$ test/pbc Pairing-Based Calculator > a=rnd(G1) > b=rnd(G2) > c=pairing(a,b,A) > c [8123908995412397222629407861526403178767561618899656268507645810910469570940171 354920981464587606639849486738202862428348258236992210185732214124221043399 1895 53814264885989040711088624722149213923285853653986751240825585711288561007379288 8682665226785064897799276077038762941403815137279201878124496544381814] > r=rand(Zr) > c^r [3657835355267111517147932281225731429445945576520458069770856379924948048294629 981309298603543337841873858888814047590238596753897868865331802933313743255 5062 40043246682709738369359568183546905789682883656306401246404807118581570274256476 4691903194225678537056515561674449527079685938158385917551215894965196] > ar=a^r > pairing(ar, b) expect three arguments runtime error (error code = 0) > pairing(ar,b,A) [3657835355267111517147932281225731429445945576520458069770856379924948048294629 981309298603543337841873858888814047590238596753897868865331802933313743255 5062 40043246682709738369359568183546905789682883656306401246404807118581570274256476 4691903194225678537056515561674449527079685938158385917551215894965196] > br=b^r > pairing(a,br,A) [3657835355267111517147932281225731429445945576520458069770856379924948048294629 981309298603543337841873858888814047590238596753897868865331802933313743255 5062 40043246682709738369359568183546905789682883656306401246404807118581570274256476 4691903194225678537056515561674449527079685938158385917551215894965196]
PBC Library
The Pairing-Based Cryptography Library
News Archive 11
Mailing List Created
Hovav Shacham and I created a mailing list to discuss the development of the PBC library.
From now, if you have any PBC-related questions please send them to pbc-devel at googlegroups dot com.
The URL for the list is: http://groups.google.com/group/pbc-devel
Mon Oct 2 16:57:54 PDT 2006
pbc-0.3.9 Released
I spent most of my time since the last release on a new test program confusingly named pbc. It allows interactive testing of the library. During the development I felt I may have been better off working on performance improvements instead of squandering time on a hand-written parser and interpreter, but now that it works, I’m pleased with the results. I have yet to document it. The following session shows how it can be used:
There are actually no prompts. I edited them in afterwards to show exactly what I was typing.
I made a couple of minor fixes so that mingw can compile PBC. The resulting binaries for Windows are on the download page.
I generally get worse times with the Windows binaries, and they seem to vary more from run to run.
Fri Sep 29 12:33:33 PDT 2006
pbc-0.3.8 Released
I rewrote element_vfprintf() so it does not use GNU C extensions. PBC should now compile under mingw, though I have to test this.
Thu Sep 28 15:06:39 PDT 2006
pbc-0.3.7 Released
I implemented finite fields using Montgomery representation. Multiplication is faster, though inversion slows down a little. This improves the running time of all pairings except E (this pairing type isn’t useful anyway).
I enjoyed the challenge of writing it, but I can’t help feel that there ought be an implementation of integer mod rings in GMP. After all, GMP already has Montgomery reduction in its mpz_powm() function, and it has modular inversion routines too. With a little more coding they could easily get a fast integer mod ring library. I would much rather focus on elliptic curves.
There are some changes which may break compatibility with previous releases. I had forgotten to write element_sgn for the new finite fields code (which broke a few things). I have now fixed this, but I have changed the way it works. This means compressed elements from earlier PBC versions will be incompatible.
Also, there are minor change in the element_from_hash() functions, and they behave differently now.
Thu Sep 28 13:31:56 PDT 2006
pbc-0.3.6 Released
Besides minor bugfixes and cleanup, finite fields are now much faster, which benefits all pairings. I also added some optimizations for type F pairings in particular. I eliminated memset() calls (see previous post) in several places by introducing a flag.
I have also included a CMakeLists.txt file which allows the PBC to be built using CMake. I prefer CMake because it is faster and does not increase the package size [more on this].