In case of password security I often read, that the use of rainbow tables is appreciated. It is possible, that I don't get it right, but my current perspective is just confusion.  You save a couple of salts in a table, but you must reference them in the table with password hash, which allows you to rebuild the password hash. So I would do it like this:  By creating a new password, save hash ( input + salt ) into the table  Table: Password: hash, Salt reference: 123  I thought, this is used to prevent "dictionary attacks", but what happens, when the user uses a password, which is contained by the dictionary. The attacker can easily pass through.  Just a list with events, which are happening in my point of view:   User/Attacker "types" in this login data Email/Username is looked up and returns salt reference Look up salt with reference Build password Check password in table with email/username   So how can the salt matter, if it is automatically looked up? This might be a bit confusing, but in the end it makes all sense to me.
I'm having some trouble understanding the purpose of a salt to a password.  It's my understanding that the primary use is to hamper a rainbow table attack.  However, the methods I've seen to implement this don't seem to really make the problem harder.  I've seen many tutorials suggesting that the salt be used as the following:  $hash =  md5($salt.$password)   The reasoning being that the hash now maps not to the original password, but a combination of the password and the salt.  But say $salt=foo and $password=bar and $hash=3858f62230ac3c915f300c664312c63f.  Now somebody with a rainbow table could reverse the hash and come up with the input "foobar".  They could then try all combinations of passwords (f, fo, foo, ... oobar, obar, bar, ar, ar).  It might take a few more milliseconds to get the password, but not much else.  The other use I've seen is on my linux system.  In the /etc/shadow the hashed passwords are actually stored with the salt.  For example, a salt of "foo" and password of "bar" would hash to this: $1$foo$te5SBM.7C25fFDu6bIRbX1.  If a hacker somehow were able to get his hands on this file, I don't see what purpose the salt serves, since the reverse hash of te5SBM.7C25fFDu6bIRbX is known to contain "foo".  Thanks for any light anybody can shed on this.  EDIT:  Thanks for the help.  To summarize what I understand, the salt makes the hashed password more complex, thus making it much less likely to exist in a precomputed rainbow table.  What I misunderstood before was that I was assuming a rainbow table existed for ALL hashes.
If banks offer a fixed rate lower than the variable rate, is that an indication interest rates may head down? This is one of the major banks in Australia:   At present time, the variable rate is 7.80% but the fixed rate is 6.99% for one year.  And it seems most banks in Australia, if you fix the rate (at the moment), you will get a lower rate.  Is this an indication that in the eyes of the banks, that they believe the interest rates are going to down? I just ask because it seems most people in the media think the rates are going up and they've risen about 6 times in a row now.  Could it be that the banks are secretly preparing for rates to drop? Calculate sums of inverses of binomial coefficients How to calculate the sum of sequence $$\frac{1}{\binom{n}{1}}+\frac{1}{\binom{n}{2}}+\frac{1}{\binom{n}{3}}+\cdots+\frac{1}{\binom{n}{n}}=？$$ How about its limit? how to get rid of arm64 in apt W: Invalid 'Date' entry in Release file /var/lib/apt/lists/_var_cuda-repo-8-0-local_Release N: Skipping acquire of configured file 'non-free/binary-arm64/Packages' as repository 'http://repository.spotify.com stable InRelease' doesn't support architecture 'arm64' E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-updates/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-backports/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-security/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Some index files failed to download. They have been ignored, or old ones used instead.   After I installed Jetpack for Jetson tx1, my ubuntu constantly tries to fetch arm updates. Is there a way to disable this?  