Digital signatures provide authentication, integrity, and non-repudiation for digital documents. Symmetric key encryption uses the same key for encryption and decryption, while hashing algorithms like MD5 and SHA produce a digest or fingerprint of a message to verify integrity. Birthday attacks can allow multiple messages to produce the same hash value, so longer hash lengths like 128 bits or more are recommended to prevent collisions. Modern standards like SHA-256 provide stronger security than older algorithms like MD5.