Expanded Gabidulin Codes and Their Application to Cryptography

This paper presents a new family of linear codes, namely the expanded Gabidulin codes. Exploiting the existing fast decoder of Gabidulin codes, we propose an efficient algorithm to decode these new codes when the noise vector satisfies a certain condition. Furthermore, these new codes enjoy an excellent error-correcting capability because of the optimality of their parent Gabidulin codes. Based on different masking techniques, we give two encryption schemes by using expanded Gabidulin codes in the McEliece setting. According to our analysis, both of these two cryptosystems can resist the existing structural attacks. Our proposals have an obvious advantage in public-key representation without using the cyclic or quasi-cyclic structure compared to some other code-based cryptosystems

Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

In online marketplaces, customers have access to hundreds of reviews for a single product. Buyers often use reviews from other customers that share their type -- such as height for clothing, skin type for skincare products, and location for outdoor furniture -- to estimate their values, which they may not know a priori. Customers with few relevant reviews may hesitate to make a purchase except at a low price, so for the seller, there is a tension between setting high prices and ensuring that there are enough reviews so that buyers can confidently estimate their values. Simultaneously, sellers may use reviews to gauge the demand for items they wish to sell. In this work, we study this pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types, one by one, over a series of $T$ rounds. At each round, the seller first sets a price. Then a buyer arrives and examines the reviews of the previous buyers with the same type, which reveal those buyers' ex-post values. Based on the reviews, the buyer decides to purchase if they have good reason to believe that their ex-ante utility is positive. Crucially, the seller does not know the buyer's type when setting the price, nor even the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue. When there are $d$ types, after $T$ rounds, our algorithm achieves a problem-independent $\tilde O(T^{2/3}d^{1/3})$ regret bound. However, when the smallest probability $q_{\text{min}}$ that any given type appears is large, specifically when $q_{\text{min}} \in \Omega(d^{-2/3}T^{-1/3})$, then the same algorithm achieves a $\tilde O(T^{1/2}q_{\text{min}}^{-1/2})$ regret bound. We complement these upper bounds with matching lower bounds in both regimes, showing that our algorithm is minimax optimal up to lower-order terms

Composite Disturbance Filtering: A Novel State Estimation Scheme for Systems With Multi-Source, Heterogeneous, and Isomeric Disturbances

State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the disturbances of complicated systems are physically multi-source, mathematically heterogenous, affecting the system dynamics via isomeric (additive, multiplicative and recessive) channels, and deeply coupled with each other. In traditional filtering schemes, the multi-source heterogenous disturbances are usually simplified as a lumped one so that the "single" disturbance can be either rejected or attenuated. Since the pioneering work in 2012, a novel state estimation methodology called {\it composite disturbance filtering} (CDF) has been proposed, which deals with the multi-source, heterogenous, and isomeric disturbances based on their specific characteristics. With the CDF, enhanced anti-disturbance capability can be achieved via refined quantification, effective separation, and simultaneous rejection and attenuation of the disturbances. In this paper, an overview of the CDF scheme is provided, which includes the basic principle, general design procedure, application scenarios (e.g. alignment, localization and navigation), and future research directions. In summary, it is expected that the CDF offers an effective tool for state estimation, especially in the presence of multi-source heterogeneous disturbances

McEliece-type encryption based on Gabidulin codes with no hidden structure

This paper presents a new McEliece-type encryption scheme based on Gabidulin codes, which uses linearized transformations to disguise the private key. When endowing this scheme with the partial cyclic structure, we obtain a public key of the form $GM^{-1}$, where $G$ is a partial circulant generator matrix of Gabidulin code and $M$ as well as $M^{-1}$ is a circulant matrix of large rank weight, even as large as the code length. Another difference from Loidreau\u27s proposal at PQCrypto 2017 is that both $G$ and $M$ are publicly known. Recovering the private key can be reduced to deriving from $M$ a linearized transformation and two circulant matrices of small rank weight. This new scheme is shown to resist all the known distinguisher-based attacks, such as the Overbeck attack and Coggia-Couvreur attack, and also has a very small public key size. For instance, 2592 bytes are enough for our proposal to achieve the security of 256 bits, which is 400 times smaller than Classic McEliece that has been selected into the fourth round of the NIST Post-Quantum Cryptography (PQC) standardization process