Final answer:
RSA (Rivest-Shamir-Adleman) is the most widely used asymmetric encryption algorithm, based on the difficulty of factoring large prime numbers.
Step-by-step explanation:
The most widely used asymmetric encryption algorithm is RSA (Rivest-Shamir-Adleman). Asymmetric encryption, also known as public-key cryptography, involves a pair of keys; one for encryption (public key) and one for decryption (private key). RSA is favoured for its strong security measures, which are based on the difficulty of the factoring of the product of two large prime numbers.
Other encryption algorithms mentioned, such as Vigenère and Caesar Cipher, are symmetric, which means they use the same key for both encryption and decryption. DES (Data Encryption Standard) is also a symmetric algorithm, though not as widely used as RSA for asymmetric encryption.