Related papers: Combinatorics on words in information security: Un…
In the recent years, several practical methods have been published to compute collisions on some commonly used hash functions. In this paper we present a method to take into account, at the symbolic level, that an intruder actively…
Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent,…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash…
In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…
The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…
Combinatorial properties of maximal repetitions (runs) in formal words are studied. We classify all maximal repetitions in a word as primary and secondary where the set of all primary repetitions determines all the other repetitons in the…
We present an explicit formula that produces hash collisions for the Merkle-Damg{\aa}rd construction. The formula works for arbitrary choice of message block and irrespective of the standardized constants used in hash functions, although…
Consider the situation where a word is chosen probabilistically from a finite list. If an attacker knows the list and can inquire about each word in turn, then selecting the word via the uniform distribution maximizes the attacker's…
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
We investigate combinatorial properties of a kind of insets we defined in an earlier paper, interpreting them now in terms of restricted ternary words. This allows us to give new combinatorial interpretations of a number of known integer…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical…
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…