feat: BW6-761 emulated pairing #846

yelhousni · 2023-10-04T14:14:36Z

Description

This PR implements BW6-761 emulated pairing circuit. It is based on #589 (mainly for the tower arithmetic). It follows https://hackmd.io/@gnark/BW6-761-changes:

da202f3 implements equation (4')
118edc3 implements equation (2)
a266590 implements equation (1)

All these equations are implemented using similar tricks to BN254 and BLS12-381 emulated pairings (tower hints, affine coordinates, sparser lines, iterations isolation...).
I was expecting (4') to be the optimal choice, for a single pairing, in terms of constraints but it seems not. I will need to try with the optimal Tate equations.

Todo:

~~equation (5)~~
~~equation (5')~~
equation (6) ⭐️ 7fc5925
~~equation (6')~~
~~Torus-based final exponentiation~~
(not enough multiplications in Expt for torus-based FE to be worth it vs. 46 Karabina squarings in a row)

Type of change

New feature (non-breaking change which adds functionality)

How has this been tested?

Pairing (and multi-pairing) and final exponentiation results compared to gnark-crypto. ~~This needs to change the gnark-crypto branch to feat/bw6761-pairing~~. The final chosen algorithm is the same as gnark-crypto master, so no nothing to do there anymore.

How has this been benchmarked?

Number of constraints:

	Miller Loop	Final exp	1 pairing	2 pairings
R1CS	1,548,496	1,037,242	2,585,738	3,746,835
SCS	16,520,533	11,372,377	27,892,910	39,656,303

Checklist:

I have performed a self-review of my code
I have commented my code, particularly in hard-to-understand areas
I have made corresponding changes to the documentation
I have added tests that prove my fix is effective or that my feature works
I did not modify files generated from templates
golangci-lint does not output errors locally
New and existing unit tests pass locally with my changes
Any dependent changes have been merged and published in downstream modules

std/algebra/emulated/sw_bw6761/pairing.go

std/algebra/emulated/fields_bw6761/e6_pairing.go

std/algebra/emulated/fields_bw6761/e3.go

std/algebra/emulated/fields_bw6761/e6.go

… feat/bw6761-pairing

ivokub

I think almost good. I'm not understanding the thing with Ext6.Expc1, but I guess it is some ongoing optimization? Otherwise, there is still one open issue from last review (method signature to take *baseEl instead of baseEl for consistency)

std/algebra/emulated/fields_bw6761/e3.go

std/algebra/emulated/sw_bw6761/pairing_test.go

yelhousni · 2023-10-11T00:28:24Z

I think almost good. I'm not understanding the thing with Ext6.Expc1, but I guess it is some ongoing optimization? Otherwise, there is still one open issue from last review (method signature to take *baseEl instead of baseEl for consistency)

Re-posting here for visibility #846 (comment).

github-actions · 2023-10-11T02:04:32Z

Summary

✅ Passed: 5737
❌ Failed: 0
🚧 Skipped: 21

🚧 Skipped

TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bn254/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestCircuitInclusionProof (github.com/consensys/gnark/examples/rollup)
TestCircuitUpdateAccount (github.com/consensys/gnark/examples/rollup)
TestCircuitFull (github.com/consensys/gnark/examples/rollup)
TestFrobeniusFp12 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByNonResidueFp2 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByFp2Fp6 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestIssue348UnconstrainedLimbs (github.com/consensys/gnark/std/math/emulated)
TestSolverConsistency (github.com/consensys/gnark/test)

github-actions · 2023-10-11T02:54:37Z

Summary

✅ Passed: 5737
❌ Failed: 0
🚧 Skipped: 21

🚧 Skipped

TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bn254/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestCircuitInclusionProof (github.com/consensys/gnark/examples/rollup)
TestCircuitUpdateAccount (github.com/consensys/gnark/examples/rollup)
TestCircuitFull (github.com/consensys/gnark/examples/rollup)
TestFrobeniusFp12 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByNonResidueFp2 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByFp2Fp6 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestIssue348UnconstrainedLimbs (github.com/consensys/gnark/std/math/emulated)
TestSolverConsistency (github.com/consensys/gnark/test)

ivokub · 2023-10-11T11:38:34Z

SCS cost when rebasing #749 on top of this:

