# Ring signature and key images for dummies?

So I think I understand the Pedersen commitment math on the curve to hide amounts, but I'm struggling to understand how ring signatures obfuscate your transaction even further.

If only one set of the inputs in a ring can be proven to equal the outputs (zero Pedersen commitment), don't you know exactly which inputs were used? I'm assuming I'm just missing some more math and I don't want to read an entire book today and hope to figure it out (I'm not good at math). My apologies if this is a stupid question.

Also, if a key image can't be directly linked to the TXO because it's a one-way function of the one-time destination keys, how does the network know that the key image included in a transaction is legitimate?

One more thing, with the Pedersen commitment: `c=r*G+a*H`

Where a is the actual amount, `r` is a random number that you generate, `G` and `H` are known points on the curve. If someone ever finds a single combination of `a`s and `r`s that result in the same `c`, can they now just print monero by using the smaller `a` as an input but the larger amount as an output? I understand that's very computationally unlikely to be found, but if only one is ever found the whole chain is screwed, right?

Sorry if these are stupid questions or if they should be asked elsewhere. I love the idea of Monero and I'm just trying to wrap my head around how it works. I think asking someone here who knows to explain it would do me more good than trying to learn from the whitepaper or a book.

If only one set of the inputs in a ring can be proven to equal the outputs (zero pederson commitment), don't you know exactly which inputs were used? I'm assuming I'm just missing some more math...

See this answer which details well: https://monero.stackexchange.com/a/6797/7493

Also, if a key image can't be directly linked to the TXO because it's a one-way function of the one-time destination keys, how does the network know that the key image included in a transaction is legitimate?

And for that, see this answer: https://monero.stackexchange.com/a/12390/7493

...but if only one is ever found the whole chain is screwed, right?

Lastly, no, see this answer: https://monero.stackexchange.com/a/11214/7493

• I really appreciate you using your time to find this information for me. Sorry I asked a bunch of questions that have already been answered before. I'm still confused about this: If you are proving that the key image was calculated using the same private key that applied to the output one-time public key, then wouldn't that prove which output was real and which ones were decoys? May 29, 2022 at 18:59
• You're proving you know one of the ring members, not which. May 29, 2022 at 19:01
• Aha! Hot damn monero is neat. Thank you again for all your help! You rock! May 29, 2022 at 19:03