Table of Contents
The PBC library needs the GMP library. Multiple ways to install PBC are provided.
This build system has been tested and works on Linux and Mac OS X with a fink installation.
$ ./configure $ make $ make install
By default the library is installed in /usr/local/lib. On some systems, this
may not be in the library path. One way to fix this is to edit
/etc/ld.so.conf and run ldconfig.
Due to its speed and simplicity, I use simple.make during development.
Naturally it is less portable.
$ make -f simple.make
PBC uses some GNU C extensions, notably nested functions.
We shall use the following notation. For our purposes, the pairing is a bilinear map from two cyclic groups, G1 and G2 to a third group GT, where each group has prime order r.
Run pbc/pbc and type:
g := rnd(G1); g;
The first line generates a random element g of the group G1,
while the second prints out the value of g. (The syntax was influenced
by bc, an arbitrary precision calculator.)
Next, enter:
h := rnd(G2); h;
This assigns h to a random element of the group G2. Actually, the default
pairing pbc uses is symmetric so G1 and G2 are in fact the same group, but in
general they are distinct. To compute the pairing applied to g and h, type:
pairing(g,h);
The order of both g and h is r. Let’s generate two random numbers between 1 and r:
a := rnd(Zr); b := rnd(Zr);
By bilinearity, the resulting output of both of these lines should be identical:
pairing(g^a,h^b); pairing(g,h)^(a*b);
This program has other features but the commands shown here should be enough to quickly and interactively experiment with many pairing-based cryptosystems using real numbers.