scholarly journals Card-Based Cryptographic Logical Computations Using Private Operations

2020 ◽  
Author(s):  
Hibiki Ono ◽  
Yoshifumi Manabe
Keyword(s):  
Cryptographic Protocols ◽  
The Other ◽  
General Logic ◽  
Private Values ◽  
Minimum Number ◽  
Logic Functions ◽  
Logical Functions

Abstract This paper proposes new card-based cryptographic protocols to calculate logic functions with the minimum number of cards using private operations under the semi-honest model. Though various card-based cryptographic protocols were shown, the minimum number of cards used in the protocol has not been achieved yet for many problems. Operations executed by a player where the other players cannot see are called private operations. Private operations have been introduced in some protocols to solve a particular problem or to input private values. However, the effectiveness of introducing private operations to the calculation of general logic functions has not been considered. This paper introduces three new private operations: private random bisection cuts, private reverse cuts, and private reveals. With these three new operations, we show that all of AND, XOR, and copy protocols are achieved with the minimum number of cards by simple three-round protocols. This paper then shows a protocol to calculate any logical functions using these private operations. Next, we consider protocols with malicious players.

scholarly journals Minimum Round Card-Based Cryptographic Protocols Using Private Operations

Cryptography ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 17
Author(s):  
Hibiki Ono ◽  
Yoshifumi Manabe
Keyword(s):  
Boolean Functions ◽  
Cryptographic Protocols ◽  
Secure Multiparty Computation ◽  
The Other ◽  
Multiparty Computation ◽  
Minimum Number

This paper shows new card-based cryptographic protocols with the minimum number of rounds, using private operations under the semi-honest model. Physical cards are used in card-based cryptographic protocols instead of computers to achieve secure multiparty computation. Operations that a player executes in a place where the other players cannot see are called private operations. Using three private operations—private random bisection cuts, private reverse cuts, and private reveals—the calculations of two variable Boolean functions and copy operations were realized with the minimum number of cards. Though the number of cards has been discussed, the efficiency of these protocols has not been discussed. This paper defines the number of rounds to evaluate the efficiency of the protocols, using private operations. Most of the meaningful calculations using private operations need at least two rounds. This paper presents a new two-round committed-input, committed-output logical XOR protocol, using four cards. Then, we show new two-round committed-input, committed-output logical AND and copy protocols, using six cards. Even if private reveal operations are not used, logical XOR, logical AND, and copy operations can be executed with the minimum number of rounds. Protocols for general n-variable Boolean functions and protocols that preserve an input are also shown. Lastly, protocols with asymmetric cards are shown.

scholarly journals Discrete Optimization of a Gear Pump after Tooth Root Undercutting by Means of Multi-Dimensional Logic Functions

2020 ◽  
Vol 10 (13) ◽  
pp. 4682
Author(s):  
Marian A. Partyka ◽  
Maria Natorska
Keyword(s):  
Discrete Optimization ◽  
Independent Method ◽  
The Other ◽  
Total Efficiency ◽  
Gear Pump ◽  
Tooth Root ◽  
Logic Functions ◽  
Logical Functions

In this paper, the optimization of a gear pump after tooth root undercutting has been investigated; this requires the volumetric, mechanical and total efficiencies of the pump to be calculated. Due to conflict in the existing model, the total efficiency is often calculated with the assumption that the other efficiencies have acceptable values. Multiple-dimensional logical functions are an additional independent method that can be used for the optimization of a pump.

scholarly journals Skyrmion Logic-In-Memory Architecture for Maximum/Minimum Search

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 155
Author(s):  
Luca Gnoli ◽  
Fabrizio Riente ◽  
Marco Vacca ◽  
Massimo Ruo Roch ◽  
Mariagrazia Graziano
Keyword(s):  
High Efficiency ◽  
Digital Design ◽  
Control Logic ◽  
Minimum Number ◽  
Physical Simulations ◽  
Good Energy ◽  
Logic Functions ◽  
Time And Energy ◽  
Cmos Implementation ◽  
Maximum Minimum

In modern computing systems there is the need to utilize a large amount of data in maintaining high efficiency. Limited memory bandwidth, coupled with the performance gap between memory and logic, impacts heavily on algorithms performance, increasing the overall time and energy required for computation. A possible approach to overcome such limitations is Logic-In-Memory (LIM). In this paper, we propose a LIM architecture based on a non-volatile skyrmion-based recetrack memory. The architecture can be used as a memory or can perform advanced logic functions on the stored data, for example searching for the maximum/minimum number. The circuit has been designed and validated using physical simulations for the memory array together with digital design tools for the control logic. The results highlight the small area of the proposed architecture and its good energy efficiency compared with a reference CMOS implementation.

scholarly journals A Novel Graphical Technique for Combinational Logic Representation and Optimization

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Vedhas Pandit ◽  
Björn Schuller
Keyword(s):  
Boolean Functions ◽  
Discrete Systems ◽  
Boolean Logic ◽  
Decision Diagrams ◽  
New Paradigm ◽  
Binary Decision ◽  
Graphical Technique ◽  
A New Technique ◽  
Logic Functions ◽  
Logical Functions

We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘implementation-free” description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use.

What is Legal Logic?

