Virendra R. Sule

Virendra R. Sule
Indian Institute of Technology Bombay | IIT Bombay ·  Department of Electrical Engineering

Ph.D.

About

54
Publications
7,482
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
370
Citations
Citations since 2017
23 Research Items
79 Citations
2017201820192020202120222023051015
2017201820192020202120222023051015
2017201820192020202120222023051015
2017201820192020202120222023051015
Introduction
I am working on following types of problems: 1. Local inversion problem of functions in finite fields and application to cryptanalysis of symmetric and public key crfyptography. 2. Representing and computing all solutions to Boolean systems arising in Cryptanalysis, rational solutions of polynomials over finite fields. 3. Application of systems theory to Boolean dynamical systems.

Publications

Publications (54)
Article
Full-text available
This paper proposes an application of a new observer theory for non-linear systems developed previously to solve the Cryptanalysis problem of a special class of pseudorandom generators which are commonly used in Cryptography. The Cryptanalysis problem addressed here is that of the recovery of internal state of the non-linear dynamic stream generato...
Preprint
Full-text available
This paper is a short summery of results announced in a previous paper on a new universal method for Cryptanalysis which uses a Black Box linear algebra approach to computation of local inversion of nonlinear maps in finite fields. It is shown that one local inverse $x$ of the map equation $y=F(x)$ can be computed by using the minimal polynomial of...
Article
Full-text available
This paper develops the analysis of discrete-time periodically time-varying linear systems over finite fields. It is shown that the conditions for the existence of Floquet Transform for periodic linear systems over reals (or complex) do not carry forward for this case over finite fields. The existence of Floquet Transform is shown to be equivalent...
Preprint
Full-text available
This paper presents algorithms for local inversion of maps and shows how several important computational problems such as cryptanalysis of symmetric encryption algorithms, RSA algorithm and solving the elliptic curve discrete log problem (ECDLP) can be addressed as local inversion problems. The methodology is termed as the \emph{Local Inversion Att...
Article
Full-text available
This paper considers dynamical systems over finite fields (DSFF) defined by a map in a vector space over a finite field. An associated linear dynamical system is constructed over the space of functions. This system constitutes the well known Koopman linear system framework of dynamical systems, hence called the Koopman linear system (KLS). It is fi...
Preprint
Full-text available
For a map (function) $F(x):\ftwo^n\rightarrow\ftwo^n$ and a given $y$ in the image of $F$ the problem of \emph{local inversion} of $F$ is to find all inverse images $x$ in $\ftwo^n$ such that $y=F(x)$. In Cryptology, such a problem arises in Cryptanalysis of One way Functions (OWFs). The well known TMTO attack in Cryptanalysis is a probabilistic al...
Article
Full-text available
This paper proposes an internal state recovery attack on special class of stream generators called non-linear combiners and filter generators over finite fields consisting of linear feedback shift registers (LFSRs) and nonlinear functions combining internal states to form output stream. This attack utilizes the concept of an observer well known in...
Chapter
Kammadanam, Vamshi KrishnaSule, VirendraHong, YiThe paper explores conditions to be satisfied by feedback shift registers (FSRs) to generate a permutation (alternatively a nonsingular map) of the state space over various fields. Such a condition is well known over the binary field F2. This is extended to small finite fields and a simple sufficient...
Preprint
Full-text available
This paper formulates and solves the problem of robust compensation of multiport active network. This is an important engineering problem as networks designed differ in parameter values due to tolerance during manufacture from their actual realizations in chips and hardware. Parameters also undergo changes due to environmental factors. Hence, pract...
Preprint
Full-text available
This paper proposes a symbolic representation of non-linear maps $F$ in $\ff^n$ in terms of linear combination of basis functions of a subspace of $(\ff^n)^0$, the dual space of $\ff^n$. Using this representation, it is shown that the inverse of $F$ whenever it exists can also be represented in a similar symbolic form using the same basis functions...
Preprint
Full-text available
Given a discrete dynamical system defined by a map in a vector space over a finite field called Finite State Systems (FSS), a dual linear system over the space of functions on the state space is constructed using the dual map. This system constitutes the well known Koopman linear system framework of dynamical systems, hence called the Koopman linea...
Article
Full-text available
This paper develops an approach for point addition and doubling on elliptic curves over finite fields using one variable polynomial arithmetic based on Euclidean division. This approach succeeds in computing these operations on realistic curves over large finite fields due to a striking observation about computing the gcd of two polynomials one whi...
Chapter
This paper proposes an attack on shift register based stream ciphers. The attack consists of recovering the internal state of the registers at a starting clock instant from which the output stream is available. For a given output stream the evolution of the output function at the clocking times is first computed in symbolic form as a sequence of Bo...
Preprint
Full-text available
This paper develops methods for analyzing periodic orbits of states of linear feedback shift registers with periodic coefficients and estimating their lengths. These shift registers are among the simplest nonlinear feedback shift registers (FSRs) whose orbit lengths can be determined by feasible computation. In general such a problem for nonlinear...
