I am  always wondering about the seemingly odd syntax $1^n$ which designates the security strength of a cryptographic algorithm.  Who invented this (odd) syntax and what was the reason for inventing it?
In my lecture, the lecturer said:      Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public key and the private (or secret) key, respectively.    My question is: When I want to implement the cryptosystem, how should I represent this $1^k$?  When I implement the key generation procedure, do I literally require callers to pass me a string of $k$ one-bits that the procedure will never use?  And, if so, why is it there in the first place?
Can't plot with gnuplot on my Mac What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for all.  $$\frac{\partial y}{\partial x}, \frac{\delta y}{\delta x}, \frac{\mathrm{d} y}{\mathrm{d} x}$$   For what I know, $\mathrm{d}$ is used as a small infinitisemal change (and I guess the straight-up letter $\mathrm{d}$ is usual notation instead of italic $d$, simply to tell the difference from a variable). Of course we also have the big delta $\Delta$ to describe a finite (non-negligible) difference. And I have some vague idea that $\partial$ is used for partial derivatives in case of e.g. three-dimensional variables. Same goes for $\delta$, which I would have sworn was the same as $\partial$ until reading this answer on Math.SE:    Then to make the confusion total I noticed an equation like $\delta Q=\mathrm{d}U+\delta W$ and read in a physics text book that:     The fact that the amount of heat [added between two states] is dependent on the path is indicated by the symbol $\delta$...   So it seems $\delta$ means something more? The text book continues and says that:     a function [like the change in internal energy] is called a state function and its change is indicated by the symbol $\mathrm{d}$...   Here I am unsure of exactly why a $\mathrm d$ refers to a state function.   So to sum it up: down to the bone of it, what is $\delta$, $\partial$ and $\mathrm{d}$ exactly, when we are talking derivatives in physics.  Addition  Especially when reading a mathematical process on a physical equation like this procedure:  $$\delta Q=\mathrm{d}U+p\mathrm{d}V \Rightarrow\\ Q=\Delta U+\int_1^2 p \mathrm{d}V$$  It appears that $\delta$ and $\mathrm{d}$ are the same thing. An integral operation handles it the same way apparently? Is there a definitive list of which episodes / scenes that they used for the classic doctors in The Day of The Doctor? How to return multiple objects from a Java method? There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  How to make it blue on black, or at least something light on something dark?  This is on Ubuntu 12.04, using bash in Gnome Terminal.  In Konsole, the blue is slightly darker, and possible to read, though could be way better. How do I perform a Perl substitution on a string while keeping the original? I'm looking for a free RAW editor/converter on Windows. Can you tell me some strong/weak points of them comparing with Capture NX and/or Adobe Photoshop Elements?       - conversion &amp; EXIF  - white balance  - registration not possible anymore   EXIF editing would be a nice bonus.  Related: I've been getting this undefined symbol building with this command line:  $ gcc test.cpp Undefined symbols:   "___gxx_personality_v0", referenced from:   etc...   test.cpp is simple and should build fine.  What is the deal? Vim-latex adds extra brackets when typing empty brackets How do I install a .tar.gz (or .tar.bz2) file? I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file? Display error message if same record exist with combination of some fields? I have taken three fields from case object called AccountName, IntegrationTo__c and SfType__c (checkbox).  I have created one case record with a specific combination of three fields.  For the second time I create a record with that combination, then  display error message only if SfType__c is true in first record otherwise allow  for record creation.  trigger AvoidDuplicate on Case(before insert)  {          set&lt;string&gt; newNameSet = new set&lt;string&gt;();     newNameSet = new set&lt;string&gt;();      set&lt;string&gt; newEmailSet = new set&lt;string&gt;();      set&lt;string&gt; dbNameSet = new set&lt;string&gt;();      set&lt;string&gt; dbEmailSet = new set&lt;string&gt;();      for(Case newLead : trigger.new){          newNameSet.add(newLead.Account.Name);          newEmailSet.add(newLead.IntegrationTo__c);      }      for(Case dbLead : [select id, Case.Account.Name, IntegrationTo__c from Case where IntegrationTo__c IN: newEmailSet OR Case.Account.Name IN: newNameSet]){          dbNameSet.add(dbLead.Account.Name);          dbEmailSet.add(dbLead.IntegrationTo__c);      }      for(Case newLead : trigger.new){          if(dbNameSet.contains(newLead.Account.Name) &amp;&amp; dbEmailSet.Contains(newLead.IntegrationTo__c))              newLead.addError('You are inserting Duplicate Case');      }  }   i wrote this this not checking the account field name and integration__c values only with combination of account and integration__c shows error @username auto-completion for comments was , and is already active on MSO.  However, it only seems to auto-complete the usernames of people who have commented on the post. According to , the list of users who can be explicitly notified also includes:   Anyone who edited the post Anyone who started a bounty on the question The &diams; moderator or  who cast a binding close vote on the question   Why not auto-complete those, as well? Will free-fall object into black hole exceed speed of light $c$ before hitting black hole surface? In Newtonian mechanics, if we throw an object in against direction of gravity with speed $v$ and it achieve max height of $h$. Now if we allow object to fall from that height $h$, it will eventually attain speed $v$ when it reach position where we launch it.   Now applying same idea to a black hole in general relativity. Speed require to escape black hole gravity is greater than $c$, so if we throw something into black hole with almost the speed of light, the object speed will exceed speed of light $c$ before hitting black hole surface! How relativity explain this? Can space-time curvature reduce speed of this freely falling object from attaining speed of light? How to fix AppArmor `could not open` error when installing php+mysql? It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest. multiple choice question on number theory E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? I'm having trouble writing a regular expression that matches valid IPv6 addresses, including those in their compressed form (with :: or leading zeros omitted from each byte pair).    Can someone suggest a regular expression that would fulfill the requirement?  I'm considering expanding each byte pair and matching the result with a simpler regex. When Ron broke his wand, why didn't he apply for Hogwarts financial aid? Historical flight data outside of the USA?