EDIT:   $dpkg --print-architecture amd64  $dpkg --print-foreign-architectures i386 arm64   I see that arm64 is included in foreign architectures. How do I remove it? My gaming computer is currently downloading Napoleon: Total War and Supreme Commander 2 which I purchased on Steam, and which will take some time to complete. While this download is going on, I would like to play some of my other multiplayer games on my laptop, but I would rather not interrupt the download to do so.   Is it possible to have both computers logged in at once? I know if I was playing a single player game, I could set Steam into offline mode, then resume the download on the other computer, but this won't work for multi player games. Do we have any other evidence other than red shift? Is anyone trying to disapprove inflation? Also, can red shift occur because of large distance, not only because two objects are going farther from each other? Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$. It seems that I'm missing something about this.  First of all, the series is convergent: $\lim_{n\rightarrow\infty}\frac{2^{-n-1} (n+1)^2}{2^{-n} n^2}=\frac{1}{2}$ (ratio test)  What I tried to do is to find a limit of a partial sum $\lim_{n\rightarrow\infty}S_n$ as follows: $S_n=\frac{\frac{1}{6} n (n+1) (2 n+1)}{\frac{1-\left(\frac{1}{2}\right)^n}{2 \left(1-\frac{1}{2}\right)}}$. Still, the limit is $\infty$ and I'm clearly doing something wrong. How do I root my Android device? This is a common question asked by those who want to root their phones. How exactly do I root my Android device? Are there risks involved? Just as background, I should say I am a mathematics grad student who is trying to learn some physics. I've been reading "The Theoretical Minimum" by Susskind and Hrabovsky and on page 134, they introduce  transformations. Here's the first example they use:  Consider a particle moving in the x,y plane under the influence of a potential, $V$, which depends only on the radius, with Lagrangian:   $L=\frac{m}{2}(\dot{x}^2+\dot{y}^2)-V(x^2+y^2)$  This is clearly invariant under rotations:  $x \rightarrow x\cos \theta + y\sin \theta$  $y \rightarrow -x\sin \theta + y\cos \theta$  All well and good. Now they say "consider what happens ... when the angle $\theta$ is replaced by an infinitesimal angle $\delta$." Already I could say "What the heck is $\delta$ really?", but I'm willing to play along with my intuition. Since $\delta$ is infinitesimal, we work to first order and say   $\cos \delta=1$ and $\sin \delta= \delta$.  Plugging this into our rotation formulas above, we obtain:  $x \rightarrow x+y\delta$  $y \rightarrow y-x\delta$  By differentiating, we see that:  $\dot{x} \rightarrow \dot{x}+\dot{y}\delta$  $\dot{y} \rightarrow \dot{y}-\dot{x}\delta$  Plugging these into the Lagrangian and ignoring terms higher than first order, we see that the Lagrangian is invariant under this transformation.  My main problem with all of this is that I don't understand what the physical nature of an infinitesimal transformation actually is. All I got from the above was that if you do this formal calculation by following rules like "only work to first order in $\delta$," then the Lagrangian is invariant. This is in contrast to the case where we have an actual transformation, like a rotation, where there is no question about what is going on physically.  I would also like to know how all of this relates to rigorous mathematics. In mathematics, I can't recall ever using infinitesimals in an argument or calculation, so it would be useful if there was some way of formulating the above in terms of limits/ derivatives/ differential forms (for example). I sense a connection to Lie Algebras, as the infinitesimal version of the rotation is $(I+A)$ where $I$ is the identity matrix and $A$ is an element of the Lie Algebra of $SO(2)$.   Here are some questions whose answers I believe may be useful to me (feel free to answer some or all):  -What is an infinitesimal quantity like $\delta$ to the physicist?   -Why do physicists argue using infinitesimals rather than "standard" calculus?  -What is the physical meaning of infinitesimal transformation? How does it relate to Lie Algebras?   -Is there a rigorous theoretical apparatus for justifying the computations shown above?  -What is meant by the Lagrangian being invariant under infinitesimal transformations?  