Conference Paper
This paper proposes a method of embedding block cipher algorithms in a new algorithm in order to create variations and improving security of the original algorithm. The method is concretely explained for embedding AES128 block cipher. In practice there is often a need to develop a bank of secure cipher algorithms in short time. Designing such algor...
Article
This paper proposes a method of embedding block cipher algorithms in a new algorithm in order to create variations and improving security of the original algorithm. The method is concretely explained for embedding AES128 block cipher. In practice there is often a need to develop a bank of secure cipher algorithms in short time. Designing such algor...
Article
A cryptocurrency (or crypto currency) is a digital asset designed to work as a medium of exchange that uses strong cryptography to secure financial transactions, control the creation of additional units, and verify the transfer of asset. Cryptocurrencies use decentralized control as opposed to centralized digital currency and central banking system...
Conference Paper
Full-text available
This paper explores an elementary idea for searching factors of numbers in terms of residues of the number with respect to small moduli and reconstructing the factors using the Chinese remainder theorem (CRT). If n is a number required to be factored the factors can be obtained from search through factors of residues n mod m i in Z mi for small pai...
Article
Full-text available
This paper considers the well-known problem of deriving a linear model of dynamics of periodically switched circuits w.r.t. small perturbations in duty cycle (or switching instances) as external control inputs. A rigorous approach to this problem is developed and is shown that the linearized model is shift invariant and discrete time in nature. Thi...
Article
Full-text available
A theory of stable interconnection of multiport active networks is developed using the stable coprime fractional representation of hybrid network functions at their ports. One of the difficulties in designing stable port interconnection of networks has been that the feedback signal flow graph of the interconnection cannot be easily obtained apart f...
Conference Paper
An approach is presented for solving linear systems of equations over the Boolean algebra B0 = {0, 1} based on implicants of Boolean functions. The approach solves for all implicant terms which represent all solutions of the system. Traditional approach to solving such linear systems is to consider them over the field GF(2) and solve either by Gaus...
Article
Full-text available
This paper develops a parallel computational solver for computing all satifying assignments of a Boolean system of equations defined by Boolean functions of several variables. While there are well known solvers for satisfiability of Boolean formulas in CNF form, these are designed primarily for deciding satisfiability of the formula and do not addr...
Conference Paper
Full-text available
This paper presents an approach for point addition and doubling on elliptic curves over finite fields F p which is based on one variable polynomial division. This is achieved by identifying the plane F p × F p with the extension field F p2 and transforming the elliptic curve equation as well as line equations arising in point addition or doubling i...
Article
Full-text available
This paper proposes a theory for designing stable interconnection of linear active multi-port networks at the ports. Such interconnections can lead to unstable networks even if the original networks are stable with respect to bounded port excitations. Hence such a theory is necessary for realising interconnections of active multiport networks. Stab...
Article
Full-text available
Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a fallout of the previous work by authors on Boolean satisfiability \cite{sul1, sul2,sude}, however the algorith...
Article
Full-text available
We propose an approach for decomposing Boolean satisfiability problems while extend-ing recent results of [12] on solving Boolean systems of equations. Developments in [12] were aimed at the expansion of functions f in orthonormal (ON) sets of base functions as a generalization of the Boole-Shannon expansion and the derivation of the consistency co...
Article
Full-text available
The well known Boole-Shannon expansion of Boolean functions in several variables (with coefficients in a Boolean algebra B) is also known in more general form in terms of expansion in a set Φ of orthonormal functions. However, unlike the one variable step of this expansion an analogous elimination theorem and consistency is not well known. This art...
Article
Full-text available
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments based on the generalized Boole-Shannon orthonormal (ON) expansion discussed in \cite{sule}. Paper \cite{sule} develops a condition fo...
Article
Full-text available
The well known Boole-Shannon expansion of Boolean functions in several variables (with co-efficients in a Boolean algebra $B$) is also known in more general form in terms of expansion in a set $\Phi$ of orthonormal functions. However, unlike the one variable step of this expansion an analogous elimination theorem and consistency is not well known....
Article
Full-text available
This paper shows that if exponentiation b = X k in groups of finite field units or B = [k]X in elliptic curves is considered as encryption of X with exponent k treated as symmetric key, then the decryption or the computation of X from b (respectively B) can be achieved in polynomial time with a high probability under random choice of k. Since given...
Article
Full-text available
Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillatio...
Conference Paper
Full-text available
In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable, called "time". We define in a natural way causality and stability of input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonst...
Article
