On neural network techniques in the secure management of communication systems through improving and quality assessing pseudorandom stream generators

Abstract

Random components play an especially important role in the management of secure communication systems, with emphasis on the key management of cryptographic protocols. For this reason, the existence of strong pseudo random number generators is highly required. This paper presents novel techniques, which rely on Artificial Neural Network (ANN) architectures, to strengthen traditional generators such as IDEA and ANSI X.9 based on 3DES and IDEA. Additionally, this paper proposes a non-linear test method for the quality assessment of the required non-predictability property, which relies on feedforward neural networks. This non-predictability test method along with commonly used empirical tests based on statistics is proposed as a methodology for quality assessing strong pseudorandom stream generators. By means of this methodology, traditional and Neural Network based pseudorandom stream generators are evaluated. The results show that the proposed generators behave significantly better than the traditional ones, in particular, in terms of non-predictability.

Introduction

The security of many cryptographic protocols such as electronic payment systems, authentication and integrity, digital signature scheme and key management techniques depends upon the use of random quantities, which are obtained by using true or strong pseudorandom number generators. For instance, authentication mechanisms may use nonces, i.e. random numbers to protect against replay attacks (Gollmann, Beth, & Damm, 1993) like the related mechanisms in ITU X.509 (Schneier, 1996). Symmetric and asymmetric cryptographic systems like DES, IDEA, RSA (Schneier, 1996) and AES (AES2001, 2001) that are employed for confidentiality purposes and as basic element of various security protocols require possibly real or at least strong pseudorandom cryptographic keys, should the crypto-analysis remain a hard problem.

Furthermore, integrity mechanisms such as ISO 8731-2 (Schneier, 1996) or cryptographic key exchange mechanisms such as the Diffie–Hellman Protocol (Diffie & Hellman, 1976) or the construction of digital signatures such as the Digital Signature Scheme (Schneier, 1996) require the generation and use of random numbers. In addition, random numbers are used for the generation of pseudonyms and of traffic and message padding, in order to protect against traffic analysis attacks and for the computation of strong and efficient stream ciphers (Schneier, 1996, Zeng et al., 1991, Simmons, 1992).

True sources of randomness are preferred for the generation of random bit sequences. Unfortunately they are not widely applied. However, in cases such sources are indeed exploited for the generation of random bit sequences, the resulting generators, i.e. bit sequences should be validated. In the absence of true random generators strong pseudorandom number generators are desired, which should lead to the production of bit sequences of good quality, i.e. of good behavior in statistical and unpredictability terms. Otherwise, it would be possible for a cryptoanalyst, given a segment of this bit sequence and reasonable computer resources, to calculate the next bits or more about them (Zeng et al., 1991). In the last two decades considerable work has been made in the design and analysis of pseudorandom number or bit generators (Karras and Zorkadis, 1998, Pfleeger, 1997, Schneier, 1996, Stallings, 1995).

In this paper, we briefly survey some of these generators, propose a methodology to enhance them and to evaluate their behavior and strength.

The level of randomness of a sequence can be defined in terms of statistical tests, which emulate computations encountered in practice, and check that the related properties of the sequence under investigation agree with those predicted if every bit (or number) was drawn from a uniform probability distribution (Stinson, 1995). The generators we consider in this paper are those used by the system-theoretic approach to the construction of stream ciphers. Secure key-stream generators have to satisfy design criteria, such as long period, ideal k-tuple distributions, large linear complexity, confusion, diffusion and nonlinearity criteria (Stinson, 1995). Most of them are contained in the proposed evaluation methodology.

In the Section 2 a method is outlined to strengthen these generators by means of neural network based mechanisms. The Section 3 is dedicated to the proposed evaluation methodology for random number generators, namely to the non-predictability test and to the appropriate statistical and non-linearity tests. In Section 4, we present evaluation results obtained by applying the proposed methodology on various traditional and strengthened generators. Finally, we conclude our paper and outline future work on this subject.