktop connection, which works fine.  It did happen every time I tried last week.  However, I did the same from my laptop in a meeting room today, and I didn't have any problem. I'm a bit confused about the concept of ground, and perhaps voltage as well, particularly when trying to analyze a circuit. When I learned about Ohm's law in grade school, I learned how to apply the law to calculate current, voltage, and resistance of simple circuits.   For instance, if we were given the following circuit:    We would be could be asked to calculate the current passing through the circuit. At the time, I'd simply compute (based on the rules given) 1.5V/1Ohms=1.5A.  Later on, however, I learned that the reason the voltage of the resistor would be 1.5V is because voltage is really the difference in potential between two points, and that the difference of the voltage across the battery would be the same as that of the resistor (correct me if I'm mistaken), or 1.5V. I got confused, however, after the introduction of the concept of ground.   The first time I tried to do the current calculation for a circuit similar to the previous circuit on a simulator, the program complained about not having a ground and "floating voltage sources". After a bit of searching, I learned that circuits need ground as a reference point or for safety reasons. It was mentioned in one explanation that one can pick any node for ground, although it's customary to design circuits so there is a "easy place" to pick ground.   Thus for this circuit    I picked ground at the bottom, but would it be okay to pick ground between the 7 ohm and 2 ohm resistor - or any other place? And what would be the difference when analyzing the circuit?  I've read that there are 3 typical ground symbols with different meanings - chassis ground, earth ground, and signal ground. A lot of circuits I've seen used in exercises either use earth ground or signal ground. What purpose is there in using earth ground? What is the signal ground connected to?  Another question: since the ground is at unknown potential, wouldn't there be current flowing to or from ground to the circuit? From what I've read we treat the ground as 0V, but wouldn't there be some sort of effect because of a difference in potential of the circuit and ground? Would the effect be different depending on what ground was used?  Finally: In nodal analysis, one customarily picks a ground at the negative terminal of the battery. However, when there are multiple voltage sources, some of them are "floating". What meaning does the voltage of a floating voltage source have? My brother owns Skyrim on steam. We use Steam Family Share, but we were wondering how both of us could play it at the same time? Triggered send status queued, need to get an alert Intuition behind $k$-algebra, $k$-algebra morphisms? Intuition for uniform continuity of a function on $\mathbb{R}$ I understand the formal definition of uniform continuity of a function, and how it is different from standard continuity.  My question is: Is there an intuitive way to classify a function on $\mathbb{R}$ as being uniformly continuous, just like there is for regular continuity? I mean, that for a "nice" function $f:\mathbb{R} \to \mathbb{R}$, it is usually easy to tell if it is continuous on an interval by looking at or thinking of the graph of the function on the interval, or on all of $\mathbb{R}$. Can I do the same for uniform continuity? Can I tell that a function is uniformly continuous just by what it looks like? Ideally, this intuition would fit with the Heine-Cantor theorem for compact sets on $\mathbb{R}$. Can I create a shortcut to open a specific application on OS X? I want to create a keyboard shortcut to i.e. open Firefox while I am working in another application. I know I can use ⌘ CMD+T when I am in Firefox to open a new tab.   I haven't found a way to create that kind of shortcuts in System Preferences.  Any ideas? Windows 7 shows red "X" on network icon, but I'm connected All my properties are zero, and my array is zero, even though I have populated them with numbers and objects Merging multiple vector layers to one layer using QGIS Control custom properties How can I add remove and create a callback/event for a custom property using bpy. I have a scene, called scene, and I want to add a custom property named x, defulat value 2 (as intereger), and a callback foo, to run when it is changed. I also need to be able to read the value from it, and delete it. How do I do this? Ramanujan log-trigonometric integrals I discovered the following conjectured identity numerically while studying a family of related integrals.  Let's set $$ R^{+}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2}  \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x, \tag1 $$ $$ R^{-}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\frac{1}{\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x}} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2} \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x. \tag2 $$ We may numerically observe with at least 500 digits of precision that $$  \begin{align} &amp; R^{+}R^{-} \stackrel{?}{=}1 \tag 3 \\\\ &amp; R^{+} \stackrel{?}{=} \sqrt[\normalsize{4}]{\ln 2} \tag4 \\\\ &amp; R^{-} \stackrel{?}{=}\frac{1}{\sqrt[\normalsize{4}]{\ln 2}}. \tag5 \end{align} $$  How can we prove it?  A version of this has been sent to Eric Weisstein, these integrals are on Mathworld as . How to tell Google to crawl distinct part of the webpage? What approach should I take to make the website Google-friendly, .  The problem is that when a specific content is being requested (eg. ) user is taken to the page using scrollbar, though the surrounding content is still being loaded. How to tell Google that for this URL  only the #36 entry should be crawled.  Is there a tag or other way to select the surrounding content as irrelevant for the URL?