Nistala V.E.S. Murthy

Publications

• Elliptic Curve Cryptography-Diffie-Hellman Technique Extended ForMultiple Two Party Keys At A Time

  Vankamamidi S. Naresh, Nistala V.E.S. Murthy, V.V. Narasimha Rao

  International Journal of Computer Science Issues. 01/2011; Vol. 8:P167-172.

  In recent years Elliptic Curve Cryptography (ECC) is emerging as an alternative to traditional public key crypto systems (DSA, RSA, AES etc.). ECC offers equivalent security with smaller key sizes resulting in faster computations, lower power consumption, as well as memory and bandwidth savings. In ... [more] In recent years Elliptic Curve Cryptography (ECC) is emerging as an alternative to traditional public key crypto systems (DSA, RSA, AES etc.). ECC offers equivalent security with smaller key sizes resulting in faster computations, lower power consumption, as well as memory and bandwidth savings. In this paper, we present elliptic Diffie-Helmann tecgnique to generate multiple shared keys at a time with reduced Key Exchange Operations (KEOs) for increasing security and widening applicability. A comparative study between proposed protocol and other crypto systems is made and satisfactory results have been obtained. Also an upper bound for the number of shared keys in terms of the number of exchanged keys and for a given number of shared keys, the minimum required number of keys to be exchanged are obtained.

• Representation of L-Fuzzy Relational Substructures via a Galois Connection

  Nistala V.E.S. Murthy, Peruru G Prasad

  Communicated. 01/2011;

• L-Fuzzy (Binary) Relations, Equivalences and, Partitions, and Their Representations

  Nistala V.E.S. Murthy, Pusuluri V.N.H. Ravi

  International Journal of Computational Cognition,. 01/2011; vol 9:p51-74.

  In this Paper, for any L-fuzzy set X, we construct a crisp set in such a way that there is a Galois connection between the set of all L-fuzzy reflexive (irreflexive, symmetric, antisymmetric, transitive) relations on the former and certain reflexive (irreflexive, symmetric, antisymmetric, transitive... [more] In this Paper, for any L-fuzzy set X, we construct a crisp set in such a way that there is a Galois connection between the set of all L-fuzzy reflexive (irreflexive, symmetric, antisymmetric, transitive) relations on the former and certain reflexive (irreflexive, symmetric, antisymmetric, transitive) relations on the later. The above Galois connection is also shown to have extended to between L-fuzzy equivalence relations, L-fuzzy I-ary relations and L-fuzzy partitions on the former and certain I-ary relations, equivalence relations and partitions respectively on the later. Further, we also construct a Galois connection between the set of all L-fuzzy partitions and the set of all L-fuzzy equivalence relations on the L-fuzzy set X. For each of these Galois Connections, both the onward and return order preserving maps are characterized in terms of the complete lattice L being certain chains.

• Extended Diffie-Hellman Technique to Generate Multiple Shared Keys at a Time with Reduced KEOs and its Polynomial Time Complexity

  Nistala V.E.S. Murthy, Vankamamidi S. Naresh

  International Journal of Computer Science Issues. 01/2010;

  Recently Biswas[1] extended Diffie-Hellman technique to generate multiple two-person-shared keys by exchange of two public keys. In this paper, we further generalize the Diffie-Hellman technique to generate multiple two-person-shared keys by exchange of any number of public keys and study its Polyno... [more] Recently Biswas[1] extended Diffie-Hellman technique to generate multiple two-person-shared keys by exchange of two public keys. In this paper, we further generalize the Diffie-Hellman technique to generate multiple two-person-shared keys by exchange of any number of public keys and study its Polynomial Time Complexity, Security etc. Also, an upper bound for the number of shared keys in terms of the number of exchanged keys and for a given number of shared keys, the minimum required number of keys to be exchanged, were arrived at. Lastly, a comparative study between the proposed technique and the Diffie-Hellman technique repeated m-times is made.

