A large quantum computer would break the elliptic curves behind Ethereum's accounts, validator signatures, blob commitments and most zero-knowledge verifiers.
The idea: Ordinary computers attack factoring and discrete logs by clever searching, and the work grows extremely fast with key size. A quantum computer can instead recast these problems as finding the repeating period of a sequence, and quantum interference finds periods efficiently. RSA, Diffie-Hellman and elliptic curves all hide their secret in exactly such a period. Lattices, codes and hashes have no hidden period known to quantum algorithms, which is why they are the replacements.
Why it matters: It's why Ethereum's roadmap moves to hash-based cryptography by around 2029.
On the map: Shor breaks secp256k1, P-256, BLS12-381 and BN254: accounts, validators, blobs and most ZK verifiers
A large, error-corrected quantum computer running Shor's algorithm would compute elliptic-curve discrete logs efficiently[1, 2]. That breaks secp256k1 (account signatures), P-256 (passkeys), BLS12-381 (validator signatures, KZG blobs) and BN254 (most ZK verifiers on Ethereum).
Hashes and symmetric crypto only face Grover's square-root speedup[3], which longer outputs absorb, which is why the post-quantum roadmap moves to hash-based signatures and proofs.
The most exposed part is accounts: any account that has sent a transaction has revealed its public key onchain, and a quantum attacker could derive the private key from it. Nobody can say when such a machine will exist, but resource estimates have fallen steadily[4], and Ethereum's roadmap targets post-quantum security before the end of the decade[5].
If any of these breaks, this breaks too.
If this breaks, these break with it.