Assuring authenticity, integrity, and non-repudiation using asymmetric key pairs.

Using the RSA key generation properties, where e and d are mathematically linked modular inverses:

Signing: S = H(M)^d mod n | Verification: H(M)' = S^e mod n

Proof: S^e mod n = (H(M)^d)^e mod n = H(M)^(d*e) mod n = H(M)^1 mod n = H(M)

Because only the owner has the private key d, only they can generate signature S. Anyone with the public key e can verify it, proving the message's origin (authentication) and that it has not been modified (integrity).