Ph.D, MSc, BSc

Dr. Lakshmy K. V. currently serves as Assistant Professor at TIFAC-CORE in Cyber Security, Coimbatore Campus.


2009-2015 PhD in Mathematics Amrita Vishwa Vidyapeetham, Coimbatore
2005-2007 MSc. in Mathematics University of Calicut, Kerala
2002-2005 BSc. in Mathematics University of Calicut, Kerala


Year Affiliation
September 1, 2014 - November 1, 2015 Research Associate
Project Title : ADRIN-DEA
Principal Investigator : Prof. M. Sethumadhavan
TIFAC-CORE in Cyber Security
June 18, 2008 - August 3, 2009 Junior Research Fellow
Project Title :
VLSI Development of Finite Field Arithmetic
Principal Investigator : Prof. M. Sethumadhavan, Dr. T. R. Padmanabhan
TIFAC-CORE in Cyber Security


  • Cryptographic Boolean Functions, National Level Instructional Workshop on Cryptology on May 10, 2011 Amrita Vishwa Vidyapeetham, Coimbatore
  • Rotation Symmetric Boolean Functions, Society for Electronic Transactions and Secutrity (SETS) on February 13, 2013 Chennai
  • Fundemental from Real Analysis, Coimbatore Institute of Engineering and Technology on December 3, 2016, Coimbatore


Publication Type: Journal Article

Year of Conference Publication Type Title


Journal Article

T. W. Cusick, Dr. Lakshmy K. V., and Sethumadhavan, M., “Affine equivalence of monomial rotation symmetric Boolean functions: A Pólya's theorem approach”, Journal of Mathematical Cryptology, vol. 10, pp. 145-156, 2016.[Abstract]

there have been efforts to investigate the affine equivalence of Boolean functions. Due to the complexity of the general problem, only affine equivalence under certain groups of permutations is usually considered. Boolean functions which are invariant under the action of cyclic rotation of the input variables are known as rotation symmetric (RS) Boolean functions. Due to their speed of computation and the prospect of being good cryptographic Boolean functions, this class of Boolean functions has received a lot of attention from cryptographic researchers. In this paper, we study affine equivalence for the simplest rotation symmetric Boolean functions, called MRS functions, which are generated by the cyclic permutations of a single monomial. Using Pólya's enumeration theorem, we compute the number of equivalence classes, under certain large groups of permutations, for these MRS functions in any number n of variables. If n is prime, we obtain the number of equivalence classes under the group of all permutations of the variables.

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Journal Article

Dr. Lakshmy K. V., Sethumadhavan, M., and Cusick, T. W., “Counting rotation symmetric functions using Polya's theorem”, Discrete Applied Mathematics, vol. 169, pp. 162-167, 2014.[Abstract]

Homogeneous rotation symmetric (invariant under cyclic permutation of the variables) Boolean functions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an explicit formula for the number of homogeneous rotation symmetric functions over the finite field GF(pm) using Polya's enumeration theorem, which completely solves the open problem proposed by Yuan Li in 2008. This result simplifies the proof and the nonexplicit counting formula given by Shaojing Fu et al. over the field GF(p). This paper also gives an explicit count for n-variable balanced rotation symmetric Boolean functions with n=pq, where p and q are distinct primes. Previous work only gave an explicit count for the case where n is prime and lower bounds for the case where n is a prime power.

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Publication Type: Conference Proceedings

Year of Conference Publication Type Title


Conference Proceedings

A. Nandakumar, Amritha, P. P., Dr. Lakshmy K. V., and Talluri, V. S., “Non linear secret sharing for gray scale images”, Procedia Engineering, vol. 30. Coimbatore, pp. 945-952, 2012.[Abstract]

Most of the image secret sharing schemes employ linear secret sharing such as Shamir's secret sharing scheme. Linear secret sharing threshold schemes are vulnerable to cheating problem (Tompa-Woll attack), where a participant can submit a false share and only he will be able to obtain the correct secret. Every Linear (k,n) threshold schemes are equivalent to some Maximum distance separable (MDS) codes. Finding more MDS linear codes is difficult and therefore finding more linear threshold schemes is not easy. In 1996, A.Renvall and C. Ding proposed a non-linear secret sharing scheme based on quadratic forms. In 2001 Pieprzyk and Zhang proposed a non linear scheme based on highly non linear balanced Boolean function. Even though work on nonlinear secret sharing schemes has been done on numbers, no significant work on images has been done so far. In this paper, concept of non-linear secret sharing scheme is extended to gray scale images. Experimental results concluded that non linear secret sharing can be applied for secret image sharing. It resists the Tompa-Woll attack and also able to retrieve the correct secret image, even if some of the shares are modified by a cheater.

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