Which statement best describes the difference between lattice-based cryptography and factorization-based public-key cryptography?

• A. Lattice-based relies on lattice problems for security, not on factoring integers
• B. Lattice-based uses factoring, while others do not
• C. Lattice-based is not quantum-resistant
• D. Lattice-based is only used for hashing

Answer: (A)

The main idea is that the security basis differs: lattice-based cryptography relies on hard lattice problems, such as learning with errors or the shortest vector problem, whereas factorization-based public-key cryptography depends on the difficulty of factoring large integers. That distinction is what makes the statement the best description: it directly names the underlying hard problems that give each system its security.

In practical terms, RSA and similar schemes are protected because factoring a very large number is hard; if an efficient factoring algorithm or quantum computer could factor quickly, those systems would be broken. Lattice-based schemes, on the other hand, are designed around lattice problems, and there is no known efficient algorithm (classical or quantum) that solves those problems in a way that would break them across the typical parameter sizes used today. This is also why lattice-based cryptography is often discussed in the context of post-quantum security, while factoring-based systems are known to be vulnerable to quantum attacks like Shor’s algorithm.

It's not accurate to say lattice-based cryptography relies on factoring, nor that it's only used for hashing, or that it isn't quantum-resistant. Lattice-based methods are used for encryption and signatures and are regarded as resistant to known quantum attacks under current understanding.