Which asymmetric encryption algorithm leverages characteristics of prime numbers and utilizes variable key lengths (1024-4096)?

The Rivest Shamir Adleman (RSA) algorithm is a widely recognized asymmetric encryption method that fundamentally relies on the mathematical properties of prime numbers. It utilizes the difficulty of factoring the product of two large prime numbers to enhance security. This characteristic makes RSA robust against attacks that involve attempting to derive the original prime factors from the public key.

One of the key features of RSA is its support for variable key lengths, typically ranging from 1024 to 4096 bits. The choice of key length plays a critical role in determining the security level of the encryption; longer keys provide increased security against brute-force attacks. As key lengths increase, the computational effort required for encryption and decryption also increases, which is an important consideration in practical applications.

In contrast, other options listed do not share the same characteristics: Elliptic Curve Cryptography (ECC) also relies on different mathematical principles and typically uses shorter keys for equivalent security; DES is a symmetric encryption standard with a fixed key length of 56 bits; and AES, while a strong symmetric encryption standard, does not employ asymmetric techniques or the properties of prime numbers in its operation. Thus, RSA stands out as the correct answer for this question.