What are the differences between lattice-based and elliptic curve cryptography?

What are the differences between lattice-based and elliptic curve cryptography?

Lattice-based cryptography relies on the hardness of lattice problems, while elliptic curve cryptography is based on the algebraic structure of elliptic curves. Lattice-based schemes are believed to be more resistant to quantum attacks.

Can you explain why lattice-based cryptography is considered more secure against quantum attacks?

Lattice-based cryptography is considered more secure against quantum attacks because it relies on problems like the Shortest Vector Problem, which are not efficiently solvable by quantum algorithms like Shor's algorithm, unlike integer factorization or discrete logarithm problems used in traditional cryptography.

What are some practical applications of lattice-based cryptography?

Practical applications include secure multiparty computation, homomorphic encryption, and post-quantum secure digital signatures.

How does the performance of lattice-based cryptography compare to elliptic curve cryptography?

Lattice-based cryptography generally has larger key sizes and slower performance compared to elliptic curve cryptography, but it offers stronger security guarantees in a post-quantum world.