Bitcoin private keys exist for two distinct purposes, protecting
your funds and proving your ownership of them, they are accomplished by
distinct techniques such as signing Bitcoin transactions and signing
separate emails for distinct purposes, they are used in apps as proof of
collateral funds, airdrops, audits and others.
Signing emails with Bitcoin private keys and P2PKH addresses is well
known, but since the implementation of segwit with bech32 and P2SH modes
makes it difficult how to differentiate these three addresses, developer
Christopher Gilliard has suggested a new BIP to set a standard for
messages to be signed and checked by separate customers.
The signatures are produced with two different numbers known as
R and S,
by the process of public key cryptography, we can use mathematical
algorithms to determine that it was originally produced from a certain
private key without knowing the private key, a process with is known in
cryptography as a Signature
The formalization comes by attaching 1 byte of header data to the 64
bytes of the R and S values in the signature, this header byte will
have a value that if is between 31 and 34 indicates that this is a
address, if the value is between 35 and 38 inclusive then its a p2sh
segwit address and if between 39 and 42 then its a bech32 address.
This BIP allows Bitcoin wallets to be inter-operable as they will
use the same conventions to determine its validity, it could also support
new signature formats when future addresses formats exist.
You can read the BIP proposal here