Although applied quasigroup cryptography is just in the nascent state and its bibliography is poor, one may see that it already now makes possible to construct very effective, fast, and highly secure quasigroup-based cryptosystems, such as block and stream ciphers, almost truly random number generators, weakly and strongly collision-free hash functions [7, 8, 9, 10, 12]. What is more, quasigroup cryptography generates new problems in cryptology, concerning, among other things, quasigroup cryptographic protocols (authentication, secret splitting, secret sharing, key exchange). Since Maple is very well adapted to study and examine these new issues, in the contribution detailed implementation of one from many possible byte oriented systems of synchronous quasigroup stream ciphers with a huge keyspace has been presented. Since the keyspace of the considered cipher is very huge indeed, some significant portion of a secret key can be made public. Such an approach allows to use the cipher as a partly public key cryptosystem , authenticating the addressee or the sender, or simultaneousely both the addressee and the sender of a secret message, as well. Besides, its structural redundancy makes the generation of session keys significantly easier.