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readme for finalExponentiate

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Paul Miller 2023-07-11 16:59:40 +00:00
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@ -72,7 +72,7 @@ const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c12623
const pub2 = secp256k1.getPublicKey(privHex); const pub2 = secp256k1.getPublicKey(privHex);
``` ```
#### All imports #### Everything
```typescript ```typescript
import { secp256k1, schnorr } from '@noble/curves/secp256k1'; import { secp256k1, schnorr } from '@noble/curves/secp256k1';
@ -85,6 +85,7 @@ import { pallas, vesta } from '@noble/curves/pasta';
import { bls12_381 } from '@noble/curves/bls12-381'; import { bls12_381 } from '@noble/curves/bls12-381';
import { bn254 } from '@noble/curves/bn254'; import { bn254 } from '@noble/curves/bn254';
import { jubjub } from '@noble/curves/jubjub'; import { jubjub } from '@noble/curves/jubjub';
import { bytesToHex, hexToBytes, concatBytes, utf8ToBytes } from '@noble/curves/abstract/utils';
``` ```
#### ECDSA public key recovery & ECDH #### ECDSA public key recovery & ECDH
@ -574,7 +575,12 @@ const aggSignature3 = bls.aggregateSignatures(signatures3);
const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys); const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys);
console.log({ publicKeys, signatures3, aggSignature3, isValid3 }); console.log({ publicKeys, signatures3, aggSignature3, isValid3 });
// bls.pairing(PointG1, PointG2) // pairings // Pairings, with and without final exponentiation
// bls.pairing(PointG1, PointG2);
// bls.pairing(PointG1, PointG2, false);
// bls.fields.Fp12.finalExponentiate(bls.fields.Fp12.mul(eGS, ePHm));
// Others
// bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE // bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE
// bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr // bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr
@ -768,7 +774,7 @@ const derived = hkdf(sha256, someKey, undefined, 'application', 40); // 40 bytes
const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n); const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n);
``` ```
### abstract/utils: General utilities ### abstract/utils: Useful utilities
```ts ```ts
import * as utils from '@noble/curves/abstract/utils'; import * as utils from '@noble/curves/abstract/utils';