An elliptic curve cryptosystem is an asymmetric algorithm. What sets it apart from other asymmetric algorithms?

A.
It provides digital signatures, secure key distribution, and encryption.

B.
It computes discrete logarithms in a finite field.

C.
It uses a larger percentage of resources to carry out encryption.

D.
It is more efficient.

Explanation:
D: Elliptic curves are rich mathematical structures that have shown usefulness in many different types of applications. An elliptic curve cryptosystem (ECC) differs from other
asymmetric algorithms due to its efficiency. ECC is more efficient than any other asymmetric algorithm because of less intensive mathematics. In most cases, the longer the key, the
more protection that is provided, but ECC can provide the same level of protection with a key size that is shorter than what RSA requires. Because longer keys require more resources
to perform mathematical tasks, the smaller keys used in ECC require fewer resources of the device. And fewer resources make for a more efficient algorithm.
A is incorrect because ECC is not the only asymmetric algorithm that provides digital signatures, secure key distribution, and encryption. These services are also provided by RSA
and other asymmetric algorithms. Using its one-way function, ECC provides encryption and signature verification, and the inverse direction performs decryption and signature
generation. It can also be used as a key exchange protocol, meaning it is used to encrypt the symmetric key to get it securely to its destination.
B is incorrect because Diffie-Hellman and El Gamal calculate discrete logarithms in a finite field. In the field of mathematics that deals with elliptic curves, points on the curves
compose a structure called a group. These points are the values used in mathematical formulas for ECC’s encryption and decryption processes. The algorithm computes discrete
logarithms of elliptic curves, which is different from calculating discrete logarithms in a finite field.
C is incorrect because ECCs use much fewer resources when compared to other asymmetric algorithms. Some devices, like wireless devices and cellular phones, have limited
processing capacity, storage, power, and bandwidth. With these types of devices, efficiency of resource use is very important.