Design and Implementation of a Statistical Testing Framework for a Lightweight Stream Cipher

Abstract

The Shrinking Generator (SG) is a popular synchronous, lightweight stream cipher that uses minimal computing power. However, its strengths and weaknesses have not been studied in detail. This paper proposes a statistical testing framework to assess attacks on the SG. The framework consists of a d-monomial test that is adapted to SG by applying the algebraic normal form (ANF) representation of Boolean functions, a test that uses the maximal degree monomial test to determine whether the ANF follows the proper mixing of bit values, and a proposed unique window size (UWS) scheme to test the randomness properties of the keystream. The proposed framework shows significant weaknesses in the SG output in terms of dependence between the controlling linear-feedback shift register (LFSR) and non-linearity of the resulting keystream. The maximal degree monomial test provides a better understanding of the optimal points of SG, demonstrating when it is at its best and worst according to the first couple of results. This paper uses UWS to illustrate the effect of the LFSR choice on possibly distinguishing attacks on the SG. The results confirm that the proposed UWS scheme is a viable measure of the cryptographic strength of a stream cipher. Due to the importance of predictability and effective tools, we used neural network models to simulate the input data for the pseudo-random binary sequences. Through the calculation of UWS, we obtained solid results for the predictions.

Practical Improvement in the Implementation of Two Avalanche Tests to Measure Statistical Independence in Stream Ciphers

“…However, this approach has the limitation of omitting the evaluation of other essential elements in determining the security of a stream cipher. One of these factors is the statistical independence between the internal state (comprising all the variables that determine the operation of the PRNG, including the input) of the cipher and its outputs [29]. Their determination is essential to avoid powerful cryptographic attacks such as the correlation attack [30,31], the differential attack [32], or the attack on neutral bits [33].…”