• Diffie-Hellman Technique Extended to Efficient and Simpler Group Key Distribution Protocol

  Vankamamidi S. Naresh, Nistala V.E.S. Murthy

  International Journal of Computer Applications. 01/2010;

  Ever since 2-party Diffie-Hellman exchange wasfirst proposed in 1976, there have been efforts toextend its simplicity and elegance to a groupsetting. Notable solutions have been proposed bymichael Steiner Gene Tsudik Waidner(in 1996)and Recently G.P.Biswas was proposed acontributory group key agreem... [more] Ever since 2-party Diffie-Hellman exchange wasfirst proposed in 1976, there have been efforts toextend its simplicity and elegance to a groupsetting. Notable solutions have been proposed bymichael Steiner Gene Tsudik Waidner(in 1996)and Recently G.P.Biswas was proposed acontributory group key agreement protocol forgeneration of multiparty key and compared withother protocol and satisfactory results obtained.In this paper an m-party DH key distributionfor group (improved group DH) was proposed bymodifying G.P.Biswas protocol and we argued thatour protocol is optimal with respect to most of theaspects of protocol complexity and also it‟ssecurity discussed.

• Properties of (Inverse) Images of Intuitionistic L-Fuzzy Subsets and Correspodence and Isomorphism Theorems for Intuitionistic L-Fuzzy Subgroups

  Nistala V.E.S. Murthy, Aguru G. Vasanti

  International Journal of Computational Cognition. 01/2010;

  The aim of this paper is basically two fold. First, we make a study of some of the standard (lattice) algebraic properties of the L-intuitionistic fuzzy/L-vague images and L-intuitionistic fuzzy/L-vague inverse images of L-intuitionistic fuzzy/L-vague subsets of a set under a crisp map. Next, we app... [more] The aim of this paper is basically two fold. First, we make a study of some of the standard (lattice) algebraic properties of the L-intuitionistic fuzzy/L-vague images and L-intuitionistic fuzzy/L-vague inverse images of L-intuitionistic fuzzy/L-vague subsets of a set under a crisp map. Next, we apply parts of this theory to generalize such results as First Isomorphism Theorem, Second Isomorphism Theorem, Third Isomorphism Theorem, Correspondence Theorem, etc.. Also studied are L-intuitionistic fuzzy/L-vague (normal) subgroups, L-intuitionistic fuzzy/L-vague normalizer etc..

• Some (Fuzzy) Binary Relations Are Fixed Points Of Certain Operators-Revisited

  Nistala V.E.S. Murthy, Pusuluri V.N.H. Ravi

  Reflections des ERA Journal of Mathematics. 01/2010; vol.5(4):p289-308.

  An L-Set is any function X from a set U to a complete lattice L. For any L-Set X, first we make a study of lattice theoretic relations between various (complete) sub (semi) lattices due to L-fuzzy binary relations like L-(ir)reflexive/L-(anti)symmetric/L-transitive relations on the L-set X and lastl... [more] An L-Set is any function X from a set U to a complete lattice L. For any L-Set X, first we make a study of lattice theoretic relations between various (complete) sub (semi) lattices due to L-fuzzy binary relations like L-(ir)reflexive/L-(anti)symmetric/L-transitive relations on the L-set X and lastly, we construct certain operators on the complete lattice of all L-binary relations on the L-set X whose fixed points are precisely the L-(ir)reflexive, L-(anti)symmetric, L-transitive relations on the L-set X.

• Some (Fuzzy) Binary Relations Are Fixed Points Of Certain Operators

  Nistala V.E.S. Murthy, Peruru G Prasad

  Reflections des ERA Journal of Mathematics,. 01/2010; vol.5(3):p273-288.

