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I am looking through the whole Monero privacy system, wondering why Monero needs ring signature? One can use stealth address to protect the identities of both sender and receiver. Suppose the longtime public and private keys of sender are $ltsk=(x_1,x_2)$ and $ltpk=(g^{x_1},g^{x_2})$, the one time public key and private keys for one UTXO coin are $otpk=(pk=g^{x_1}g^{H((g_{x_2})^r)},R_{ot}=g^{r_{ot}})$ and $otsk={x_1+H(R_{ot}^{x_2})}$, and the lone time public key for receiver is $ltpk'=(g^{x'_1},g^{x'_2})$ (may be many receivers). If the sender needs to transfer this coin to the receiver, it just needs to use the $otsk$ to sign this transaction since $otsk$ is only known to the sender (the signature scheme can be ECDSA or Schnorr). Since anyone cannot link $otpk$ to $ltpk$, this will protect the sender's identity. So I think the ring signature is no longer needed. For the privacy of the receiver and the amount is consistent with the above system. Meanwhile, the key image is also consistent with the above system. Can anyone tell me why the ring signature is needed here? Thank you!

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  • Can anyone plz help me? Thank you!
    – Felix LL
    Oct 21 at 6:26
  • This SE site does not have the MathJax extension (as you can see from your rendered post). Please remove the MathJax formatting.
    – jtgrassie
    Oct 21 at 23:12
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Why Monero needs ring signature?

So that transaction outputs are not traceable.

From https://www.getmonero.org/resources/moneropedia/ringsignatures.html:

... ring signatures ensure that transaction outputs are untraceable. Moreover, there are no fungibility issues with Monero given that every transaction output has plausible deniability (e.g. the network can not tell which outputs are spent or unspent).

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  • Sir, I know the ring signature is to hide the source of the coin the sender spends. However, I think the goal of Monero is to hide the identities of the sender and the receiver. To accomplish this goal, only the stealth address is needed, this will make the whole system less complicated.
    – Felix LL
    Oct 24 at 8:55
  • The "goal" of Monero is private, untraceable digital cash. Without ring signatures in Monero, coins could be traced, and thus lose fungibility, a key property of cash.
    – jtgrassie
    Oct 24 at 12:30

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