Krzysztof Podlaski

Synthesis of reversible circuits: A view on the state-of-the-art

Four main approaches to synthesis of reversible circuits are considered: cycle-based, transformation-based, ESOP-based and BDD-based as well as their advantages and disadvantages are discussed. It is indicated that the decisions in them are based on local information only what leads to very redundant designs. Suggestions for making global decisions are also presented. New directions of research are also described.

Entanglement and tensor product decomposition for two fermions

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not the proper entanglement measure in this case. The explicit formula for the entanglement of formation is found. This formula shows that the entanglement of a given state depends on the tensor product decomposition of a Hilbert space. It is shown that the set of separable states is narrower than in the two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.

Applications of QR Codes in Secure Mobile Data Exchange

In the paper new method of secure data transmission between mobile devices is proposed. Already existing applications demand on the user to care about secure issues himself or herself. Derived method focuses on secure channel creation using well known QR codes technology, which allows prevent the eavesdropper from interception transmitted data during connection establishing process.

Applications of Secure Data Exchange Method Using Social Media to Distribute Public Keys

The concern about the data security is still growing. The applications we use still lack basic security. The security can be obtained easily without heightening the awareness of the users by simply implementing methods that allow end-to-end security. In the paper we present the new method of public key distribution using Social Media Networks. We use groups or circles that users can create there and publish images in the gallery with proper public or private access. After establishing secure session user can switch into different medium of communication, e.g. different messenger or text-SMS to share their data in secure way. Then there are described several applications of the presented method Secure Data Exchange (SDEx), e.g. secure SMS texting, Social Media Networking and data sharing. We propose frame format of the published QRcode as a public key and data message frame format.

Secure Data Exchange Based on Social Networks Public Key Distribution

The mobile devices became the most spread tools used for everyday communication. The users of mobile applications demand high level of security. All existing encryption protocols require from the users additional knowledge and resources. On the other hand the common user does not have required knowledge and skills about security. In this paper we discuss the problem of public key distribution between interested parties. We propose to use a popular social media as a channel to publish public keys. That way of keys distribution allows the owner of the key to connect easily with the desired person or institution, that is not always easy. Recognizing that the mobile devices are the main tool of communication, we present example of a mobile application that uses the proposed security method.

Study of Reversible Ternary Functions with Homogeneous Component Functions

Reversible computation is one of the intensively developing research areas nowadays in the field of computer science and engineering. Although the field of reversible circuit synthesis has been studied during the last 15 years few attempts have been published to propose classification of reversible functions. In an earlier paper we considered whether all component functions of a reversible Boolean function either can have the same property in the sense of classical logic synthesis or can belong to the same equivalent class under some equivalence relations. This problem has a direct relationship to studying different aspects of classification of reversible functions. In this paper we present reversible ternary functions of any number of variables with all component functions having the same property or belonging to the same equivalence class.

Enhancements of Encryption Method Used in SDEx

In the paper, we present enhancements of the encryption method for secure data transmission used in Secure Data Exchange method (SDEx) [1, 2, 3]. Potential weaknesses and possible attacks have been previously described in [4]. The new version of the encryption method is immune to indicated in [4] vulnerabilities connected with the potential knowledge of the part of the original message and uneven distribution of bits in the message blocks. In the new solution, we use also Davies-Meyer scheme in order to enhance immunity to meet-in-the-middle attacks.

Reversible circuit synthesis Using Binary Decision Diagrams

Reversible circuit synthesis is an important branch of low power consumption circuit design. The idea of a logic circuit without loss of information during computation has an impact on power consumption and on the other hand makes the use of classical circuit synthesis algorithms not applicable. In the area of reversible circuit design there is still lack of satisfactory algorithms. During last 15 years many heuristic algorithms have been developed, however, they construct circuit implementations which are far from optimal. In the paper a new implementation of the known transformation based algorithm is presented. The existing transformation based algorithms use truth table during computation. This leads to important memory restrictions on the algorithm. On the other hand any Boolean function can be represented using Binary Decision Diagrams (BBD). This representation is more compact and uses less memory than truth table representation. Presented new implementation of transformation based algorithm can be used for synthesis of much larger reversible functions than for original version of the algorithm.

Reversible circuit synthesis with particle swarm optimization using crossover operator

Reversible circuit synthesis is an important branch of low power consumption circuit design. The idea of a logic circuit with no losses of information during computation has impact on power consumption and on the other hand makes the use of classical circuit synthesis algorithms impossible. In the area of reversible circuit design there is still lack of good algorithms. During last 15 years many heuristic algorithms have been developed, however, they construct circuit implementations which are far from optimal. In the paper the metaheuristic evolutionary algorithm is used. The algorithm combines two of known metaheuristic approaches: particle swarm optimization (PSO) and genetic algorithms (GA). In the frame of PSO the new crossover genetic operator is used. The proposed Best Circuit Cost Crossover (BCCC) operator is designed especially for reversible circuit synthesis. In the result the hybrid PSO-GA algorithm is used for reversible circuit synthesis. Many of the existing approaches use Toffoli gates with positive controls only, while the presented algorithm operates on Toffoli gates with both positive and negative controls. The presented, approach applied to known benchmark functions, gives satisfactory results when compared with the approaches known in the literature. The resulting circuits are less redundant than those obtained via heuristic algorithms and for some of benchmarks are optimal or near optimal.