  For any set X, first we make a study of lattice theoretic relations between various (complete) sub (semi) lattices due to (L-fuzzy) binary relations like (L-)(ir)reflexive/(L-)(anti)symmetric/(L-)transitive relations on the set X and lastly, we construct certain operators on the complete lattice of ... [more] For any set X, first we make a study of lattice theoretic relations between various (complete) sub (semi) lattices due to (L-fuzzy) binary relations like (L-)(ir)reflexive/(L-)(anti)symmetric/(L-)transitive relations on the set X and lastly, we construct certain operators on the complete lattice of all (L-)binary relations on the( L-)set X whose fixed points are precisely the (L-)(ir)reflexive, (L-)(anti)symmetric, (L-)transitive relations on the (L-)set X.

• Representation Of L-Fuzzy Relations Via A Galois Connection

  Nistala V.E.S. Murthy, Peruru G Prasad

  Tamkang Journal of Mathematics. 01/2009; vol 40:P287-305.

  In the above paper, Galois connections between various types of fuzzy binary relations and fuzzy I-ary relations on a crisp set with truth values in a complete lattice and same type of crisp binary and I-ary relations on the associated fuzzy point set are established.... [more] In the above paper, Galois connections between various types of fuzzy binary relations and fuzzy I-ary relations on a crisp set with truth values in a complete lattice and same type of crisp binary and I-ary relations on the associated fuzzy point set are established.

• Mu-Modules

  Nistala V.E.S. Murthy

  Acta Ciencia Indica. 01/2005; vol 31M:p379-386.

  Continuing the study of algebraic structures on f-sets, in this paper, for any f-ring ScR=(R,RBar, L_R), for any abelian f-group ScM=(M,MBar,L_M) and for any complete homomorphism between complete lattices mu from L_R to L_M, the notion of ScM being left mu-module over ScR is introduced. In the firs... [more] Continuing the study of algebraic structures on f-sets, in this paper, for any f-ring ScR=(R,RBar, L_R), for any abelian f-group ScM=(M,MBar,L_M) and for any complete homomorphism between complete lattices mu from L_R to L_M, the notion of ScM being left mu-module over ScR is introduced. In the first proposition we show that this notion properly generalizes the existing notions of both crisp left R-module and L-fuzzy left R-module.Further, the algebra of nu-sub modules, f-sub object generation, f-sum of nu-sub modules etc. are studied.

• Correspondence and Isomorphism Theorems for Mu-Modules

  Nistala V.E.S. Murthy

  Acta Ciencia Indica. 01/2005; vol 31M:p1001-1004.

  Continuing the study of nu-sub modules of a mu-module, in this paper, the notion of f-homomorphism between a left mu-module and a left nu-module is introduced. Further, the First, Second and Third Isomorphism theorems and the Correspondence theorems for mu-modules are established, from which the cor... [more] Continuing the study of nu-sub modules of a mu-module, in this paper, the notion of f-homomorphism between a left mu-module and a left nu-module is introduced. Further, the First, Second and Third Isomorphism theorems and the Correspondence theorems for mu-modules are established, from which the corresponding study of mu-vector spaces is redundant.

• About A New Notion of Image for Subsystems of Partial Algebra

  Nistala V.E.S. Murthy, Vaddiparthi Yogeswara

  Acta Ciencia Indica. 01/2005; vol 31M:P1005-1008.

  In this paper, for any pair of partial algebras (A,s_A) and (B,s_B) of types tau and omega respectively, for any map f between A and B and for any partial algebra (C,s_C) of type alpha which is a sub type of both tau and omega, via the Axiom of Choice, we introduce the notion of an image for (C,s_C)... [more] In this paper, for any pair of partial algebras (A,s_A) and (B,s_B) of types tau and omega respectively, for any map f between A and B and for any partial algebra (C,s_C) of type alpha which is a sub type of both tau and omega, via the Axiom of Choice, we introduce the notion of an image for (C,s_C) and study its properties. Further, algebraic properties of this and other substructures of partial algebras under images and inverse images of an omega partial algebra homomorphism are studied.

