Shor’s Algorithm

Classical computers can factor large integers, but the time required grows so quickly with key size that RSA's typical key sizes are considered computationally infeasible to factor within any practical timeframe using classical methods. Shor's algorithm changes this calculation entirely for a quantum computer: it solves the same factoring problem with a runtime that scales far more favorably, turning what was computationally infeasible into merely difficult — assuming the quantum computer running it has enough qubits and low enough error rates to execute the algorithm reliably at the key sizes real-world cryptography uses.

The precision Shor's algorithm adds to the general "quantum computing threat" narrative matters because it clarifies exactly which cryptographic functions are at risk and which are not: algorithms whose security rests on factoring or discrete logarithm hardness — RSA, Diffie-Hellman key exchange, elliptic curve cryptography — are the direct target, while symmetric algorithms like AES face a much more modest quantum speedup that larger key sizes can generally address without requiring an entirely different algorithmic approach. This distinction is exactly why post-quantum cryptography's algorithm families focus specifically on replacing the factoring- and discrete-logarithm-based algorithms Shor's algorithm threatens, rather than needing to replace symmetric cryptography wholesale. For CE verticals, understanding Shor's algorithm specifically — rather than treating "quantum threat" as an undifferentiated risk — clarifies migration priority: asymmetric key exchange and digital signature algorithms are the urgent post-quantum migration targets, while symmetric encryption used for bulk data protection faces a comparatively manageable adjustment.