Merge branch 'master' into update_vyper_contract

README.md

@@ -2,7 +2,9 @@
 
 [![Join the chat at https://gitter.im/ethereum/sharding](https://badges.gitter.im/ethereum/sharding.svg)](https://gitter.im/ethereum/sharding?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
 
-This repo hosts the current eth2.0 specifications. Discussions about design rationale and proposed changes can be brought up and discussed as issues. Solidified, agreed upon changes to spec can be made through pull requests. 
+To learn more about sharding and eth2.0/Serenity, see the [sharding FAQ](https://github.com/ethereum/wiki/wiki/Sharding-FAQs) and the [research compendium](https://notes.ethereum.org/s/H1PGqDhpm).
+
+This repo hosts the current eth2.0 specifications. Discussions about design rationale and proposed changes can be brought up and discussed as issues. Solidified, agreed upon changes to spec can be made through pull requests.
 
 # Specs
 

specs/bls_signature.md

@@ -14,6 +14,9 @@
     - [Helpers](#helpers)
         - [`hash_to_G2`](#hash_to_g2)
         - [`modular_squareroot`](#modular_squareroot)
+    - [Aggregation operations](#aggregation-operations)
+        - [`bls_aggregate_pubkeys`](#bls_aggregate_pubkeys)
+        - [`bls_aggregate_signatures`](#bls_aggregate_signatures)
     - [Signature verification](#signature-verification)
         - [`bls_verify`](#bls_verify)
         - [`bls_verify_multiple`](#bls_verify_multiple)
@@ -99,6 +102,16 @@ def modular_squareroot(value: int) -> int:
     return None
 ```
 
+## Aggregation operations
+
+### `bls_aggregate_pubkeys`
+
+Let `bls_aggregate_pubkeys(pubkeys: [uint384]) -> uint384` return `pubkeys[0] + .... + pubkeys[len(pubkeys)-1]`, where `+` is the elliptic curve addition operation over the G1 curve.
+
+### `bls_aggregate_signatures`
+
+Let `bls_aggregate_signatures(signatures: [[uint384]]) -> [uint384]` return `signatures[0] + .... + signatures[len(signatures)-1]`, where `+` is the elliptic curve addition operation over the G2 curve.
+
 ## Signature verification
 
 In the following `e` is the pairing function and `g` is the G1 generator with the following coordinates (see [here](https://github.com/zkcrypto/pairing/tree/master/src/bls12_381#g1)):