If any of the questions seem too vague, please say so. Thanks in advance for your insights! What does really attracts a water stream to a charged object? I saw  by  and I was not 100% sure about the third phenomena, a statically charged object attracting a stream of water, especially because he explicitly mentioned that it is not due to the  of the water. A week later he uploaded an  all five phenomena and he says it is because of repelled equally charged ions, back up the water flow, such that the water actually falling along the charged object would be oppositely charged and therefore attracted. Here is a still image from the video illustrating this:    However this explanation seems strange to me, since this would mean that this way you could build up a charge in the water which has exited the tap (as well as in the water inside the tap as well). Therefore it should get harder to push those ions back over time, and therefore there also would be a decrease in the attraction of the water (assuming there is no other way to discharge it). I have tried a simple similar experiment, where I catched the water leaving the tap in an insulated bowl, but I did not notice a decrease in attraction.  There a couple of reasons why my experiment does not rule out his theory:   I was holding the charged (plastic) object by hand, which caused that its distance to the water stream varied, making it difficult to observe a decrease in attraction. I only conducted my experiment for roughly 30 seconds, which might be enough time for a opposite charge to build up.   The reason that he mentioned why permittivity can't cause this phenomena is because the electric field would be homogeneous and therefore the attractive and repulsive force of both dipoles of a water molecule would cancel out. However the electric field would only be homogeneous if the charged object would be an infinitely large plate, which it isn't. Thus water molecules would be attracted to the charged object. In order to make the permittivity theory more plausible I thought of maybe doing a order of magnitude calculation to see if it could generate a large enough force would be able the water stream by the observed amount. However I do not know what a good guess would be for variables such as the amount charge on the charged object and how the electric field would fall off over distance.   So, my question is whether his theory is really correct, or if the permittivity of the water can cause it. This was working perfectly on 17.10 but after upgrading to 18.04 yesterday, when the lid is closed the screen turns off but doesn't suspend properly.  I travel around a lot and immediately noticed the heat (and battery draining) when taking it out of the travel case.  I've tried uncommenting these lines in /etc/systemd/logind.conf  HandleLidSwitch=suspend HandleLidSwitchDocked=suspend   and restarted but didn't make any difference. Better HTTPS support for Stack Exchange sites Make the network profile editable on the main Stack Exchange page Currently, the Stack Exchange Network Profile links to all the network accounts and acts as a centralized profile page. Seeing that the ability to edit the profile is available from the profile pages of all *.SE sites, I think the ability to edit profiles should be available on that Network Profile page as well.  It will be consistent with the nature of the centralized profile page and will better the user experience.   EDIT: As the current Network profile, is actually the oldest profile on the Network, providing an edit option on the Network profile which links to the oldest profile edit page, would be one way to implement this. Scorched3d will not launch Scorched3d worked then stopped. Unistalled and reinstalled did not help. Running Ubuntu 16.04.04LTS. I think it was after installing new release.  I think the problem is the Ubuntu 16.04.4LTS. The newer version has no Scorched3d in the Ubuntu Software Center. I have 3 systems. After updating to new version. Scorched3D will not install and work after updating.  ron@RonsComputer:~$ sudo objdump -p $(type -p scorched3d) | grep NEEDED  NEEDED libwx_gtk2u_adv-3.0.so.0  NEEDED libwx_gtk2u_core-3.0.so.0 NEEDED libwx_baseu-3.0.so.0 NEEDED libfreetype.so.6 NEEDED libz.so.1 NEEDED libSDL-1.2.so.0 NEEDED libSDL_net-1.2.so.0 NEEDED libexpat.so.1  NEEDED libstdc++.so.6 NEEDED libm.so.6 NEEDED libgcc_s.so.1 NEEDED libpthread.so.0 NEEDED libc.so.6   ron@ron-desktop ~ $ objdump -p $(type -p scorched3d) | grep NEEDED | awk '{print $2}' | xargs -n 1 dpkg -S  libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0.2.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6.12.1 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6.12.