Unicity distance of linear and non-linear pseudonoise sequence generators for direct-sequence spread spectrum systems

The unicity distance is a quantity which measures the minimum theoretical amount of ciphertext required by an eavesdropper to break a cryptographic code. This quantity depends on the number of possible keys for a given cryptosystem. Three different types of PN sequences are considered; linear maximal-length, Gold codes, and non-linear maximal length sequences. The unicity distances of systems employing each of these sequences as a function of complexity are compared. It is shown that linear maximal-length PN sequences are susceptible to known-plaintext attacks, and thus provide little security. Furthermore, the paper demonstrates that non-linear maximal length sequences have many more possible keys than Gold codes or linear m-sequences for a given register order and are less susceptible to known-plaintext attacks, thus providing a higher level of security compared to the other types of PN sequences considered.<>