Which public-key cryptosystem uses prime factorization as the basis for its security?

The public-key cryptosystem that relies on prime factorization for its security is Rivest-Shamir-Adleman, commonly known as RSA. RSA's security model is built upon the mathematical difficulty of factoring the product of two large prime numbers. When two prime numbers are multiplied together, the resulting product is relatively easy to compute. However, determining the original prime factors from that product is computationally intensive and time-consuming for large numbers. This asymmetry forms the foundation of RSA's encryption and decryption processes.

In RSA, a public key is generated from the product of two prime numbers, which can be shared freely. Conversely, the private key, which is needed to decrypt any message or to sign something digitally, revolves around the secure knowledge of those two prime factors. Since there are no efficient algorithms available for factoring large prime products, RSA remains secure as long as the key sizes are sufficiently large.

Other choices like the Digital Signature Algorithm (DSA) and the Elliptic Curve Digital Signature Algorithm (ECDSA) rely on different mathematical principles related to discrete logarithms and elliptic curves, respectively. Meanwhile, the Diffie-Hellman key exchange predominantly operates on the assumption of the difficulty of computing discrete logarithms in a finite field rather than