Related papers: LWE from Non-commutative Group Rings
An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in…
Predicate encryption is a new paradigm of public key encryption that enables searches on encrypted data. Using the predicate encryption, we can search keywords or attributes on encrypted data without decrypting the ciphertexts. In predicate…
Frame theory has been a popular subject in the design of structured signals and codes in recent years, with applications ranging from the design of measurement matrices in compressive sensing, to spherical codes for data compression and…
We study chains of lattice ideals that are invariant under a symmetric group action. In our setting, the ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus, these chains will fail to…
Given a supersingular elliptic curve E and a non-scalar endomorphism $\alpha$ of E, we prove that the endomorphism ring of E can be computed in classical time about disc(Z[$\alpha$])^1/4 , and in quantum subexponential time, assuming the…
Secure software leasing (SSL) is a quantum cryptographic primitive that enables users to execute software only during the software is leased. It prevents users from executing leased software after they return the leased software to its…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative…
At CRYPTO 2017, Rosca, Sakzad, Stehle and Steinfeld introduced the Middle--Product LWE (MPLWE) assumption which is as secure as Polynomial-LWE for a large class of polynomials, making the corresponding cryptographic schemes more flexible in…
Known key exchange schemes offering information-theoretic (unconditional) security are complex and costly to implement. Nonetheless, they remain the only known methods for achieving unconditional security in key exchange. Therefore, the…
According to constructivist theory, students learn software security more effectively when examples are grounded in their own code. Generic examples often fail to connect with students' prior work, limiting engagement and understanding.…
The decision-Diffie-Hellman problem (DDH) is a central computational problem in cryptography. It is known that the Weil and Tate pairings can be used to solve many DDH problems on elliptic curves. Distortion maps are an important tool for…
In this note, an LWE problem with a hidden trapdoor is introduced. It is used to construct an efficient public-key crypto-system EHT. The new system is significantly different from LWE based NIST candidates like FrodoKEM. The performance of…
In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of a solution for all instances. Our main results establish that suitable…
Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having…
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…
The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be…
By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman…
Recently, Dor\"oz et al. (2017) proposed a new hard problem, called the finite field isomorphism problem, and constructed a fully homomorphic encryption scheme based on this problem. In this paper, we generalize the problem to the case of…