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.
Highlights
Cryptography is used to transform information from plain text to cipher text and vice versa in order to prevent unauthorized access to information [1, 2]
The shrinking generator (SG) was first introduced in [7]. It is composed of two shift registers, namely shift register B, linear-feedback shift register (LFSR) and LFSRA
LFSRB is designated as a control register that orchestrates what is produced by LFSRA
Summary
Cryptography is used to transform information from plain text to cipher text and vice versa in order to prevent unauthorized access to information [1, 2]. This paper focuses on symmetric encryption, synchronous stream ciphers, of which the shrinking generator (SG) is an example. LFSRA generates the output bits and LFSRB generates the controlling bits. The bit from LFSRA is output as part of the keystream whenever the bit from LFSRB is 1, otherwise the output is not selected by the cipher. The SG is still studied, and its practical advantages continue to be appreciated. While the study was simplistic in its approach, the SG was useful. The SG continues to attract interest because of its reputation as a standard and a model for enlightening cryptanalysis techniques. Lessons learned from the SG can be transferred to the cryptanalysis of other cipher techniques
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