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Journal ArticleDOI: 10.1080/09720529.2012.10698381

Fundamental circuits and cut-sets used in cryptography

01 Jul 2012-Journal of Discrete Mathematical Sciences and Cryptography (Informa UK Limited)-Vol. 15, pp 287-301
Abstract: Many network applications involve data transfer; therefore there is a need to have a secure network, which can be achieved through the use of cryptography In this paper, we present an innovative algorithm for encryption and decryption using connected graphs Message represented by a connected graph can be encrypted by using a spanning tree of the graph Any message represented in the graph is either on a branch or on a chord with respect to the spanning tree Depending whether it is a branch or a chord graph theorems are applied to the spanning tree for both encryption and decryption purposes This approach used to encrypt leads to more secure data transfer more

Topics: Spanning tree (70%), Distributed minimum spanning tree (63%), Encryption (61%) more

Open accessBook
11 Aug 2003-
Topics: Active networking (77%), Software-defined networking (71%), Networking hardware (71%) more

85 Citations

Open accessJournal ArticleDOI: 10.1016/J.PROCS.2015.08.071
Abstract: Trellis representation of codes helps in analyzing and understanding the nature of the codes. Trellis has the connected graph nature where all paths from the ‘root’ vertex to ‘goal’ vertex forms the codewords. Efficient encoding and decoding algorithms are existing for communication over trellis. In the conventional communication system, Trellis is constructed for the encoded message at the sender and the algorithm such as Viterbi is used to decode the encoded message at the receiver. Any receiver with such decoding mechanism can be able to decode the message, which gives the chance for the intruder to get the message making the communication insecure. In this paper we propose a reliable and secure communication system which provides reliability by the Error Correction Techniques and Security by the graph based Cryptosystem. Using such system intruder's access to the informa- tion can be avoided and also if any errors occurred during transmission over noisy channel can be corrected. We have used Kernel codes and it's Trellis representation to demonstrate the construction of reliable and secure cryptosystem. more

Topics: Space–time trellis code (66%), Decoding methods (54%), Error detection and correction (54%) more

2 Citations

Open accessJournal ArticleDOI: 10.1155/2021/6614172
Abstract: In today’s technological world, confidentiality is an important issue to deal with, and it is carried out through different proficiencies. Cryptography is a scientific technique of securing a communication from unauthenticated approach. There exist many encryption algorithms in cryptography for data security. The need of new nonstandard encryption algorithms has been raised to prevent the communication from traditional attacks. This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages. more

Topics: Encryption (70%), Secure transmission (65%), Cryptography (63%) more

1 Citations

Journal ArticleDOI: 10.1080/09720529.2021.1932896
Abstract: In this work, a new graph has been defined as a main point to design a new version of an asymmetric encryption scheme. This graph is formed based on the scalar multiplication operation on elliptic ... more

Proceedings ArticleDOI: 10.1109/ICSTM.2015.7225441
06 May 2015-
Abstract: Forney's representation of Trellis code received wide attention by researchers and engineers with its simplicity in representing codes and elegant nature to analyze codes with sys- tem theoretic properties, graph theoretic properties with efficient encoding and decoding procedures. In this paper, we consider the connected graph nature of trellis and propose security feature over Trellis using fundamental cut-set and fundamental circuits principle. We use the graph theoretic approach, by generating limited spanning trees of trellis, fundamental cut-sets and fundamental circuits, private key cryptosystem is defined in which fundamental cut-set acts as a key to encrypt and decrypt. We have used a class of group codes called Kernel codes and its trellis, to show that private key cryptosystem can be used over Trellis and fundamental cut-set acts as a key to encrypt and decrypt message at sender and receiver respectively. more

Topics: Trellis (graph) (68%), Space–time trellis code (66%), Cryptosystem (55%) more


Open accessBook
01 Jan 1969-
Topics: Wagner graph (81%), Ladder graph (76%), Graph theory (72%) more

15,318 Citations

Journal ArticleDOI: 10.1109/PROC.1975.9996
N.R. Malik1Institutions (1)
01 Oct 1975-
Abstract: Introductory Graph Theory with ApplicationsGraph Theory with ApplicationsResearch Topics in Graph Theory and Its ApplicationsChemical Graph TheoryMathematical Foundations and Applications of Graph EntropyGraph Theory with Applications to Engineering and Computer ScienceGraphs Theory and ApplicationsQuantitative Graph TheoryApplied Graph TheoryChemical Graph TheoryA First Course in Graph TheoryGraph TheoryGraph Theory with ApplicationsGraph Theory with ApplicationsSpectra of GraphsFuzzy Graph Theory with Applications to Human TraffickingApplications of Graph TheoryChemical Applications of Graph TheoryRecent Advancements in Graph TheoryA Textbook of Graph TheoryGraph Theory and Its Engineering ApplicationsGraph Theory, Combinatorics, and ApplicationsAdvanced Graph Theory and CombinatoricsTopics in Intersection Graph TheoryGraph Theory with Applications to Engineering and Computer ScienceGraph Theory and Its Applications, Second EditionHandbook of Research on Advanced Applications of Graph Theory in Modern SocietyGraph Theory with Applications to Algorithms and Computer ScienceGraph TheoryGraph Theory with Algorithms and its ApplicationsGraph TheoryGraph Theory with ApplicationsGraph Theory ApplicationsHandbook of Graph TheoryGraph Theory and Its Applications to Problems of SocietyBasic Graph Theory with ApplicationsTen more

Topics: Sorting (60%), Graph theory (56%), Application software (53%)

756 Citations

Proceedings ArticleDOI: 10.1109/ICM.2005.1590056
M.I. Aziz1, S. AkbarInstitutions (1)
13 Dec 2005-
Abstract: in today's world of communications if you assume that you are not being monitored then perhaps you are not aware of the threats. Since now every communication, now, takes place via electronic media it is very necessary to implement some kind of security, whether it is implemented through hardware like FPGAs, μ-Controllers, or through software in your PCs. more

Topics: Cryptography (53%), Electronic media (52%), Software (52%)

290 Citations

Open accessBook
11 Aug 2003-
Topics: Active networking (77%), Software-defined networking (71%), Networking hardware (71%) more

85 Citations

Open accessJournal ArticleDOI: 10.1016/S0898-1221(98)00177-1
Hung-Min Sun1, Shiuh-Pyng Shieh2Institutions (2)
Abstract: A secret sharing scheme for the prohibited structure is a method of sharing a master key among a finite set of participants in such a way that only certain prespecified subsets of participants cannot recover the master key. A secret sharing scheme is called perfect, if any subset of participants who cannot recover the master key obtains no information regarding the master key. In this paper, we propose an efficient construction of perfect secret sharing schemes for graph-based prohibited structures where a vertex denotes a participant and an edge does a pair of participants who cannot recover the master key. The information rate of our scheme is 2n, where n is the number of participants. more

Topics: Verifiable secret sharing (64%), Key distribution (64%), Homomorphic secret sharing (63%) more

7 Citations

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