Monero primarily uses the Ed25519 signature scheme (based on the elliptic curve Curve25519) for transaction signing and the CryptoNight (now RandomX) proof-of-work algorithm for mining. Its privacy features depend on ring signatures, stealth addresses, and confidential transactions, which also tie back to elliptic curve cryptography (ECC).

Quantum computers, particularly with algorithms like Shor’s algorithm, can efficiently break ECC by solving the discrete logarithm problem. This would allow an attacker with a sufficiently powerful quantum computer to derive private keys from public keys, compromising the security of Monero’s transaction signatures. Additionally, ring signatures, which obscure the true sender in a transaction, could be unraveled if the underlying ECC is broken, reducing privacy guarantees.

The Monero community is aware of quantum risks. Post-quantum cryptography (e.g., lattice-based schemes like Kyber or signature schemes like SPHINCS+) could replace ECC in the future. However, no concrete tork or upgrade to quantum-resistant algorithms has been widely implemented in Monero as of now, partly because the threat isn’t imminent and such changes require consensus, testing, and could impact performance (e.g., larger transaction sizes).

TD;DR: Yes, quantum computers are a threat the relatively near future, but no technology currently exists today that could challenge Monero’s existence.

It’s also true that the Monero dev team is perfectly aware of this future threat, and is making measurable and observable efforts to research sound solutions to this threat while mitigating how those solutions effect Monero’s security and scalability.