bplib 0.0.5

A bilinear pairing library for petlib.

The bplib is a library implementing support for computations on groups supporting bilinear pairings, as used in modern cryptography.

It is based on the OpenPairing library by Diego Aranha (https://github.com/dfaranha/OpenPairing), which is itself based on, and compatible with, OpenSSL math functions (bn and ec). The bplib is compatible with petlib types including petlib.bn and the group G1 is a petlib.ec EC group. Along with petlib, they provide easy to use support for maths and ciphers used in modern Privacy Enhancing Technologies.”

A set of bilinear EC groups is defined as:

>>> G = bp.BpGroup()

Such a BpGroup describes 3 groups G1, G2 and GT such that pair(G1,G2)->GT. Generators for the groups G1 and G2 are denoted by:

>>> g1, g2 = G.gen1(), G.gen2()

The special pair operation computes to pairing into GT:

>>> gt = G.pair(g1, g2)

Operations are defined on all elements of G1, G2 or GT in a natural additive infix notation for G1 and G2, and a multiplicative notation for GT:

>>> gt6 = gt**6

As expected the pair operations is additive:

>>> G.pair(g1, 6*g2) == gt6
True
>>> G.pair(6*g1, g2) == gt6
True
>>> G.pair(2*g1, 3*g2) == gt6
True