Add pairings & more tests.

README.md

@@ -85,6 +85,7 @@ const HASH_MESSAGES = ["deadbeef", "111111", "aaaaaabbbbbb"];
 - [`aggregatePublicKeys(publicKeys)`](#aggregatepublickeyspublickeys)
 - [`aggregateSignatures(signatures)`](#aggregatesignaturessignatures)
 - [`verifyMultiple(hashes, publicKeys, signature, domain)`](#verifymultiplehashes-publickeys-signature-domain)
+- [`pairing(4dPoint, 2dPoint)`](#pairing4dpoint-2dpoint)
 - [Helpers](#helpers)
 
 ##### `getPublicKey(privateKey)`
@@ -94,7 +95,7 @@ function getPublicKey(privateKey: Uint8Array | string | bigint): Uint8Array;
 - `privateKey: Uint8Array | string | bigint` will be used to generate public key.
   Public key is generated by executing scalar multiplication of a base Point(x, y) by a fixed
   integer. The result is another `Point(x, y)` which we will by default encode to hex Uint8Array.
-- Returns `Uint8Array`: endcoded publicKey for signature verification
+- Returns `Uint8Array`: encoded publicKey for signature verification
 
 ##### `sign(hash, privateKey, domain)`
 ```typescript
@@ -106,8 +107,8 @@ function sign(
 ```
 - `hash: Uint8Array | string` - message hash which would be signed
 - `privateKey: Uint8Array | string | bigint` - private key which will sign the hash
-- `domain: Uint8Array | string | bigint` - version of signature. Different domains will give different signatures. Setting a new domain in an upgraded system prevents it from being affected by the old messages and signatures.
-- Returns encoded signature.
+- `domain: Uint8Array | string | bigint` - signature version. Different domains will give different signatures. Setting a new domain in an upgraded system prevents it from being affected by the old messages and signatures.
+- Returns `Uint8Array`: encoded signature
 
 ##### `verify(hash, publicKey, signature, domain)`
 ```typescript
@@ -121,21 +122,21 @@ function verify(
 - `hash: Uint8Array | string` - message hash that needs to be verified
 - `publicKey: Uint8Array | string` - e.g. that was generated from `privateKey` by `getPublicKey`
 - `signature: Uint8Array | string` - object returned by the `sign` or `aggregateSignatures` function
-- Returns `Promise<boolean>`: `Promise<true>` if `signature == hash`; otherwise `Promise<false>`
+- Returns `Promise<boolean>`: `true` / `false` whether the signature matches hash
 
 ##### `aggregatePublicKeys(publicKeys)`
 ```typescript
 function aggregatePublicKeys(publicKeys: Uint8Array[] | string[]): Uint8Array;
 ```
 - `publicKeys: Uint8Array[] | string[]` - e.g. that have been generated from `privateKey` by `getPublicKey`
-- Returns `Uint8Array`: one aggregated public key which calculated from putted public keys
+- Returns `Uint8Array`: one aggregated public key which calculated from public keys
 
 ##### `aggregateSignatures(signatures)`
 ```typescript
 function aggregateSignatures(signatures: Uint8Array[] | string[]): Uint8Array;
 ```
 - `signatures: Uint8Array[] | string[]` - e.g. that have been generated by `sign`
-- Returns `Uint8Array`: one aggregated signature which calculated from putted signatures
+- Returns `Uint8Array`: one aggregated signature which calculated from signatures
 
 ##### `verifyMultiple(hashes, publicKeys, signature, domain)`
 ```typescript
@@ -149,7 +150,20 @@ function verifyMultiple(
 - `hashes: Uint8Array[] | string[]` - messages hashes that needs to be verified
 - `publicKeys: Uint8Array[] | string[]` - e.g. that were generated from `privateKeys` by `getPublicKey`
 - `signature: Uint8Array | string` - object returned by the `aggregateSignatures` function
-- Returns `Promise<boolean>`: `Promise<true>` if `signature == hashes`; otherwise `Promise<false>`
+- Returns `Promise<boolean>`: `true` / `false` whether the signature matches hashes
+
+##### `pairing(4dPoint, 2dPoint)`
+```typescript
+function pairing(
+  4dPoint: Point<[bigint, bigint]>,
+  2dPoint: Point<bigint>,
+  withFinalExponent: boolean = true
+): Point<[bigint, bigint, bigint, bigint, bigint, bigint, bigint, bigint, bigint, bigint, bigint, bigint]>
+```
+- `4dPoint: Point<[bigint, bigint]>` - 4d point ((`(x, x_1), (y, y_1)`))
+- `2dPoint: Point<bigint>` - simple point (`x, y` are encoded in the `bigint`).
+- `withFinalExponent: boolean` - if the flag setted as true then result will be powered by curve order else will be not.
+- Returns `Point<BigintTwelve>`: paired 12 dimensional point.
 
 ##### Helpers
 
@@ -159,6 +173,28 @@ bls.P // 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabf
 
 // Prime order
 bls.PRIME_ORDER // 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n
+
+// Base point for Hash
+bls.G1 // 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n
+// x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
+// y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
+
+// Base point for Signature
+bls.G2
+// x = 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758, 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
+// y = 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582, 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
+
+// Class for subgroup number representation
+bls.Fp
+
+// Class for subgroup two dimensional number representation
+bls.Fp2
+
+// Class for subgroup twelve dimensional number representation
+bls.Fp12
+
+// Class for elliptic curve point representation
+bls.Point
 ```
 
 ## Curve Description