1968 ◽  
Vol 3 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ch. Perelman
Keyword(s):  
Twentieth Century ◽  
Legal Reasoning ◽  
Formal Logic ◽  
The Other ◽  
Contemporary Philosophy ◽  
Specific Nature ◽  
Legal Thought ◽  
General Logic ◽  
The Subject ◽  
Practical Logic

That the question what is legal logic should still arise today appears paradoxical, for law is after all one of the oldest of human disciplines and logic has in the twentieth century become one of the most developed of the disciplines of contemporary philosophy. Yet comparison of a number of recent works dealing with the subject, all of which, not being without merit, have enjoyed a measure of success, is enough to show that the problem exists and is even strongly disputed.Of four such works, two—those by E. Levi and K. Engisch—do not use the word “logic” in their titles, though they deal with legal reasoning and legal thought. The other two, on the contrary, expressly purport to deal with legal logic. Strangely enough, however, their authors explicitly deny the specific existence of such a discipline, whereas Levi and Engisch underscore, without any hesitation, the specific nature of legal reasoning and the existence of a particular logic, legal logic.Thus in the first paragraph of his work, where Klug attempts to define the concept of legal logic, he states that it comprises the study of the rules of formal logic as used in the judicial application of rules of law (p. 6); that legal logic is therefore practical logic, consisting of the application to law of the rules of pure or theoretical logic which is general logic (p. 7).

scholarly journals Growth sequences of finite semigroups

1987 ◽  
Vol 43 (1) ◽  
pp. 16-20 ◽  
Author(s):  
James Wiegold ◽  
H. Lausch
Keyword(s):  
Real Number ◽  
Finite Semigroup ◽  
Piecewise Linear ◽  
The Other ◽  
Direct Power ◽  
Growth Sequence ◽  
Group Of Units ◽  
Number Of Generators ◽  
Finite Semigroups ◽  
Minimum Number

AbstractThe growth sequence of a finite semigroup S is the sequence {d(Sn)}, where Sn is the nth direct power of S and d stands for minimum generating number. When S has an identity, d(Sn) = d(Tn) + kn for all n, where T is the group of units and k is the minimum number of generators of S mod T. Thus d(Sn) is essentially known since d(Tn) is (see reference 4), and indeed d(Sn) is then eventually piecewise linear. On the other hand, if S has no identity, there exists a real number c > 1 such that d(Sn) ≥ cn for all n ≥ 2.

scholarly journals Randomness in nonlocal games between mistrustful players

2017 ◽  
Vol 17 (7&8) ◽  
pp. 595-610
Author(s):  
Carl A. Miller ◽  
Yaoyun Shi
Keyword(s):  
Quantum Cryptography ◽  
Cryptographic Protocols ◽  
Related Question ◽  
The Other ◽  
Signaling Game ◽  
Local Randomness ◽  
Quantum Strategies

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player’s input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

scholarly journals Study of T-norms and Quantum Logic Functions on BL-algebra and Their Relationships to the Classical Probability Structures

2020 ◽  
pp. 591-599
Author(s):  
Ahmed AL-Adilee ◽  
Habeeb Kareem Abdullah ◽  
Hawraa A. AL-Challabi
Keyword(s):  
Quantum Logic ◽  
Probability Space ◽  
Binary Operation ◽  
The Other ◽  
Symmetric Difference ◽  
Logic Function ◽  
Classical Probability ◽  
Binary Operations ◽  
Basic Probability ◽  
Logic Functions

This paper is concerned with the study of the T-norms and the quantum logic functions on BL-algebra, respectively, along with their association with the classical probability space. The proposed constructions depend on demonstrating each type of the T-norms with respect to the basic probability of binary operation. On the other hand, we showed each quantum logic function with respect to some binary operations in probability space, such as intersection, union, and symmetric difference. Finally, we demonstrated the main results that explain the relationships among the T-norms and quantum logic functions. In order to show those relations and their related properties, different examples were built.

scholarly journals Regarding Two Conjectures on Clique and Biclique Partitions

10.37236/9564 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Dhruv Rohatgi ◽  
John C. Urschel ◽  
Jake Wellens
Keyword(s):  
Upper Bounds ◽  
The Other ◽  
Lower And Upper Bounds ◽  
Minimum Number ◽  
Other Regarding

For a graph $G$, let $cp(G)$ denote the minimum number of cliques of $G$ needed to cover the edges of $G$ exactly once. Similarly, let $bp_k(G)$ denote the minimum number of bicliques (i.e. complete bipartite subgraphs of $G$) needed to cover each edge of $G$ exactly $k$ times. We consider two conjectures – one regarding the maximum possible value of $cp(G) + cp(\overline{G})$ (due to de Caen, Erdős, Pullman and Wormald) and the other regarding $bp_k(K_n)$ (due to de Caen, Gregory and Pritikin). We disprove the first, obtaining improved lower and upper bounds on $\max_G cp(G) + cp(\overline{G})$, and we prove an asymptotic version of the second, showing that $bp_k(K_n) = (1+o(1))n$.

scholarly journals Automatic determination of the dual system width of to a bivalent system

2018 ◽  
Vol XIX (1) ◽  
pp. 58-64
Author(s):  
Vasiliu Paul
Keyword(s):  
Dual System ◽  
The Other ◽  
Automatic Determination ◽  
Stable States ◽  
System A ◽  
Minimum Number

A system is a set of elements that can be found in one of the following states: operating state and fault. Any system has two stable states: functioning and defect, which is why, in the theory of reliability, it is called a bivalent system. A subset of defective elements is called the system cut if all the other elements of the system are in operation and the system is defective. The width of a bivalent system is equal to the minimum number of elements the system cuts have. In this paper is presented an algorithm for automatic determination of the dual system width to a bivalent system, a Matlab script that implements the algorithm, a case study and subsequent directions of development.

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