Testing the Randomness and Using the Digital Sequences of GF(5) in Cryptography

Abstract

In this paper, first, the Golomb’s postulates of randomness are expanded to construct a good mathematical base, and then expand the binary standard randomness tests to be suitable to be applied on penta-sequences this mean the elements of the sequence belong to Galois Field GF(5). Second we will show usefulness of using penta-sequences in cryptography. The paper also includes some
tables describe the tests results of the penta-sequences generated from some digital generators, like the Multiplicative Cyclic Group System (MCGS). The proposed cryptosystem using the GF(5)-sequences will compress or minimizing the ciphertext
size comparing with the cryptosystems using GF(2)-sequences.