BLS12-381
BLS12-381 is a paring-friendly elliptic curve.
SmartPy supports all associated Michelson types and constructions including in tests in the interpreter.
See reference BLS12 template.
Types
Scalar field Fr
An element of the scalar field Fr, used for scalar multiplication on the BLS12-381 curves G1 and G2.
Written as raw bytes, using a little-endian encoding.
See sp.TBls12_381_fr type.
Curve Points
Points on the BLS12-381 curves G1 and G2, respectively.
Written as raw bytes, using a big-endian point encoding, as specified here.
See sp.TBls12_381_g1 type.
See sp.TBls12_381_g2 type.
Operations
Convert to int
sp.to_int(<expression>)
a Convert an expression of type sp.TBls12_381_fr into sp.TInt .
Example
fr = sp.bls12_381_fr("0x2ef123703093cbbbd124e15f2054fa5781ed0b8d092ec3c6e5d76b4ca918a221")
anInt = sp.to_int(fr)
Negation
- expr
Negate a curve point or field element.
Example
g1 = sp.bls12_381_g1("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1")
g2 = sp.bls12_381_g2("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")
fr = sp.bls12_381_fr("0x2ef123703093cbbbd124e15f2054fa5781ed0b8d092ec3c6e5d76b4ca918a221")
negatedG1 = - g1
negatedG2 = - g2
negatedFr = - frAddition
expr1 + expr2
Add two curve points or field elements.
Adding sp.TBls12_381_g1 withsp.TBls12_381_g1 producessp.TBls12_381_g1
Addingsp.TBls12_381_g2 withsp.TBls12_381_g2 producessp.TBls12_381_g2
Addingsp.TBls12_381_fr withsp.TBls12_381_fr producessp.TBls12_381_fr
Example
g1 = sp.bls12_381_g1("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1")
g2 = sp.bls12_381_g2("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")
fr = sp.bls12_381_fr("0x2ef123703093cbbbd124e15f2054fa5781ed0b8d092ec3c6e5d76b4ca918a221")
resultG1 = g1 + g1
resultG2 = g2 + g2
resultFr = fr + frMultiplication
sp.mul(expr1, expr2)
Multiply a curve point or field element by a scalar field element.
Multiplying sp.TBls12_381_g1with sp.TBls12_381_fr producessp.TBls12_381_g1
Multiplying sp.TBls12_381_g2with sp.TBls12_381_fr producessp.TBls12_381_fr
Multiplying sp.TBls12_381_frwith sp.TBls12_381_fr producessp.TBls12_381_fr
Multiplying sp.TNat withsp.TBls12_381_fr producessp.TBls12_381_fr
Multiplying sp.TInt withsp.TBls12_381_fr producessp.TBls12_381_fr
Example
g1 = sp.bls12_381_g1("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1")
g2 = sp.bls12_381_g2("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")
fr = sp.bls12_381_fr("0x2ef123703093cbbbd124e15f2054fa5781ed0b8d092ec3c6e5d76b4ca918a221")
resultG1 = sp.mul(g1, fr)
resultG2 = sp.mul(g2, fr)
resultFr1 = sp.mul(fr, fr)
resultFr2 = sp.mul(sp.nat(1), fr)
resultFr3 = sp.mul(sp.int(1), fr)Pairing check
sp.pairing_check(<pairs>)
Verify that the product of pairings of the given list of points is equal to 1 in Fq12. Returns true if the list is empty.
pairs must be of type sp.TList(sp.TPair(sp.TBls12_381_g1, sp.TBls12_381_g2))
Example
listOfPairs = sp.list([
sp.pair(
sp.bls12_381_g1("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1"),
sp.bls12_381_g2("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")
),
sp.pair(
sp.bls12_381_g1("0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1"),
sp.bls12_381_g2("0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801")
)
])
isValid = sp.pairing_check(listOfPairs)