BGLS

Master: Develop:

Aggregate and Multi Signatures based on BGLS over Alt bn128 and BLS12-381

This library provides no security against side channel attacks. We provide no security guarantees of this implementation.

Design

The goal of this library is to create an efficient and secure ad hoc aggregate and multi signature scheme. It supports the curves bls12-381 and alt bn128. It implements hashing of arbitrary byte data to curve points, the standard BGLS scheme for aggregate signatures, and a custom multi signature scheme. Further documentation for the bgls scheme is contained here

Curves

See here for documentation on the supported curves.

Benchmarks

The following benchmarks are from a 3.80GHz i7-7700HQ CPU with 16GB ram. The aggregate verification is utilizing parallelization for the pairing operations. The multisignature has parellilization for the two involved pairing operations, and parallelization for the pairing checks at the end. Note, all of the benchmarks need to be updated.

For reference, the pairing operation on Altbn128 (the slowest operation involved) takes ~1.9 milliseconds.

BenchmarkPairing-8   	    1000	   1958898 ns/op

and for Bls12 its:

BenchmarkPairGT-8               	    1000	   1539918 ns/op

• Signing ~.22 milliseconds
• Signature verification ~3.1 milliseconds, using two pairings.
• Multi Signature verification ~2 milliseconds + ~1.1 microseconds per signer, two pairings + n point additions
• Aggregate Signature verification ~.36 milliseconds per signer/message pair, with n+1 pairings run in parallel. (4.45x speedup with 8 cores)

The following benchmarks are done with altbn128, before the product of pairings abstraction was included. These need to be updated.

$ go test github.com/Project-Arda/bgls/bgls/  -v -bench .
BenchmarkKeygen-8                  	    3000	    434484 ns/op
BenchmarkAltBnHashToCurve-8        	   20000	     91947 ns/op
BenchmarkSigning-8                 	   10000	    218670 ns/op
BenchmarkVerification-8            	     500	   3079415 ns/op
BenchmarkMultiVerification64-8     	    1000	   2056798 ns/op
BenchmarkMultiVerification128-8    	    1000	   2140613 ns/op
BenchmarkMultiVerification256-8    	     500	   2334271 ns/op
BenchmarkMultiVerification512-8    	     500	   2617277 ns/op
BenchmarkMultiVerification1024-8   	     500	   3243045 ns/op
BenchmarkMultiVerification2048-8   	     300	   4325183 ns/op
BenchmarkAggregateVerification-8   	    5000	    361270 ns/op
PASS
ok  	github.com/Project-Arda/bgls	31.043s

For comparison, the ed25519 implementation in go yields much faster key generation signing and single signature verification. However, at ~145 microseconds per verification, the multi signature verification is actually faster beyond ~26 signatures.

$ go test golang.org/x/crypto/ed25519 -bench .
BenchmarkKeyGeneration-8   	   30000	     51878 ns/op
BenchmarkSigning-8         	   30000	     54050 ns/op
BenchmarkVerification-8    	   10000	    145063 ns/op
PASS
ok  	golang.org/x/crypto/ed25519	5.750s

Future work

• Optimize bigint allocations.
• Add hashing to G2
• Integrations with bgls-on-evm.
• Add tests to show that none of the functions mutate data.
• More complete usage documentation.
• Add buffering for the channels used in parallelization.
• Make upstream libraries implement product of pairings algorithms

References

• Dan Boneh Methods to prevent the rogue public key attack
• Dan Boneh, Craig Gentry, Ben Lynn, and Hovav Shacham. Aggregate and verifiably encrypted signatures from bilinear maps
• Pierre-Alain Fouque and Mehdi Tibouchi. Indifferentiable Hashing to Barreto–Naehrig Curves