Avishek Adhikari

Professor and Head of the Department

• Visiting Scientist at Linkoping University, Sweden, 2006.
• Post-Doctoral fellow at INRIA-Rocquencourt, Paris, France, 2005.

• Ph.D. from Indian Statistical Institute in 2004 under the supervision of Professor Bimal Ray, former Director of Indian Statistical Institute and  Padma Shree Awardee.

• M.Sc in Pure Mathematics from the Department of Pure Mathematics, the University of Calcutta in 2001. Stood 1st and the Recipient of Gold Medal.
• B.Sc. with Hons. in Mathematics from St. Xaviers' College, University of Calcutta, in 1999. Stood second at the University of Calcutta.

After completing the Masters in 2001 from the Department of Pure Mathematics, University of Calcutta, I joined the Statistics and Mathematics Unit of Indian Statistical Institute, Kolkata as a JRF. After successful completion of the Course Work, I started my research on Cryptology under the supervision of Professor Bimal Ray, the former Director of the Indian Statistical Institute. During my Ph.D., I worked on Secret Sharing, Visual Cryptography, and Combinatorial Designs.  After my Ph.D. in 2004, I joined INRIA, Paris, France as a Post Doc Fellow and worked with Professor Anne Canteaut on Cryptographic Boolean Functions. Then I joined Linkoping University, Sweden as a Visiting Scientist and worked with Professor Erik Trell on DNA Secret Sharing. In July, 2006, I joined the Department of Pure Mathematics, the University of Calcutta as a Lecturer. I continued there as a faculty member till January 16, 2019.

Research Activities:

My broad area of research is Cryptology and Combinatorics. In cryptology, I am mainly interested in secret sharing schemes, cryptanaysis of stream and block ciphers. Currently I am exploring quantum cryptography. In combinatorics, I am interested in finding structures of critical sets in Latin squares and graph coloring. I have active academic research collaboration with Kyushu University (Japan), University of North Texas, USA, University of Calgary, Canada,  University of Wollongong, Australia, Indian Statistical Institute, IIT Madras, IIT Kharagpur. In a nutshell, my research interest includes  Applications of Algebra, Graph Theory, Cryptography, Cryptanalysis of Stream and Block Ciphers, Secret Sharing, DNA Cryptography, Visual Cryptography, Image Encryption, Wireless Sensor Networks. I worked as a Principal and Co-Investigator of the twelve projects funded by DRDO, DIT, DST, DST-SERB, DST-FIST, NBHM, etc. For more details regarding the project, please click here.

Administrative and Professional Responsibilities:

1. Head of the Department of Mathematics, Presidency University (Since 1st November, 2021)
2. Founder Secretary of the and  Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC), having branches in Sweden and Japan (since 2006).
3. Treasurer of Cryptology Research Society of India (CRSI) since 2008
4. Former NBHM Eastern Zonal Coordinator for conducting MSc and Ph.D. Fellowship Examinations in Eastern Region.
5. One of the Editors of the Research Monograph entitled "Mathematical and Statistical Applications in Life Sciences and Engineering" published by Springer, 2017.
6. Member of the Board of Studies of many institutes. 
7. Program Committee Member of many International Conferences.

My field of interest is Algebra and its applications to different interdisciplinary fields such as cryptology, coding theory, and graph theory. My future plan is to offer a few contemporary interdisciplinary topics in which students will explore how their known knowledge of Abstract Algebra, Linear Algebra, Number Theory is useful in solving real-life practical challenging problems using the concepts of cryptology, coding theory, and graph theory.

The online classes offered by him during the LockDown period are uploaded systematically to the YouTube Channel. To view the classes, please click here. 

Apart from teaching, I am engaged with the following activities:

1. Worked as a paper setter, moderator, examiner of different examinations organized by different Universities and Institutes.

2. Worked as Thesis Reviewer of Ph.D. Thesis of different Universities.
3. Worked as an external expert member of the Thesis Viva organized by different Universities.
4. Worked as reviewers of leading journals such as AMS MathSciNet, Discrete Mathematics, Discrete Applied Mathematics, Design Codes and Cryptography, IEEE journals, IEICE, many other Springer and Elsevier Journals, etc
5. Worked as an external Committee member of interview for the recruitment of Project Linked personnel at Indian Statistical Institute.
6. Worked as External Member for the M.Tech (CS) and M.Math Dissertation of Indian Statistical Institute.
7. Worked as a member of the Board of Studies of different Institutions. 

Ph.D. Students Received Ph.D. under my supervision:

1. Dr. Angsuman Das (Currently at Presidency University, Kolkata) (Click here for more details)                                                                                                 

Thesis Title: On Some Mathematical Aspects of Security Notions and Constructions of Public Key Cryptosystems and Secret Sharing Schemes

Awarded in 2014 from the University of Calcutta.

2. Dr. Partha Sarathi Roy (Currently at School of Computing and Information Technology University of Wollongong, Australia) (Click here for more details)

Thesis Title: On Some Aspects of Secret Sharing Schemes and Oblivious Transfer Protocols Using Mathematical Tools,

Awarded in 2015 from the University of Calcutta.

3. Dr. Sabyasachi Dutta (Currently at Department of Computer Science, University of Calgary, Canada) (Click here for more details)

Thesis Title: Algebraic And Combinatorial Aspects Of Visual Cryptography,

Awarded in 2016 from the University of Calcutta.

4. Dr. Ushnish Sarkar (Currently at Netaji Subhas Open University) (Click here for more details)

Thesis Title: On Some Combinatorial Studies of Radio k-coloring Problems of Graphs and Related Issues,

Awarded in 2017 from the University of Calcutta.

