What are the most common misconceptions and myths about elliptic curve and lattice-based cryptography in IT?

1 What is elliptic curve cryptography?

Elliptic curve cryptography (ECC) is a type of public-key cryptography that uses mathematical curves to generate and verify keys. ECC offers higher security and efficiency than traditional methods, such as RSA, which use large numbers and factorization. ECC keys are much shorter and faster to compute, which reduces the storage and bandwidth requirements. ECC is widely used in applications such as SSL/TLS, Bitcoin, and smart cards.

2 What is lattice-based cryptography?

Lattice-based cryptography is a type of post-quantum cryptography that uses complex structures called lattices to create and encrypt keys. Lattices are sets of points that form regular patterns in multidimensional spaces. Lattice-based cryptography is based on hard problems that are believed to be resistant to quantum attacks, such as finding the shortest vector or the closest vector in a lattice. Lattice-based cryptography is still an active research area, but it has potential applications in digital signatures, homomorphic encryption, and secure multiparty computation.

3 Myth 1: ECC is not secure enough

One of the most common myths about ECC is that it is not secure enough because it relies on a limited number of curves and parameters. Some people claim that these curves and parameters are chosen by secret agencies or corporations, and that they could contain hidden weaknesses or backdoors. However, this is not true. There are many different types of curves and parameters, and they are chosen based on rigorous criteria and standards. Moreover, there are ways to verify the security and integrity of the curves and parameters, such as using random or verifiable generation methods, or using provably secure curves.

4 Myth 2: Lattice-based cryptography is too complex and impractical

Another common myth about lattice-based cryptography is that it is too complex and impractical to implement and use. Some people argue that lattice-based cryptography requires too much computation and memory, and that it produces too large keys and ciphertexts. However, this is not true either. Lattice-based cryptography has made significant progress in recent years, and there are many efficient and optimized algorithms and schemes that can reduce the complexity and overhead. For example, there are techniques such as ring lattices, NTRU, and LWE that can simplify the lattice operations and structures, and there are methods such as compression, pruning, and reconciliation that can shrink the key and ciphertext sizes.

5 Myth 3: ECC and lattice-based cryptography are incompatible

A third common myth about ECC and lattice-based cryptography is that they are incompatible and cannot work together. Some people believe that they are based on different assumptions and models, and that they have different strengths and weaknesses. However, this is not true either. ECC and lattice-based cryptography are complementary and can be combined to achieve better security and performance. For example, there are hybrid schemes that use ECC for key exchange and lattice-based cryptography for encryption or signature, or vice versa. There are also schemes that use ECC to construct lattices, or lattices to construct curves.