• Embedding of Complete Lattices of Chang and Lowen Fuzzy Topologies

  Nistala V.E.S. Murthy

  Acta Ciencia Indica. 01/2004; vol 30M:p823-831.

  This paper unifies both Chang and Lowen fuzzy topologies on a set via the new notion of f-topology on an f-set introduced earlier by this author and imbeds the complete lattices of Chang and Lowen fuzzy topologies on the underlying crisp set of an f-set into the complete lattice of f-topologies on t... [more] This paper unifies both Chang and Lowen fuzzy topologies on a set via the new notion of f-topology on an f-set introduced earlier by this author and imbeds the complete lattices of Chang and Lowen fuzzy topologies on the underlying crisp set of an f-set into the complete lattice of f-topologies on the f-set. Further, some Galois connections between f-topologies on an f-set and Chang and Lowen fuzzy topologies on the underlying crisp set of the f-set are also established.

• Galois Connections Between Fuzzy, Binary And Equivalence Relations And The Crisp, Binary And Equivalence Relations

  Nistala V.E.S. Murthy, Peruru G. Prasad

  Proceedings of The National Seminar on Topology, Category Theory and their applications to Computer Science, P120-129, March 11-13, 2004, Department of Mathematics, St Joseph’s College, Irinjalaguda, Kerala (organized by the Kerala Mathematical Society.); 01/2004

• f-Topological Spaces

  Nistala V.E.S. Murthy

  Proceedings of The National Seminar on Topology, Category Theory and their applications to Computer Science, Department of Mathematics, St Joseph’s College, Irinjalaguda, Kerala (organized by the Kerala Mathematical Society. Invited Talk); 01/2004

  With the advent of f-sets and f-maps of Murthy, in which 1. an f-set is a fuzzy set that carries along, its underlying set, its complete lattice where the fuzzy set takes its truth values for members of its underlying set and its fuzzy map that specifies membership values for all members in its und... [more] With the advent of f-sets and f-maps of Murthy, in which 1. an f-set is a fuzzy set that carries along, its underlying set, its complete lattice where the fuzzy set takes its truth values for members of its underlying set and its fuzzy map that specifies membership values for all members in its underlying set; in other words, is a triplet, ScA=(A,Abar,L_A), which is a natural generalization of Goguen-fuzzy subset, which itself is a natural generalization of both, Zadeh's [0,1]-valued fuzzy subset of a set and [0,1]-sub interval valued fuzzy subset of a set, and 2. an f-map is an ordered pair consisting of, a map between underlying sets of the given f-sets and a complete homomorphism between underlying complete lattices -which may possibly be completely different, of the given f-sets, it is natural to ask which of the (fuzzy) algebraic and/or (fuzzy) topological structures (theorems) extend on to f-sets. In this paper, the notions of fuzzy topological space due to Chang and also due to Lowen and fuzzy continuity of a crisp map between fuzzy topological spaces with fuzzy direct and inverse images are generalized to, f-topological space and f-continuous map between f-topological spaces -possibly with truth values in completely different complete lattices, with f-direct and f-inverse images are extended. Further, the new notions f-interior, f-closure and the operators due to them, f-subbase, f-base, f-product etc. are shown to have the standard properties of their crisp cousins.

• A Note on Ringlets

  Nistala V.E.S. Murthy, Vaddiparthy Yogeswara

  The Mathematics Education. 01/2003; vol 36:p205-209.

  The notion of a ringlet is introduced by M.K. Singh. In this paper, the notion of a ringlet homomorphism is introduced and several ring theoretic analogues were studied. In the end the category of ringlets together with ringlet homomorphisms between pairs of ringlets is shown to be essentially algeb... [more] The notion of a ringlet is introduced by M.K. Singh. In this paper, the notion of a ringlet homomorphism is introduced and several ring theoretic analogues were studied. In the end the category of ringlets together with ringlet homomorphisms between pairs of ringlets is shown to be essentially algebraic.

