arXiv subjects

Semira Einsele

Publications and source records attributed to Semira Einsele.

4 recordsLinked to original sources

arXiv2026

Prompt Compression via Activation Aggregation

Large language models process prompts by propagating activations through dozens of layers before generating a response. We ask whether the task-relevant information contained in an instruction prompt can be compressed into a single activation vector and re-injected into the model, replacing the original token sequence? We show this is achievable using a learned weighted sum of activations extracted at an intermediate layer and injected at an early layer of the target LLM. The compressed vector preserves task-relevant information, incurring an accuracy drop of under $2\%$ relative to full prompt processing. Beyond its practical implications, including reducing per-query computation for fixed instruction prompts without reprocessing the original token sequence, our analysis reveals structure in the activation space of LLMs: (i) mid-layer representations transfer meaningfully to early layers, suggesting a degree of cross-layer compatibility in how information is encoded; (ii) a single activation vector encodes a quantifiable and recoverable amount of semantic information; (iii) a weighted sum of activations is a robust representation compressor.

cs.CL↗

arXiv2025

Bilinear Compressive Security

Beyond its widespread application in signal and image processing, \emph{compressed sensing} principles have been greatly applied to secure information transmission (often termed 'compressive security'). In this scenario, the measurement matrix $Q$ acts as a one time pad encryption key (in complex number domain) which can achieve perfect information-theoretic security together with other benefits such as reduced complexity and energy efficiency particularly useful in IoT. However, unless the matrix is changed for every message it is vulnerable towards known plain text attacks: only $n$ observations suffices to recover a key $Q$ with $n$ columns. In this paper, we invent and analyze a new method (termed 'Bilinear Compressive Security (BCS)') addressing these shortcomings: In addition to the linear encoding of the message $x$ with a matrix $Q$, the sender convolves the resulting vector with a randomly generated filter $h$. Assuming that $h$ and $x$ are sparse, the receiver can then recover $x$ without knowledge of $h$ from $y=h*Qx$ through blind deconvolution. We study a rather idealized known plaintext attack for recovering $Q$ from repeated observations of $y$'s for different, known $x_k$, with varying and unknown $h$ ,giving Eve a number of advantages not present in practice. Our main result for BCS states that under a weak symmetry condition on the filter $h$, recovering $Q$ will require extensive sampling from transmissions of $Ω\left(\max\left(n,(n/s)^2\right)\right)$ messages $x_k$ if they are $s$-sparse. Remarkably, with $s=1$ it is impossible to recover the key. In this way, the scheme is much safer than standard compressed sensing even though our assumptions are much in favor towards a potential attacker.

cs.CR↗

arXiv2024

From Worst to Average Case to Incremental Search Bounds of the Strong Lucas Test

The strong Lucas test is a widely used probabilistic primality test in cryptographic libraries. When combined with the Miller-Rabin primality test, it forms the Baillie-PSW primality test, known for its absence of false positives, undermining the relevance of a complete understanding of the strong Lucas test. In primality testing, the worst-case error probability serves as an upper bound on the likelihood of incorrectly identifying a composite as prime. For the strong Lucas test, this bound is $4/15$ for odd composites, not products of twin primes. On the other hand, the average-case error probability indicates the probability that a randomly chosen integer is inaccurately classified as prime by the test. This bound is especially important for practical applications, where we test primes that are randomly generated and not generated by an adversary. The error probability of $4/15$ does not directly carry over due to the scarcity of primes, and whether this estimate holds has not yet been established in the literature. This paper addresses this gap by demonstrating that an integer passing $t$ consecutive test rounds, alongside additional standard tests of low computational cost, is indeed prime with a probability greater than $1-(4/15)^t$ for all $t\geq 1$. Furthermore, we introduce error bounds for the incremental search algorithm based on the strong Lucas test, as there are no established bounds up to date as well. Rather than independent selection, in this approach, the candidate is chosen uniformly at random, with subsequent candidates determined by incrementally adding 2. This modification reduces the need for random bits and enhances the efficiency of trial division computation further.

cs.CR↗

arXiv2023

Average Case Error Estimates of the Strong Lucas Test

Reliable probabilistic primality tests are fundamental in public-key cryptography. In adversarial scenarios, a composite with a high probability of passing a specific primality test could be chosen. In such cases, we need worst-case error estimates for the test. However, in many scenarios the numbers are randomly chosen and thus have significantly smaller error probability. Therefore, we are interested in average case error estimates. In this paper, we establish such bounds for the strong Lucas primality test, as only worst-case, but no average case error bounds, are currently available. This allows us to use this test with more confidence. We examine an algorithm that draws odd $k$-bit integers uniformly and independently, runs $t$ independent iterations of the strong Lucas test with randomly chosen parameters, and outputs the first number that passes all $t$ consecutive rounds. We attain numerical upper bounds on the probability on returing a composite. Furthermore, we consider a modified version of this algorithm that excludes integers divisible by small primes, resulting in improved bounds. Additionally, we classify the numbers that contribute most to our estimate.

cs.CR↗