OP	SCS Count
FinalExp	6008875
MillerLoop	5973754
1 pairing	11722930
2 pairing	14963190

github-actions · 2023-10-11T12:40:11Z

Summary

✅ Passed: 5737
❌ Failed: 0
🚧 Skipped: 21

🚧 Skipped

TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bn254/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestCircuitInclusionProof (github.com/consensys/gnark/examples/rollup)
TestCircuitUpdateAccount (github.com/consensys/gnark/examples/rollup)
TestCircuitFull (github.com/consensys/gnark/examples/rollup)
TestFrobeniusFp12 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByNonResidueFp2 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByFp2Fp6 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestIssue348UnconstrainedLimbs (github.com/consensys/gnark/std/math/emulated)
TestSolverConsistency (github.com/consensys/gnark/test)

github-actions · 2023-10-11T16:33:14Z

Summary

✅ Passed: 5737
❌ Failed: 0
🚧 Skipped: 21

🚧 Skipped

TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-377/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls12-381/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-315/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bls24-317/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bn254/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-633/mpcsetup)
TestContributionSerialization (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestSetupCircuit (github.com/consensys/gnark/backend/groth16/bw6-761/mpcsetup)
TestCircuitInclusionProof (github.com/consensys/gnark/examples/rollup)
TestCircuitUpdateAccount (github.com/consensys/gnark/examples/rollup)
TestCircuitFull (github.com/consensys/gnark/examples/rollup)
TestFrobeniusFp12 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByNonResidueFp2 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestMulByFp2Fp6 (github.com/consensys/gnark/std/algebra/native/fields_bls12377)
TestIssue348UnconstrainedLimbs (github.com/consensys/gnark/std/math/emulated)
TestSolverConsistency (github.com/consensys/gnark/test)

yelhousni · 2023-10-11T16:41:49Z

SCS cost when rebasing #749 on top of this:

OP SCS Count
FinalExp 6008875
MillerLoop 5973754
1 pairing 11722930
2 pairing 14963190

After rebasing #749 on top of last commit cb9ff67, I get different SCS counts (e.g. 2 pairings 16713265). Normally without #749 the SCS count reduced from 44M to 39M for 2 pairings. Otherwise, I think we're good to go with this PR.

ivokub · 2023-10-11T16:57:10Z

SCS cost when rebasing #749 on top of this:

OP SCS Count
FinalExp 6008875
MillerLoop 5973754
1 pairing 11722930
2 pairing 14963190

After rebasing #749 on top of last commit cb9ff67, I get different SCS counts (e.g. 2 pairings 16713265). Normally without #749 the SCS count reduced from 44M to 39M for 2 pairings. Otherwise, I think we're good to go with this PR.

May it be because I measured without ExpC1 call and without asserting equality to one

yelhousni · 2023-10-11T17:13:28Z

SCS cost when rebasing #749 on top of this:
OP SCS Count
FinalExp 6008875
MillerLoop 5973754
1 pairing 11722930
2 pairing 14963190

After rebasing #749 on top of last commit cb9ff67, I get different SCS counts (e.g. 2 pairings 16713265). Normally without #749 the SCS count reduced from 44M to 39M for 2 pairings. Otherwise, I think we're good to go with this PR.

