Shor's algorithm
A quantum algorithm that factors large integers and computes discrete logarithms in polynomial time. It is the specific reason RSA, Diffie-Hellman and elliptic-curve cryptography would fail against a sufficiently large quantum computer.
In practice
Against Bitcoin, Shor's algorithm is what would let an attacker derive a private key from an exposed public key.
Related terms
A hypothetical quantum computer large and stable enough to break deployed public-key cryptography — meaning millions of physical qubits supporting thousands of stable logical qubits. No such machine exists publicly today.
A quantum search algorithm that finds an item in an unstructured set of N in roughly √N steps. Against symmetric cryptography this halves effective key strength — a nuisance answered by doubling key sizes, not a break.
The signature scheme used by Bitcoin, Ethereum and most blockchains, based on elliptic curves such as secp256k1. It is not post-quantum: Shor's algorithm would recover the private key from an exposed public key.