Abstract: A method of protecting communications through encryption is disclosed which is particularly useful for multiplexed communications. On the transmit side, each message is multiplied by an enciphering key corresponding to its destination, and the products are all added together to form a cryptogram. Each receiving station divides the entire cryptogram by its own deciphering key to obtain the message intended for that station.

Abstract: A public encryption key (c.sub.1, c.sub.2, r) in which r is the product of two relatively prime numbers, and in which c.sub.1 and r, as well as c.sub.2 and r, are relatively prime numbers, is used in an encryption algorithmx=c.sub.1 m.sub.1 +c.sub.2 m.sub.2 (mod r).The decryption algorithm will be equivalent to solving simultaneous linear equations derived from the encryption algorithm. Thus, both encrypting and decrypting are quite simplified while still maintaining a high degree of security.

Abstract: The strength of a cryptosystem is increased by providing multiple characters for one or more of the characters being encoded to thereby reduce redundancy.

Abstract: The integrated data enciphering and channel encoding system consists of a message expansion function F, a convolutional encoder G.sub.e of code rate r.sub.e greater than the computational cutoff rate R.sub.comp, and an artificial noise generator emitting a noise sequence n. The expansion function F is the key to this integrated cryptosystem and can be any linear time varying or time invariant function, with or without memory. It can also be a block code or a convolutional code itself provided that the resultant concatenated convolutional code is non-catastrophic. The concatenation of the expansion function F with G.sub.e is equivalent to a new convolutional encoder G.sub.d .ident.FG.sub.e of code rate r.sub.d less than the computational cutoff rate R.sub.comp of the equivalent channel, but without knowledge of the expansion function F or the artificial noise n, the transmitted information rate appears to exceed R.sub.comp.