May it be because I measured without ExpC1 call and without asserting equality to one

hmm even with that it's 16610107 so I'm not sure if there is a regression when combined with #749 ..

github-actions · 2023-10-12T17:16:56Z

📦 github.com/consensys/gnark/std/algebra/emulated/sw_bw6761
❌ TestFinalExponentiationTestSolve 7.28s

    pairing_test.go:61: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:61
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043109907697756569110837963364858198648652661637310544680583168 == 4043109907697756569110838191677820252800915128780054250950959763
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*FinalExponentiationCircuit).Define
        	            		pairing_test.go:47
        	Test:       	TestFinalExponentiationTestSolve

❌ TestMultiPairTestSolve 10.35s

    pairing_test.go:141: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:141
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043112557480694090907116479823769882374099025771673745203658752 == 4043112557480694090907116752333972745856101443798687026332477818
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*MultiPairCircuit).Define
        	            		pairing_test.go:118
        	Test:       	TestMultiPairTestSolve

❌ TestPairTestSolve 10.59s

    pairing_test.go:94: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:94
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043109475235519274826500990840458599565201170399850156791955456 == 4043109475235519274826501138481677465620205991927730968288058791
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*PairCircuit).Define
        	            		pairing_test.go:79
        	Test:       	TestPairTestSolve

yelhousni · 2023-10-12T17:21:45Z

📦 github.com/consensys/gnark/std/algebra/emulated/sw_bw6761 ❌ TestFinalExponentiationTestSolve 7.28s

    pairing_test.go:61: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:61
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043109907697756569110837963364858198648652661637310544680583168 == 4043109907697756569110838191677820252800915128780054250950959763
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*FinalExponentiationCircuit).Define
        	            		pairing_test.go:47
        	Test:       	TestFinalExponentiationTestSolve

❌ TestMultiPairTestSolve 10.35s

    pairing_test.go:141: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:141
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043112557480694090907116479823769882374099025771673745203658752 == 4043112557480694090907116752333972745856101443798687026332477818
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*MultiPairCircuit).Define
        	            		pairing_test.go:118
        	Test:       	TestMultiPairTestSolve

❌ TestPairTestSolve 10.59s

    pairing_test.go:94: 
        	Error Trace:	/home/runner/work/gnark/gnark/std/algebra/emulated/sw_bw6761/pairing_test.go:94
        	Error:      	Received unexpected error:
        	            	[assertIsEqual] 4043109475235519274826500990840458599565201170399850156791955456 == 4043109475235519274826501138481677465620205991927730968288058791
        	            	emulated.(*Field[...]).rsh
        	            		field_assert.go:56
        	            	emulated.(*Field[...]).assertLimbsEqualitySlow
        	            		field_assert.go:35
        	            	emulated.(*Field[...]).AssertLimbsEquality
        	            		field_assert.go:86
        	            	emulated.(*Field[...]).AssertIsEqual
        	            		field_assert.go:144
        	            	fields_bw6761.Ext3.AssertIsEqual
        	            		e3.go:382
        	            	fields_bw6761.Ext6.AssertIsEqual
        	            		e6.go:362
        	            	sw_bw6761.Pairing.AssertIsEqual
        	            		pairing.go:136
        	            	sw_bw6761.(*PairCircuit).Define
        	            		pairing_test.go:79
        	Test:       	TestPairTestSolve

Should work with Consensys/gnark-crypto#459

ivokub

LGTM

ivokub · 2023-10-12T23:24:23Z

SCS cost when rebasing #749 on top of this:
OP SCS Count
FinalExp 6008875
MillerLoop 5973754
1 pairing 11722930
2 pairing 14963190

After rebasing #749 on top of last commit cb9ff67, I get different SCS counts (e.g. 2 pairings 16713265). Normally without #749 the SCS count reduced from 44M to 39M for 2 pairings. Otherwise, I think we're good to go with this PR.

May it be because I measured without ExpC1 call and without asserting equality to one

hmm even with that it's 16610107 so I'm not sure if there is a regression when combined with #749 ..

Yes, I'm now getting the same results you are. I guess I removed too much when I was measuring :/ Or it may also be that I had some dirty state in the tree as I was debugging the dereferences.

In any case, I think the PR is good to go - we only have to merge Consensys/gnark-crypto#459 first and then update go.mod here.

Great work!

yelhousni · 2023-10-17T14:52:52Z

In any case, I think the PR is good to go - we only have to merge Consensys/gnark-crypto#459 first and then update go.mod here.