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1.2.8 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1.2.8 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0.8.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0.8.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1.6.0 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1.6.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1 libstdc++6:amd64: /usr/share/gdb/auto-load/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21-gdb.py libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/share/gdb/auto-load/usr/lib/i386-linux-gnu/libstdc++.so.6.0.21-gdb.py libc6:amd64: /lib/x86_64-linux-gnu/libm.so.6 libc6:i386: /lib/i386-linux-gnu/libm.so.6 libgcc1:amd64: /lib/x86_64-linux-gnu/libgcc_s.so.1 libgcc1:i386: /lib/i386-linux-gnu/libgcc_s.so.1 libc6:i386: /lib/i386-linux-gnu/libpthread.so.0 libc6:amd64: /lib/x86_64-linux-gnu/libpthread.so.0 libc6:i386: /lib/i386-linux-gnu/libc.so.6 libc6:amd64: /lib/x86_64-linux-gnu/libc.so.6 ron@ron-desktop ~ $ Is 20 watts of electricity dangerous? I have a few circumstances which invlove someone being shocked with 20 watts of electricity and whether it would be deadly. So here they are:   Would 1000 volts at 20 miliamperes of AC (2MHz frequency) be dangerous or deadly? Would 1000 volts at 20 miliamperes of DC be dangerous or deadly? Would 10 Kilo volts at 2 miliamperes of AC (2MHz frequency) be dangerous or deadly? and Would 10 Kilo volts at 2 miliamperes of DC be dangerous or deadly?   Thanks for everyones help. I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework. The problem is stated as follows. Assume we have an infinite tetration as follows $$x^{x^{x^{.^{.^.}}}} \, = \, a$$ With a given $a$ find $x$. The next part of the problem was to discuss the convergence radius of a. If a is too big or too small the tetration does not converge. Below is my humble stab at the problem.  My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius. I) Initial discussion At the start it is obvious that the tetration converges when $a=1$ (just set $x=1$) Now after some computer hardwork it seems that the tetration fails to converge when a is roughly larger than 3. II) Algebraic manipulation $$ x^{x^{x^{.^{.^.}}}} \, = \, a$$ This is the same as $$ x^a \, = \, a$$ $$ \log_a(x^a) \, = \, \log_a(a)$$ $$ \log_a(x) \, = \, \frac{1}{a}$$ $$ x \, = \, a^{\frac{1}{a}}$$ Now, if we let $a=2$ then $x = \sqrt{2}$. After some more computational work, this seems to be correct, which makes me believe this formula is correct. III) Discsussion about convergence By looking at the derivative of $ \displaystyle \large a^{\frac{1}{a}} $ we see that the maxima occurs when $a=e$, which also seems to correspond to the inital computational work. Now I think, that the minima of $\displaystyle \large a^{1/a}$ is zero by looking at its graph, studying its derivative and the endpoints. So that my &quot;guess&quot; or work shows that it converges when $$ a \in [0 \, , \,  1/e] $$ VI) My questions Can my algebraic manipulations be justified? They seem rather sketchy taking the a`th logarithm and so on . (Although they seem to &quot;magically&quot; give out the right answer) By looking at Wikipedia it seems that the tetration converge when $$ a \in \left[ 1/e \, , \, e \right] $$ This is almost what I have, why is my lower bound wrong? How can  I find the correct lower bound? Physically Identify the failed hard drive How can I copy location info from geotagged phone images to images taken with my other camera around the same time? So i did quite a big trip recently, and took lots of pictures with my DSLR and occasionally Android phone. Only after coming back did i read about the whole GPX file, tracklog options in Lightroom. meaning i don't have such a tracklog file.  The android phone did geotag most photos it took. (at least, when it got a gps fix i guess)  So my question is, is there some software or way that will automatically copy the geotag from the android's photos to photos taken on the same time with my DSLR?  Or alternatively, generate a tracklog from the geotagged data in the android pictures? Eclipse Shortcut to Split Long Strings I swear I've seen someone do this, but I can't find it in the various lists of shortcuts.  Given:  String s = "A very long ............................ String";   Is there an Eclipse shortcut to turn it into:  String s = "A very long ............................ "      + "String"; Book identification: technologically-enhanced man (1970s/80s YA)