RSA

RSA is the first practical public-key cryptosystem, published in 1978 by Rivest, Shamir, and Adleman (original paper). Its security rests on the difficulty of factoring the product of two large primes: the public key includes a modulus n equal to p times q, and recovering the private key is equivalent to finding p and q. RSA provides both encryption and digital signatures, and for decades it secured most of the web through TLS certificates and key transport.

#Quantum vulnerability

Shor's algorithm factors integers in polynomial time on a large quantum computer, recovering an RSA private key directly from the public modulus (Shor 1995). A quantum computer of sufficient scale would therefore break every RSA key at any size, including 2048-bit and 4096-bit keys, since larger keys only raise the classical cost. This is why standardization efforts replace RSA key establishment with ML-KEM and RSA signatures with lattice-based schemes. Data captured today under RSA remains exposed to harvest now, decrypt later collection.