5. Dr. Prakash Dey

Thesis Title: Algebraic Aspects Of Cryptanalysis On Secret-Key Cryptosystems,

Awarded in 2017 from the University of Calcutta.

6. Dr Subarsha Banerjee (Assistant Professor, JIS University), (for more details, please click here) 

Thesis Title: Spectra of Graphs on Various Algebraic Structures.

Awarded in 2022 from the University of Calcutta.

7. Dr Jyotirmoy Pramanik (Assistant Professor, Taki Government College) (Click here for more details)

Thesis Title: Fault Tolerance In Cryptographic Secret Sharing Using Algebraic Techniques

Awarded in 2022 from the University of Calcutta.

8. Dr. Md. Kutubuddin Sardar (Assistant Professor, Sister Nivedita University) (for more details, please click here)

Thesis Title: On Some Algebraic Aspects of Secret Image Sharing

Awarded in 2023 from the University of Calcutta.

Ph.D. Students doing Ph.D. under my supervision (Registered at University of Calcutta)

1. Sandip Kumar Mondal

Ph.D. Students doing Ph.D. under my supervision (at Presidency University):

1. Chandan Goswami
2. Himadry Sekhar Roy

Membership of Learned Societies :

1. Indian Science Congress Association (Life Member)
2. Calcutta Mathematical Society (Life Member)
3. Life Member of Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC), Branches: Japan, Sweden.
4. Cryptology Research Society of India (Life Member)

• Text Books: 

1. (jointly with M R Adhikari), Basic Topology 1: Metric Spaces and General Topology, published by Springer in 2022. For more details, please visit the website "https://www.springerprofessional.de/en/basic-topology-1/23234990".

2. (jointly with M R Adhikari), Basic Topology 2: Topological Groups, Topology of Manifolds and Lie Groups, published by Springer in 2022. For more details, please visit the website "https://link.springer.com/book/10.1007/978-981-16-6577-6".

3. (jointly with M R Adhikari), Basic Modern Algebra with Applications, published by Springer. For more details, please visit the website "http://www.springer.com/mathematics/algebra/book/978-81-322-1598-1".

4. (jointly with M R Adhikari), Introduction to Linear Algebra with Application to Basic Cryptography, Asian Books Private Limited, 2007.

5. (jointly with M R Adhikari), Text Book of Linear Algebra : An Introduction to Modern Algebra, Allied Publishers, 2004.

6. (jointly with M R Adhikari), Groups, Rings and Modules with Applications, Universities Press, 2003.

• Edited Books 

1. (jointly with Ralf Küsters and Bart Preneel), Progress in Cryptology – INDOCRYPT 2021, Published by Springer, 2021. For more details, please visit the website: https://link.springer.com/book/10.1007/978-3-030-92518-5 

2. (jointly with M R Adhikari and Y. P. Chaubey), Mathematical and Statistical Applications in Life Sciences and Engineering,  published by Springer in 2017, For more details, please visit the website: http://www.springer.com/in/book/9789811053696.

3. (jointly with M R Adhikari and Y P Chaubey), Contemporary Topics in Mathematics and Statistics with Applications, Asian Books Private Limited, 2012.

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Few Selected Journal Publications (Recent): 

1. (with Md Kutubuddin Sardar and Jyotirmoy Pramanik), (t,k,n) Regional Secret Image Sharing over Finite Fields,Signal Processing, Volume 210, September 2023, 109082, Elsevier Journal, (Science Citation Index), https://doi.org/10.1016/j.sigpro.2023.109082

2. (with K, P., Dutta, S.,Sethumadhavan M.) Proactive visual cryptographic schemes for general access structures. Multimed Tools Appl (2023), Springer, (Science Citation Index Expanded).  https://doi.org/10.1007/s11042-023-14998-7
3. (with Subarsha Banerjee), On spectra of power graphs of finite cyclic & dihedral groups, to appear in Rocky Mountain Journal of Mathematics, 2022  (Science Citation Index Expanded). 
4. (with P Sarkar, SK Sahoo, C Goswami), Connectivity invariant lightweight resiliency improvement strategies for CRT-subset scheme, Ad Hoc Networks, Elsevier Journal, Volume 129, 15 April 2022, 102803 (Science Citation Index). https://doi.org/10.1016/j.adhoc.2022.102803

5. (with S K Sahoo and S Dutta), Practical attacks on a class of secret image sharing schemes based on Chinese Remainder Theorem, Computers and Electrical Engineering Elsevier Journal,  Volume 100, May 2022, 107924, (Science Citation Index). https://doi.org/10.1016/j.compeleceng.2022.107924

6. (with Md Kutubuddin Sardar), Essential secret image sharing scheme with small and equal sized shadows, Signal Processing, : Image Communication, Elsevier Journal, 2020, 87, 115923, (Science Citation Index) https://doi.org/10.1016/j.image.2020.115923

7. (with Md Kutubuddin Sardar), A New Lossless Secret Color Image Sharing Scheme with Small Shadow Size, Journal of Visual Communication and Image Representation, Elsevier Journal, 2020. (Science Citation Index Expanded) https://doi.org/10.1016/j.jvcir.2020.102768

8. (with Sabyasachi Dutta and Sushmita Ruj), Maximal contrast color visual secret sharing schemes, Designs, Codes and Cryptography, Springer Journal, , Volume 87, Issue 7, pp 1699–1711, 2019. (Science Citation Index) https://link.springer.com/article/10.1007/s10623-018-0570-6