This paper considers the Diffie-Hellman problem (DHP) over the matrix group GL n over finite fields and shows that for matrices A and exponents k, l satisfying certain conditions called the modulus conditions, the problem can be solved without solving the discrete logarithm problem (DLP) involving only polynomial number of operations in n. A specia...
Article
Full-text available
This paper develops a cryptanalysis of the pairing based Diffie Hellman (DH) key exchange schemes which have found important applications as in the tripartite exchange scheme proposed in (1). The analysis of weak keys of the standard DH scheme proposed in (2) is applied to show existence of weak sessions for tripartite schemes over super- singular...
Article
Full-text available
This paper investigates the Diffie-Hellman key exchange scheme over the group F * p m of nonzero elements of finite fields and shows that there exist exponents k, l satisfying certain conditions called the modulus conditions, for which the Diffie Hellman Problem (DHP) can be solved in polynomial number of operations in m without solving the discret...
Article
This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically defined inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external...
Article
Full-text available
In this paper, we present an efficient modeling and computational scheme for a repeated solution of an eddy-current system with different values of the supply frequency as well as of the permeability and conductivity of the eddy-current region. The scheme is based on a general parametric expression obtained for the finite-element (FE) solution with...
Article
Full-text available
In this work we study multidimensional (nD) linear differential behaviors with a distinguished independent variable, called "time." We define in a natural way causality and stability of input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstr...
Article
This paper develops an approach to behavioral systems theory in which a state space representation of behaviors is utilised. This representation is a first order hybrid representation of behaviors called pencil representation. An algorithm well known after Dirac and Bergmann (DB) is shown to be central in obtaining a constraint free and observable...
Article
Full-text available
The stabilization of line of sight (LOS) against vehicle-induced disturbance is an essential feature of an electromechanical gimbaled sighting system with an optical sensor for sighting. We describe the design of a high-performance controller for an electromechancial target-tracking system with an optical sensor for sighting. The control law is obt...
Article
Many engineering applications require efficient computation of the solution of the Poisson equation defined over one, two or three dimensions, representing a wide variety of physical systems. The most popular method used for this purpose is the finite element method (FEM). An important class of applications in modeling and simulation require repeat...
Article
The problem of vibration reduction in helicopter fuselages using the concept of active control of structural response is addressed. When the large size of the coupled gearbox-flexible fuselage system dynamics is considered, first a balanced-realization-based order reduction is employed to reduce the size of the problem. Then using the reduced-order...
Article
This paper extends the concept of steady-state frequency response, well known in the theory of linear time-invariant (LTI) systems, to linear time-varying systems with periodic co-efficients, called periodic systems. It is shown that for an internally stable periodic system there exist complete orthogonal systems of real periodic functions ff n g a...
Article
This paper provides a solution of the feedback stabilization problem over commutative rings for matrix transfer functions. Stabilizability of a transfer matrix is realised as local stabilizability over the entire spectrum of the ring. For stabilizable plants, certain modules generated by its fractions and that of the stabilizing controller are show...
Article
Full-text available
This paper provides a solution of the feedback stabilization problem over commu-tative rings for matrix transfer functions. Stabilizability of a transfer matrix is realised as local stabilizability over the entire spectrum of the ring. For stabilizable plants, certain modules gener-ated by its fractions and that of the stabilizing controller are sh...
Article
Full-text available
This paper develops a theory of feedback stabilization for SISO transfer functions over a general integral domain which extends the well-known coprime factorization approach to stabilization. Necessary and sufficient conditions for stabilizability of a transfer function in this general setting are obtained. These conditions are then refined in the...
Article
In this paper tradeoffs in multivariable sensitivity reduction are developed for a new Directional Sensitivity Function (DSF). The directions considered belong to direction modules of the nonminimum phase zeros (NMP) and unstable poles of the transfer matrices. The well known Bode Integral is extended for the DSF whenever the direction vector coinc...
Article
The term integrity of a feedback controller refers to its ability to offer closed loop stability even under failure of feedback sensors. This paper provides the theory of feedback controllers having integrity, in the setting of the stable factorization approach. The main results developed are, 1) the necessary and sufficient condition for a given f...

Questions

Question (1)
Question
What are applications of the theory of differential equations in complex domain in physical sciences or engineering? In which physical science differentiation wrt complex variable makes sense?
The theory of diferential equations in complex domain is very well developed and is one the most beautiful areas of mathematics. A well known old book on this subject is by E. Hill. There are many contemporary results in this area but all of them I found are in mathematics. I would like to know a physical science or engineering application.

Network

Cited By

Projects