Related papers: Equivalence Classes in AES -- Part 1
While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information…
Consider the following curious puzzle: call an n-tuple X=(X_1, ..., X_n) of sets smaller than another n-tuple Y if it has fewer //unordered sections//. We show that equivalence classes for this preorder are very easy to describe and…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…
Taxonomy completion, enriching existing taxonomies by inserting new concepts as parents or attaching them as children, has gained significant interest. Previous approaches embed concepts as vectors in Euclidean space, which makes it…
Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e.,…
Background: Computational analysis of next-generation sequencing data is outpaced by data generation in many cases. In one such case, paired-end reads can be produced from the Illumina sequencing method faster than they can be overlapped by…
Cryptographic algorithms like AES and RSA are widely used and they are mathematically robust and almost unbreakable but its implementation on physical devices often leak information through side channels, such as electromagnetic (EM)…
Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e.,…
Automated verification has become an essential part in the security evaluation of cryptographic protocols. In this context privacy-type properties are often modelled by indistinguishability statements, expressed as behavioural equivalences…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
This paper concerns with the construction of codes over $GF(2)$ which reach the max-flow for single source multicast acyclic networks with delay. The coding is always a bitwise XOR of packets with equal lengths, and is based on highly…
Specific vectorial boolean functions, such as S-Boxes or APN functions have many applications, for instance in symmetric ciphers. In cryptography they must satisfy some criteria (balancedness, high nonlinearity, high algebraic degree,…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
Given a permutation pattern p and an equivalence relation on permutations, we study the corresponding equivalence classes all of whose members avoid p. Four relations are studied: Conjugacy, order isomorphism, Knuth-equivalence and toric…
Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors…
Power analysis poses a significant threat to the security of cryptographic algorithms, as it can be leveraged to recover secret keys. While various software-based countermeasures exist to mitigate this non-invasive attack, they often…
This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics…
In this paper, we compute and demonstrate the equivalence of the joint distribution of the first letter and descent statistics on six avoidance classes of permutations corresponding to two patterns of length four. This distribution is in…
We theoretically analyze and compare the following five popular multiclass classification methods: One vs. All, All Pairs, Tree-based classifiers, Error Correcting Output Codes (ECOC) with randomly generated code matrices, and Multiclass…
In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…