What is the purpose of Elliptic Curve Cryptography (ECC)?

Elliptic Curve Cryptography (ECC) serves primarily to improve digital signatures and key exchanges. ECC is built on the mathematics of elliptic curves over finite fields, allowing it to offer a high level of security with smaller key sizes compared to traditional encryption methods like RSA. This means that ECC can produce stronger security for the same computational effort and bandwidth, making it particularly advantageous for environments with limited resources.

For digital signatures, ECC provides a mechanism that ensures the authenticity and integrity of messages. The use of smaller key sizes not only speeds up the signing and verification process but also reduces the overhead when transmitting key materials over networks. Similarly, in key exchange protocols, ECC enables secure negotiation of cryptographic keys between parties, enhancing the efficiency and safety of establishing secure communication channels.

This efficiency and effectiveness at enhancing cryptographic functions are why ECC is considered a valuable tool in modern cryptography, particularly in securing communications over the internet and in mobile devices. The other answer choices suggest purposes that do not fully encompass the primary capabilities and advantages that ECC offers.