• Fuzzy homomorphisms between fuzzy rings with truth values in different complete lattices

  Nistala V.E.S. Murthy

  Acta Ciencia Indica. 01/2003; vol 29:p45-66.

  With the advent of f-sets and f-maps of Murthy, in which 1. an f-set is a fuzzy set that carries along, its underlying set, its complete lattice where the fuzzy set takes its truth values for members of its underlying set and its fuzzy map that specifies membership values for all members in its und... [more] With the advent of f-sets and f-maps of Murthy, in which 1. an f-set is a fuzzy set that carries along, its underlying set, its complete lattice where the fuzzy set takes its truth values for members of its underlying set and its fuzzy map that specifies membership values for all members in its underlying set; in other words, is a triplet, ScA=(A,Abar,L_A), which is a natural generalization of Goguen-fuzzy subset, which itself is a natural generalization of both, Zadeh's [0,1]-valued fuzzy subset of a set and [0,1]-sub interval valued fuzzy subset of a set, and 2. an f-map is an ordered pair consisting of, a map between underlying sets of the given f-sets and a complete homomorphism between underlying complete lattices -which may possibly be completely different, of the given f-sets, it is natural to ask which of the (fuzzy) algebraic and/or (fuzzy) topological structures (theorems) extend on to f-sets. In this paper, the notions of fuzzy sub ring and crisp homomorphism between crisp rings with fuzzy direct and inverse images are generalized to, f-ring and and f-homomorphism between f-rings -possibly with truth values in completely different complete lattices, with f-direct and f-inverse images and their important properties are shown to have extended.

• Correspondence and Isomorphism Theorems for Fuzzy Rings

  Nistala V.E.S. Murthy

  Acta Ciencia Indica. 01/2003; vol 29:p67-70.

  Continuing the study of f-rings and f-homomorphism between f-rings -possibly with truth values in completely different complete lattices, with f-direct and f-inverse images, both of which are generalizations, by Murthy, of fuzzy sub ring and crisp homomorphism between crisp rings with fuzzy direct a... [more] Continuing the study of f-rings and f-homomorphism between f-rings -possibly with truth values in completely different complete lattices, with f-direct and f-inverse images, both of which are generalizations, by Murthy, of fuzzy sub ring and crisp homomorphism between crisp rings with fuzzy direct and inverse images, in this paper, we establish First, Second and Third Isomorphism theorems and Correspondence theorem for f-rings and f-homomorphisms.

• Representation of Fuzzy Subalgebras by Crisp Subalgebras

  U.M. Swamy, Nistala V.E.S. Murthy

  Fuzzy Sets and Systems. 01/2003; vol 136:p115-119.

  In the above paper, following the Galois Correspondence between all L-fuzzy subsets of a set X and all crisp subsets of the L-fuzzy points of X, introduced in an earlier paper, for any universal algebra of a given type, another universal algebra of the same type is constructed in such a way that the... [more] In the above paper, following the Galois Correspondence between all L-fuzzy subsets of a set X and all crisp subsets of the L-fuzzy points of X, introduced in an earlier paper, for any universal algebra of a given type, another universal algebra of the same type is constructed in such a way that the complete lattice of all L-fuzzy subalgebras of the former is meet isomorphic to the complete lattice of all closed crisp subalgebras of the later, via the Galois correspondence.

• Is The Class of all Fuzzy Rings A Fuzzy HSP-Class?

  Nistala V.E.S. Murthy

  Tamkang Journal of Mathematics. 01/2003; vol 34:P271-292.

  In this paper, the notion of fuzzy sub ring is generalized to f-ring and for f-rings, f-sub objects and their algebra, f-sub object generations, f-homomorphisms and f-isomorphism theorems, f-products, some Category theoretic properties etc. were studied.... [more] In this paper, the notion of fuzzy sub ring is generalized to f-ring and for f-rings, f-sub objects and their algebra, f-sub object generations, f-homomorphisms and f-isomorphism theorems, f-products, some Category theoretic properties etc. were studied.