Peer to Peer messaging is already applied in Bitcoin courtesy of BIP 151, but
the current way it is applied is inefficient and insecure, currently messages
transported are non-encrypted so message tampering, block delay attacks and BGP
hijacks are all valid threats using man in the middle attacks. A new BIP is
aiming at adding opportunistic encryption using
ChaCha20 as a cipher and
Poly1305 as a message authentication code, which has been lately getting
adopted in many state of the art protocol encryption schemes such as
Wireguad and tinyssh.
The computation power required for encrypting and authenticating a message using these algorithms would be almost as much the current double-SHA256 checksum.
ECDSA has been the preferred signature algorithm for most blockchain networks for verifying ownership and transfer of assets on the networks. However, this complex scheme that has been used in Bitcoin since 2008 started to show its limits. For example difficulties in producing multisignatures and added complexity in second layer Bitcoin networks like Lightning and crhoss-chain atomic swaps. Last year, a proposal called MuSig, or MultiSignature Scheme, was made. It offers many improvements over ECDSA and is probably one the most important cryptographic improvements to Bitcoin that would help increase privacy and efficiency in transactions.
Andrew Poelstra, one of the key researchers and co-author of the paper published a technical overview on this upcoming cryptographic scheme and its applications.