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Package bn256 implements a particular bilinear group.

Bilinear groups are the basis of many of the new cryptographic protocols that have been proposed over the past decade. They consist of a triplet of groups (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ is a generator of the respective group). That function is called a pairing function.

This package specifically implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve as described in Its output is compatible with the implementation described in that paper.

This package previously claimed to operate at a 128-bit security level. However, recent improvements in attacks mean that is no longer true. See


branch master:

BenchmarkG1-4        	   10000	    154995 ns/op
BenchmarkG2-4        	    3000	    541503 ns/op
BenchmarkGT-4        	    1000	   1267811 ns/op
BenchmarkPairing-4   	    1000	   1630584 ns/op

branch lattices:

BenchmarkG1-4        	   20000	     92198 ns/op
BenchmarkG2-4        	    5000	    340622 ns/op
BenchmarkGT-4        	    2000	    635061 ns/op
BenchmarkPairing-4   	    1000	   1629943 ns/op

official version:

BenchmarkG1-4        	    1000	   2268491 ns/op
BenchmarkG2-4        	     300	   7227637 ns/op
BenchmarkGT-4        	     100	  15121359 ns/op
BenchmarkPairing-4   	      50	  20296164 ns/op