Which algorithm is widely used for digital signatures and is based on factoring large prime numbers?

The RSA algorithm is well-known for its role in digital signatures and is fundamentally rooted in the mathematical challenge of factoring large prime numbers. RSA operates by generating two large prime numbers and using them to create a public and private key pair. The security of RSA's encryption and signature processes hinges on the difficulty of factoring the product of these two large prime numbers—an operation that is computationally intensive and currently impractical for sufficiently large primes.

When a digital signature is created using RSA, it involves the signer utilizing their private key to encrypt a hash of the message. This encrypted hash, along with the public key, allows anyone with the public key to verify that the signature was created by the holder of the private key and that the message has not been altered. The reliance on prime factorization for its security makes RSA highly effective for digital signatures in various applications, including secure communications over the internet.

Other algorithms mentioned serve different purposes or rely on different mathematical principles, which is why they do not fit the criteria of being based on the factoring of large prime numbers.