Structural Properties of Cryptographic Sequences - Computational Intelligence in Security for Information Systems - page 127

Structural Properties of Cryptographic
Sequences

A. Fuster-Sabater

Institute of Applied Physics, C.S.I.C.
Serrano 144, 28006 Madrid, Spain
[e-mail]

Abstract. In the present work, it is shown that the binary sequences
obtained from a cryptographic generator, the so-called generalized self-
shrinking generator, are just particular solutions of a type of linear differ-
ence equations. Cryptographic parameters e.g. period, linear complexity
or balancedness of the previous sequences can be analyzed in terms of
linear equation solutions. In brief, computing the solutions of linear dif-
ference equations is an easy method of generating new sequences with
guaranteed cryptographic parameters.

Keywords: pseudorandom sequence, linear difference equation,

sequence generator, stream cipher, cryptography.

1 Introduction

It is a well known fact that pseudorandom binary sequences are typically used in
a wide variety of applications such as: spread spectrum communication systems,
multiterminal system identification, global positioning systems, software testing,
error-correcting codes or cryptography. This work deals specifically with this last
application.
In order to keep the confidentiality of sensitive information, an encryption
function currently called cipher converts the plaintext or original message into
the so-called ciphertext . Symmetric key encryption functions are usually di-
vided into two separated classes: stream ciphers and block-ciphers depending
on whether the encryption function is applied either to each individual bit or
to a block of bits of the plaintext, respectively. Stream ciphers are the fastest
among the encryption procedures so they are implemented in many technolog-
ical applications e.g. RC4 for encrypting Internet trac [13] or the encryption
function E0 in Bluetooth specifications [1]. Stream ciphers try to imitate the
mythic one-time pad cipher or Vernam cipher [11] and are designed to generate
alongsequence(the keystream sequence ) of pseudorandom bits. See the most

This work was supported in part by CDTI (Spain) and the companies INDRA, Union
Fenosa, Tecnobit, Visual Tools, Brainstorm, SAC and Technosafe under Project
Cenit-HESPERIA; by Ministry of Science and Innovation and European FEDER
Fund under Project TIN2008-02236/TSI.