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Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multiparty computation protocols. However, it remains open whether or not there exist efficient constructions of strongly…
In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite volume hyperbolic manifolds. More…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic…
Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.
Averaging physical quantities over Lie groups appears in many contexts across the rapidly developing branches of physics like quantum information science or quantum optics. Such an averaging process can be always represented as averaging…
Stern's signature scheme is a historically important code-based signature scheme. A crucial optimization of this scheme is to generate pseudo-random vectors and a permutation instead of random ones, and most proposals that are based on…
We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error…
The Maximum Likelihood Decoding Problem (MLD) is known to be NP-hard and its complexity is strictly related to the security of some post-quantum cryptosystems, that is, the so-called code-based primitives. Analogously, the Multivariate…
Logarithmic number systems (LNS) are used to represent real numbers in many applications using a constant base raised to a fixed-point exponent making its distribution exponential. This greatly simplifies hardware multiply, divide and…
In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation.…
The article describes a new implementation of MST3 cryptosystems based on the automorphism group of the Suzuki function field. The main difference in the presented implementation is to use the logarithmic signature for encryption not only…
The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field…
On the basis of an initial interest in symmetric cryptography, in the present work we study a chain of subgroups. Starting from a Sylow $2$-subgroup of AGL(2,n), each term of the chain is defined as the normalizer of the previous one in the…
One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. We consider statistically-verifiable OWSGs (sv-OWSG), which are potentially weaker objects than OWSGs. We show that O(n/log(n))-copy sv-OWSGs (n…
The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…
This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the…
We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…
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…