260 Fortunately, \emph{hash function} seem to be more suitable for

   261 our purpose. Like encryption, hash functions scrambles data

   262 but in such a way that it is easy to calculate the output of a

   263 has function from the input. But it is hard (i.e.~practically

   264 impossible) to calculate the input from knowing the output.

   265 Therefore has functions are often called one-way functions.

   266 There are several such hashing function. For example SHA-1

   267 would has the string \pcode{"hello world"} to

   268 

   269 \begin{center}

   270 \pcode{2aae6c35c94fcfb415dbe95f408b9ce91ee846ed}

   271 \end{center}

   272 

   273 \noindent Another handy feature of hash functions is that if

   274 the input changes a little bit, the output changes 

   275 drastically. For example \pcode{"iello world"} produces under 

   276 SHA-1 the output

   277 

   278 \begin{center}

   279 \pcode{d2b1402d84e8bcef5ae18f828e43e7065b841ff1}

   280 \end{center}

   281 

   282 \noindent That means it is not predictable what the output

   283 will be from input that is ``close by''. 

   284 

   285 We can use hashes and store in the cookie the value of the

   286 counter together with its hash. We need to store both pieces

   287 of data such we can extract both components (below I will just

   288 separate them using a \pcode{"-"}). If we now read back the

   289 cookie when the client visits our webpage, we can extract the

   290 counter, hash it again and compare the result to the stored

   291 hash value inside the cookie. If these hashes disagree, then

   292 we can deduce that cookie has been tampered with.

   293 Unfortunately if they agree, we can still not be entirely sure

   294 that not a clever hacker has tampered with the cookie. The

   295 reason is that the hacker can see the clear text part of the

   296 cookie, say \pcode{3}, and its hash. It does not take much

   297 trial and error to find out that we used the SHA-1 hashing

   298 functions and then graft a cookie accordingly. This is eased

   299 by the fact that for SHA-1 many strings and corresponding

   300 hashvalues are precalculated. Type into Google for example the

   301 hash value for \pcode{"hello wolrd"} and you will actually

   302 pretty quickly find that it was generated by \pcode{"hello

   303 wolrd"}. This defeats the purpose of a hashing functions and

   304 would not help us for our web-applications. The corresponding

   305 attack is called \emph{dictionary attack}\ldots hashes are not

   306 reversed by brute force calculations, that is trying out all

   307 possible combinations.

   308 

   309 

   310 There is one ingredient missing, which happens to be called

   311 \emph{salt}. The salt is a random key, which is added to the

   312 counter before the hash is calculated. In our case we need

   313 to keep the salt secrete.  

   314 

   315 \begin{figure}[p]

   316 \lstinputlisting{../progs/App3.js}

   317 \end{figure}