Asymmetric-key cryptography, also known as public-key cryptography, is a cryptographic system that uses a pair of keys - a public key and a private key - to encrypt and decrypt data. The main advantage of asymmetric-key cryptography is that it provides a secure method for exchanging keys between two parties without the need for a previously shared secret key.

In asymmetric-key cryptography, various algorithms are used to perform key generation, encryption, and decryption. Three popular algorithms used in asymmetric-key cryptography are RSA, Diffie-Hellman, and Electronic Code Book (ECB). The question asks for the algorithm that is not used in asymmetric-key cryptography, and the correct answer is option 'C' - Electronic Code Book algorithm.

Below is an explanation of each algorithm and its role in asymmetric-key cryptography:

1. RSA algorithm:
The RSA (Rivest-Shamir-Adleman) algorithm is widely used in modern asymmetric-key cryptography. It is named after its inventors and is based on the mathematical problem of integer factorization. The RSA algorithm is used for secure communication, digital signatures, and key exchange. It involves generating a pair of keys - a public key for encryption and a private key for decryption.

2. Diffie-Hellman algorithm:
The Diffie-Hellman algorithm is another commonly used algorithm in asymmetric-key cryptography. It allows two parties to establish a shared secret key over an insecure communication channel. The algorithm relies on the difficulty of the discrete logarithm problem. It involves each party generating a public-private key pair and exchanging public keys. The shared secret key is then derived from the exchanged public keys and the party's private key.

3. Electronic Code Book (ECB) algorithm:
The Electronic Code Book algorithm, on the other hand, is not used in asymmetric-key cryptography. It is a symmetric-key algorithm that divides the plaintext into fixed-size blocks and encrypts each block separately using the same key. ECB does not provide adequate security for most applications as it suffers from several vulnerabilities, such as the same plaintext block producing the same ciphertext block.

In summary, the Electronic Code Book (ECB) algorithm is not used in asymmetric-key cryptography. Instead, it is a symmetric-key algorithm that has different security characteristics compared to asymmetric-key algorithms like RSA and Diffie-Hellman.