As the foundation of all security enhanced systems, encryptions and decryptions are defined, and homomorphic (additive or multiplicative), probabilistic, commutative, and verifiable features are extracted as the desirable ones of encryption and decryption algorithms for developing secure anonymous systems. Also encryption and decryption algorithms are classified and onetime pad, permutation and substitution, RSA, and ElGamal are introduced as typical algorithms. Among them, onetime pad, RSA, and ElGamal are extensively used to develop secure anonymous systems in the remainder of this book.