A checksum or some other identifying pattern is embedded into m so that a valid decryption can be verified. Since only X had knowledge of Dx, only X could have signed the message. The public key register of the Ei need not be read secure, since the Ei are given away freely. The registry must be protected against corruption, since that would allow fraudulent keys to be given out. These form the basis for private key ciphers such as DES and Clipper.
Security is based on the presumed difficulty of factoring large numbers.
Systems Listed below are a sampling of some important systems. The Catholic University of Louvain maintains a long list of cryptography vendors and research groups. DES is widely used in commercial and non-defense government communications. Despite initial questions about the security of DES w.r.t. Current DES is nearing the end of its life as a encryption scheme for moderate to high level security needs because of technological advances that make brute force attacks on keys feasible.