What are the risks of quantum computing ... - tlooto, The Most Powerful AcademicGPT

Quantum computers endanger today’s public-key infrastructures by upending the hard-problem assumptions on which they rely, and they weaken symmetric schemes and hash functions in predictable ways. Below we summarise the principal risks and transition challenges, drawing on recent research. 1. Breaking public-key schemes with Shor’s algorithm • Shor’s algorithm runs in polynomial time to factor integers and compute discrete logarithms, so it can recover RSA private keys, solve Elliptic-Curve Discrete Logarithm (ECDLP) problems and break Diffie–Hellman key exchanges in $$\mathrm{poly}(n)$$ time, where $$n$$ is the key length [1][2]. • Estimates suggest that breaking a 2048-bit RSA modulus would require on the order of a few thousand error-corrected logical qubits and months of runtime—ambitious but within reach as quantum hardware scales beyond noisy intermediate-scale devices [1]. • All mainstream PKI-based protocols (TLS/SSL, S/MIME, SSH, VPNs) and digital-signature schemes (RSA, ECDSA