PR Consensys/gnark-crypto#459 is merged and go.mod updated here. So I'm merging and closing this.

yelhousni added 16 commits July 7, 2023 10:31

feat: add bw6 fields

90617dc

perf(bw6/pairing): hinted inverse and division in E6

cf4cf20

feat: add bw6 final exp

4e30aee

fix: bw6 field emulation

63131b7

test(emulated/bw6): sparse mul in Fp6

9da80b9

feat: add naive bw6 miller loop

a27a7fa

Merge branch 'master' into feat/bw6761-pairing

9047136

refactor: clean comments

547d5f8

fix: use M-twist (014) for emulated BW6 pairing

81499cb

perf(emulated/bw6): first loop in binary

3ea1a49

perf: naive emulated bw6 pairing working

a266590

perf(emulated/bw6): isolate last iterations in Miller loops

c2ba96f

perf(emulated/bw6): add line by line multiplication

84a83a9

perf(emulated/bw6): init second Miller loop by the first one

118edc3

perf(emulated/bw6): new development of the optimal ate pairing

da202f3

perf(emulated/bw6): use Mul istead of MulMod in tower

337c79c

yelhousni added new feature zk-evm labels Oct 4, 2023

yelhousni added this to the v0.9.0 milestone Oct 4, 2023

yelhousni requested a review from ivokub October 4, 2023 14:14

yelhousni self-assigned this Oct 4, 2023

yelhousni marked this pull request as draft October 4, 2023 14:14

ivokub requested changes Oct 5, 2023

View reviewed changes

yelhousni added 6 commits October 5, 2023 12:14

perf(emulated/bw6): manually reduce Fp12 elements

94af6c8

perf(emulated/bw6): more use of Karabina cycloSquare

9d8302c

Merge branch 'feat/bw6761-pairing' of github.com:consensys/gnark into…

77d305e

… feat/bw6761-pairing

refactor: address PR review

849d204

refactor: consolidate emulated bw6-761 pairing with other curves

996c82f

refactor: consolidate bw6-761 tower + fix GT exp tests

70715c0

yelhousni requested a review from ivokub October 5, 2023 23:35

ivokub approved these changes Oct 10, 2023

View reviewed changes

std/algebra/emulated/fields_bw6761/e3.go Outdated Show resolved Hide resolved

std/algebra/emulated/sw_bw6761/pairing_test.go Outdated Show resolved Hide resolved

yelhousni mentioned this pull request Oct 11, 2023

Optimize BW6 final exponentiation Consensys/gnark-crypto#457

Closed

yelhousni added 2 commits October 10, 2023 21:53

perf(bw6): use more efficient addchains

6c84f3d

fix(bw6): fix Expt test

bc201ea

perf(bw6): manually reducing E12 at some places yields better perf

4027ddd

chore: avoid dereferencing into existing Elements

2cddf28

yelhousni added 2 commits October 11, 2023 11:29

refactor(bw6): remove some unnecessary computations

f4d077c

perf(bw6): lines-by-acc mul gives better results than line-by-line mul

cb9ff67

fix: test final exp without gnark-crypto hack

e9ff5ac

ivokub approved these changes Oct 12, 2023

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ivokub mentioned this pull request Oct 13, 2023

chore: avoid nonnative dereferences #861

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yelhousni mentioned this pull request Oct 16, 2023

Feat: BW6-761 KZG gadget #866

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yelhousni added 2 commits October 17, 2023 10:37

Merge branch 'master' into feat/bw6761-pairing

6c478d5

chore: update gnark-crypto to latest

d183679

yelhousni merged commit 063cad6 into master Oct 17, 2023
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yelhousni deleted the feat/bw6761-pairing branch October 17, 2023 14:53

yelhousni mentioned this pull request Oct 19, 2023

Refactor(BW6-761): use revisited Ate pairing instead of Tate #876

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feat: BW6-761 emulated pairing #846

feat: BW6-761 emulated pairing #846

yelhousni commented Oct 4, 2023 •

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feat: BW6-761 emulated pairing #846

feat: BW6-761 emulated pairing #846

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yelhousni commented Oct 4, 2023 • edited Loading

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