Have a question regarding the combination of Lightning, Schnorr and CoinJoin…

I have been working hard to understand how Lightning works.. With great help from r/bitcoin and Bitcointalk I have put together a Lightning FAQ:

The final result of my work can be found here: https://medium.com/@AudunGulbrands1/lightning-faq-67bd2b957d70#.8biw0wadf

However, some people have pointed out to me; that it might become expensive to close a Lightning channel, since this will require an on-chain transaction.

I just read the following article in Bitcoin Magazine: “The Power of Schnorr: The Signature Algorithm to Increase Bitcoin's Scale and Privacy” https://bitcoinmagazine.com/articles/the-power-of-schnorr-the-signature-algorithm-to-increase-bitcoin-s-scale-and-privacy-1460642496

To summarize; My understanding of Schnorr and CoinJoin is the following:

Schnorr will allow several signatures to be aggregated into a single, new signature.

Many inputs normally means many signatures, but Schnorr will require only one combined signature to represent all these different signatures. This means that only one signature must be included in a transaction.

CoinJoin allows different users to combine all their transactions into a single transaction.

Schnorr can enable all participants in a CoinJoin transaction to not only combine their transactions, but to also combine their signatures.

So my question is:

Can Schnorr and CoinJoin be built into Lightning in such a way that several channels can be closed with just one transaction?

So to reduce the cost of closing by having many channels share the cost of just one transaction?

submitted by /u/ABrandsen
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Bitcoin

Would quantum computing be able to deanonymize CoinJoin transactions?

Using the worst case scenario of this question, namely:

Bitcoin ECDSA algorithm would be broken. Because quantum computers can easily decrypt the private key using the public key, anyone with a quantum computer can extract Bitcoins using the corresponding public key.

Given that quantum computers would be able to obtain private keys, would they be able to deanonymize CoinJoin transactions that are already present in the blockchain?

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