Pairing-based calculator

The pbc subdirectory contains the pairing-based calculator, pbc, which is loosely based on bc, a well-known arbitrary precision calculator.

See pairing_test.pbc for an example script. Some differences: the assignment operator is :=, and newlines are ordinary whitespace and not statement terminators.

If started with the -y option, the syntax is compatible with bc: newlines are treated as statement terminators and = is assignment. Additionally, pbc displays a prompt. This mode may be easier for beginners.

Initially, the variables G1, G2, GT and Zr are represent groups associated with a particular A pairing.

An element is represented with a tree of integers, such as [[1,2], 3], or 4.

Assignments such as variable := expression; return the value of the variable.

The arithmetic operators +, -, /, *, ^ have the standard precedence. The C comparison operators and ternary operator are available.

Each statement should be terminated by a semicolon.

Comments are the same as in (original) C, or begin with "#" and end at a newline.

Some of the pbc functions:


Set the variables G1, G2, GT and Zr to the groups in a particular A pairing:


Other sample pairings can be used by replacing A with one of D, E, F, G.


Returns a random element of an algebraic structure G, e.g:

g := rnd(Zr);

Synonym: random.

pairing(g, h)

Returns the pairing applied to g and h. The element g must be an element of G1 and h of G2, e.g:

pairing(rnd(G1), rnd(G2));

Maps an element g to element of the field G, e.g:

GT([456, 789]);