Which cryptosystem is known for having a variable key size between 1,024 and 4,096?

The cryptosystem recognized for its variable key size between 1,024 and 4,096 bits is RSA. RSA (Rivest-Shamir-Adleman) is an asymmetric cryptographic algorithm widely used for secure data transmission. One of its distinctive features is the ability to use a wide range of key lengths; the larger the key size, the greater the level of security provided, making it versatile for different security needs.

RSA’s strength lies in the mathematical difficulty of factoring large prime numbers, a challenge that increases with key size, thereby enhancing security. The flexibility in key length makes it adaptable for various applications, from securing Internet connections to encrypting sensitive data.

In contrast, AES (Advanced Encryption Standard) utilizes fixed key sizes of 128, 192, or 256 bits, not allowing for the variability that RSA does. DES (Data Encryption Standard) also employs a fixed key size of 56 bits and is considered less secure due to its shorter key length. Blowfish, while capable of variable key sizes, does not reach the same lengths as RSA, with maximum key sizes of 448 bits. Thus, RSA is distinctly characterized by its extensive key size range, making it the correct answer in this context.