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Cosmetic cleanups to BLS signatures section 

Miscellaneous cosmetic cleanups to the " BLS signatures" section:

1) fix section capitalisation for spec consistency
2) avoid uncapitalised "eth2" for spec consistency
3) avoid contractions (such as `PK` for `pubkey`) for spec consistency
4) various copyedits
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Justin 2020-12-06 20:56:06 +00:00 committed by Danny Ryan
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specs/phase0/beacon-chain.md
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@ -57,7 +57,7 @@
- [Crypto](#crypto)
- [`hash`](#hash)
- [`hash_tree_root`](#hash_tree_root)
- [BLS Signatures](#bls-signatures)
- [BLS signatures](#bls-signatures)
- [Predicates](#predicates)
- [`is_active_validator`](#is_active_validator)
- [`is_eligible_for_activation_queue`](#is_eligible_for_activation_queue)
@ -600,17 +600,17 @@ def bytes_to_uint64(data: bytes) -> uint64:
`def hash_tree_root(object: SSZSerializable) -> Root` is a function for hashing objects into a single root by utilizing a hash tree structure, as defined in the [SSZ spec](../../ssz/simple-serialize.md#merkleization).
#### BLS Signatures
#### BLS signatures
Eth2 makes use of BLS signatures as specified in the [IETF draft BLS specification draft-irtf-cfrg-bls-signature-04](https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04). Specifically, eth2 uses the `BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_` ciphersuite which implements the following interfaces:
The [IETF BLS signature draft standard v4](https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04) with ciphersuite `BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_` define the following functions:
- `def Sign(SK: int, message: Bytes) -> BLSSignature`
- `def Verify(PK: BLSPubkey, message: Bytes, signature: BLSSignature) -> bool`
- `def Sign(secret_key: int, message: Bytes) -> BLSSignature`
- `def Verify(pubkey: BLSPubkey, message: Bytes, signature: BLSSignature) -> bool`
- `def Aggregate(signatures: Sequence[BLSSignature]) -> BLSSignature`
- `def FastAggregateVerify(PKs: Sequence[BLSPubkey], message: Bytes, signature: BLSSignature) -> bool`
- `def AggregateVerify(PKs: Sequence[BLSPubkey], messages: Sequence[Bytes], signature: BLSSignature) -> bool`
- `def FastAggregateVerify(pubkeys: Sequence[BLSPubkey], message: Bytes, signature: BLSSignature) -> bool`
- `def AggregateVerify(pubkeys: Sequence[BLSPubkey], messages: Sequence[Bytes], signature: BLSSignature) -> bool`
Within these specifications, BLS signatures are treated as a module for notational clarity, thus to verify a signature `bls.Verify(...)` is used.
The above functions are accessed through the `bls` module, e.g. `bls.Verify`.
### Predicates