Quote from: 60BTC on December 05, 2019, 04:41:27 PM

Consider this situation. I generate an electrum wallet. So electrum generates multiple address's from the same seed. That means all the address are somehow connected.

Those keys are connect, but through a one-way function. Like a hash is a one-way function.

Take a look at Antonopoulous, Mastering bitcoin

Quote

D Wallets (BIP-32/BIP-44)
Deterministic wallets were developed to make it easy to derive many keys from a single "seed." The most advanced form of deterministic wallets is the HD wallet defined by the BIP-32 standard. HD wallets contain keys derived in a tree structure, such that a parent key can derive a sequence of children keys, each of which can derive a sequence of grandchildren keys, and so on, to an infinite depth. This tree structure is illustrated in Type-2 HD wallet: a tree of keys generated from a single seed.

https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05.asciidoc#hd-wallets-bip-32bip-44

There is a mathematical relation between all derived private keys from the Seed, however no one can break this mathematical relation just with a signed message.

Quote from: 60BTC on December 05, 2019, 04:41:27 PM

So if i sign a message say "This is to be signed" with Address 1 and sign the same message "This is to be signed" with Address 2 in electrum wallet and post both the signature online. Then will someone be able to recover my private key of any of the address? Please need some explanation here? I am worried and confused if we sign the same message from 2 two different address of same seed and then can the private key or seed be recovered from both signatures?

When you paste only your signed message, you paste only your Public Address, a message and a signature. The signature is only related to that message, it is not a signature which could be used with any message.
If you change one letter in your message the signature will be invalid.

You can play around here to understand how signed messages work.
https://brainwalletx.github.io/