Large Language Models (LLMs) are susceptible to various attacks but can also improve the security of diverse systems. However, how well do open source LLMs behave as covertext distributions to, e.g., facilitate censorship-resistant communication? In this paper, we explore open-source LLM-based covert channels. We empirically measure the security vs. capacity of two open-source LLM models (Llama-7B and GPT-2) to assess their performance as covert channels. Although our results indicate that such channels are not likely to achieve high practical bitrates, we also show that the chance for an adversary to detect covert communication is low. To ensure our results can be used with the least effort as a general reference, we employ a conceptually simple and concise scheme and only assume public models.

In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Rønjom-Helleseth attack and the modifications due to Rønjom, Gong, and Helleseth. The first part of this paper fills some gaps in the theory of analysis in terms of the discrete Fourier transform (DFT). The second part introduces the new fast selective DFT attacks, which are closely related to the fast algebraic attacks in the literature. However, in contrast to the classical view that successful algebraic cryptanalysis of LFSR-based stream cipher depends on the degree of certain annihilators, the analysis in terms of the DFT spectral properties of the sequences generated by these functions is far more refined. It is shown that the selective DFT attack is more efficient than known methods for the case when the number of observed consecutive bits of a filter generator is less than the linear complexity of the sequence. Thus, by utilizing the natural representation imposed by the underlying LFSRs, in certain cases, the analysis in terms of DFT spectra is more efficient and has more flexibility than classical and fast algebraic attacks. Consequently, the new attack imposes a new criterion for the design of cryptographic strong Boolean functions, which is defined as the spectral immunity of a sequence or a Boolean function.

The filter generator is an important building block in many stream ciphers. The generator consists of a linear feedback shift register of length n that generates an m-sequence of period 2n-1 filtered through a Boolean function of degree d that combines bits from the shift register and creates an output bit ztat any time t. The previous best attacks aimed at reconstructing the initial state from an observed keystream, have essentially reduced the problem to solving a nonlinear system of D=Sigmai=1d(n/i) equations in n unknowns using techniques based on linear algebra. This attack needs about D bits of keystream and the system can be solved in complexity O(Domega), where omega can be taken to be Strassen's reduction exponent omega=log2(7)ap2.807. This paper describes a new algorithm that recovers the initial state of most filter generators after observing O(D) keystream bits with complexity O((D-n)/2)apO(D), after a pre-computation with complexity O(D(log2D)3)