This chapter yields a review of certain mathematical approaches for analysis and design of the basic cryptographic elements for establishing information security in information-communication systems. The following two topics are addressed: selected issues on stream ciphers for encryption and key management based on broadcast encryption. Certain coding related issues for security evaluation and design of stream ciphers are considered. The discussed security evaluation techniques corresponding to decoding approaches include one-step and iterative decoding paradigms, and the addressed design issues involve homophonic coding for joint employment of pseudorandomness and randomness. Elements for cryptographic security evaluation and advanced design of the key managements based on broadcast encryption are pointed out.