Linear solutions for cryptographic nonlinear sequence generators

This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in cryptography: the sequences generated by the class of shrinking generators. Consequently, this contribution show that shrinking generators do not provide enough guarantees to be used for encryption purposes. Furthermore, the linearization is achieved through a simple algorithm about which a full description is provided

Morpheus: stream cipher for software & hardware applications

In a world where electronic devices with different characteristics are networked, privacy is an essential element for the communicating process. Privacy can be achieved by encryption algorithms with unique features based on the application that are deployed. In this paper a word-oriented stream cipher, or Morpheus, for both hardware and software devices, is proposed. Morpheus targets multimedia applications, such as Games-On-Demand or IPTV, where data are usually streamed over different kind of networks and devices. Morpheus behaves very well in all known statistical tests and is resilient to known attacks for both synchronous and self-synchronous encryption modes

Cryptautomata: definition, cryptanalysis, example

This conference paper is an extended abstract of a recent article in Prikladnaya Diskretnaya Matematika (2017, No.36), where we presented the definition of the cryptautomata and described some cryptanalysis techniques for them. In cryptosystems, the cryptautomata are widely used as its primitives including cryptographic generators, s-boxes, filters, combiners, key hash functions as well as symmetric and public-key ciphers, and digital signature schemes. A cryptautomaton is defined as a class C of automata networks of a fixed structure N constructed by means of the series, parallel, and feedback connection operations over initial finite automata (finite state machines) with transition and output functions taken from some predetermined functional classes. A cryptautomaton key can include initial states, transition and output functions of some components in N. Choosing a certain key k produces a certain network Nk from C to be a new cryptographic algorithm. In case of invertibility of Nk, this algorithm can be used for encryption. The operation (functioning) of any network Nk in the discrete time is described by the canonical system of equations of its automaton. The structure of Nk is described by the union of canonical systems of equations of its components. The cryptanalysis problems for a cryptautomaton are considered as the problems of solving the operational or structural system of equations of Nk with the corresponding unknowns that are key k variables and (or) plaintexts (input sequences). For solving such a system E, the method DSS is used. It is the iteration of the following three actions: 1) E is Divided into subsystems E' and E ", where E' is easy solvable; 2) E' is Solved; 3) the solutions of E' are Substituted into E'' by turns. The definition and cryptanalysis of a cryptautomaton are illustrated by giving the example of the autonomous alternating control cryptautomaton. It is a generalization of the LFSR-based cryptographic alternating step generator. We present a number of attacks on this cryptautomaton with the states or output functions of its components as a key

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time

On Bijective Variants of the Burrows-Wheeler Transform

The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation conjugates of the input word, whereas the ST of order k only uses the first k letters for sorting all such conjugates. If two conjugates start with the same prefix of length k, then the indices of the rotations are used for tie-breaking. Both transforms output the sequence of the last letters of the sorted list and the index of the input within the sorted list. In this paper, we discuss a bijective variant of the BWT (due to Scott), proving its correctness and relations to other results due to Gessel and Reutenauer (1993) and Crochemore, Desarmenien, and Perrin (2005). Further, we present a novel bijective variant of the ST.Comment: 15 pages, presented at the Prague Stringology Conference 2009 (PSC 2009