What is Shor's algorithm?

Answer: A. Public-key cryptography such as RSA and elliptic-curve cryptography

The security of RSA rests on the difficulty of factoring large numbers, and that of elliptic-curve cryptography on the difficulty of the discrete logarithm problem. Shor's algorithm solves these problems in polynomial time by finding periods with the quantum Fourier transform. Keys too long to break in a realistic time on classical computers could then be broken with a sufficiently large fault-tolerant quantum computer. Against symmetric-key ciphers such as AES there is only the quadratic speed-up of Grover's algorithm, which can be countered with longer keys.

Answer: C. A huge number of gates must be executed without error, which requires many logical qubits built by error correction and an enormous number of physical qubits to support them

Breaking RSA-2048 requires executing gates on the order of billions in sequence on roughly one thousand to several thousand logical qubits. The logical error rate must therefore be extremely low, and error correction requires several hundred or more physical qubits per logical qubit. Estimates made in the 2020s put the requirement at roughly hundreds of thousands to tens of millions of physical qubits with error rates of about 0.1% (the figures vary greatly with the assumptions), orders of magnitude beyond the scale of current devices. However, these estimates have been shrinking as the algorithms improve, so preparations for migrating cryptography need to start early.