Prof. Madan Mohan Singh

Designation: Professor

Department: Basic Sciences and Social Sciences

Qualifications:

M.Sc. (Bh.U), Ph.D (P.U.)

Areas of Interest/Specialization:

Number Theory, Algebraic Number Theory, Graph Theory, Numerical Analysis, Discrete Mathematics

Experience:   

32 years at Department of Mathematics, Pachhunga University College, NEHU, Aizawl    and Department of B.S.S.S., School of Technology, NEHU, Shillong

Extension Work

Outside University:

  • Examined the Theses of Department of Mathematics Gauhati University.
  • Examined the Theses/ M.Phil Dissertations of Dibrugarh University
  • External expert( attended) in Ph. D. Viva- Voce examinations of the following Universities:
    Assam University, Silchar
    Dibrugarh University, Dibrugarh,
    Gauhati University, Gauhati
  • Member of Governing Body of Synod College, Shillong
  • Confidential works of Public Service Commissions
  • Reviewer:
    Journals of the Korean Mathematical Society
    Mathematical Reviews  published by American Mathematical Society(AMS)
    Boletim da Sociedade Paranaense de Matemática, Maringá, Brasil
    Mathematical Methods in the Applied Sciences published by Wiley,USA
    IEEE Access published by Inst. of  Electrical and Electronic Engineers Inc. USA
    Defence Science Journal published by DRDO, India

Administrative responsibilities undertaken:

  • Chairman, Departmental Purchase Committee since November27, 2013 to November 26, 2016 and November 27, 2019 to till date..
  • Head, Department of Basic Sciences & Social Sciences, NEHU, November, 2013-2016 and November, 2019 onward.
  • Member, Academic Council, NEHU (Since 2013-2016 and November,2019 onward.
  • Hostel Warden (April, 2011-2013)
  • Member of the Organising Committee of the 96th Indian Science Congress at NEHU, Shillong, January, 2009
  • Member of the Organising Committee for the event of Commemoration of Birth Anniversaries of Madam Curie & Sir C.V.Raman, November, 2015.
  • Coordinator, Centralized Evaluation Committee, School of Technology, July,2010-2011.
  • Member of B. Tech. admission committee ( June, 2009 -2011)
  • Member of the Tabulation Committee ( July 2010- Dec. 2010 )
  • Member of the Scrutiny Committee (July 2010- Dec.2010)

Academic affiliations

  • Mentor in the DST, INSPIRE Programme, NEHU, December, 2009-2011
  • Member, Board of Under-Graduate Studies, Department of Mathematics, NEHU, 1995-1998
  • Member, Board of Under-Graduate Studies of Mathematics, MZU,1995-2004
  • Examination Moderation Board Member of NEHU from 2006-till date
  • Member, Board of School of Technology, NEHU from November, 2011 to November, 2013 , November,2013 to November,2016 , and October,2017 for three years.
  • Subject Coordinator of the course of Engineering  Mathematics in the Department of B.S.S.S., School of Technology, NEHU from 2006 till date

Life Member of

  1. Indian Mathematical Society (IMS)
  2. Indian Science Congress Association (ISCA);
  3. Assam Mathematical Society.
  4. Cryptology Research Society of India (CRSI)
  5. Bona Mathematica
  6. Indian Institute of Public Administration(IIPA)

Member of :

  • Vision Parishad of India (VPI)
  • ACTA CIENCIA MATHEMATICA
  • Resonance
  • Editorial Board, NEHU JYOTI

Ph. D Awarded/Supervised          

S.No. Name PG Degree
1. Ms. Pinkimani Goswami  M.Sc., Tezpur Univ
2. Mr.  Amplify Sawkmie    M.Sc., NEHU 
3. Ms Shivangi Asthana M.Sc., NEHU
4. Ms Algracia Kharbuki  M.Sc., NEHU
5 Mr. Laithun Boro M.S., Gauhati University
6.  Mr. Kamakhya Paul  M.S., Pondicherry University
7. Ms. Diamond Kharkongor  M.Sc., NEHU

Publications

Book/Chapter:

  1. Singh, M.M., Goswami P. (2019). Integer Factorization Problem. In:  Emerging Security Algorithms and Techniques, edited by Khaleel Ahmad,et al CRC Press, Taylor & Francis Group, New York, Pp 59-78, ISBN-978-081-5361459
  2. Singh, M.M., Boro, L. (2020). Nilpotent Graphs attached to Rings Revisited”. In:  PARISAR (The Scope), Vol. II, edited by Abani Sonowal, Purbayon PublicationGuwahati – 1, India, Pp 150-164, ISBN-978-93-90589-16-6
  3. Goswami, P., Singh, M. M., Biswas (2021). XTR Algorithm: Efficient and Compact Subgroup Trace Representation (Chapter 3). In: Functional Encryption edited by Khaleel Ahmed et al, Springer, Pp 37-57, ISBN 978-3-030-60889-7.
  4. Goswami, P., Singh M. M., Rahman, K.T. (2021). Digital Signatures (Chapter 14). In: Functional Encryption edited by Khaleel Ahmed et al, Springer, Pp 243-277, ISBN 978-3-030- 60889-7.
  5. Paul, K., Singh, M.M., Goswami, P. (2022). A New Public Key Encryption Using Dickson Polynomials Over Finite Field with 2^m, In: Nonlinear Dynamics and Applications edited by S.Banergee & A. Saha, Springer Proceedings in Complexity. Springer, Cham. Pp.555-563 https://doi.org/10.1007/978-3-030-99792-2_45
  6. Goswami, P., Singh, M. M. (2023),Study of Some Properties and Behavior of the Group of Signed Quadratic Residues and its Applications to Cryptography in Novel Developments in Futuristic AI-based Technologies  Algorithms for Intelligent Systems Edited by M. Sahni, J. M. Merigo, W. Hussain, Springer, Pages 249-264
    DOI: DOI: 10.1007/978-981-99-3076-0_16  

The Publications given below are Reviewed / Indexed in the Mathematical Reviews (MR)Database(Published by American Mathematical Society(AMS)) with unique MR Number:

Selected list of significant referred International/ National Journals:

  1. D. Kharkongor, L. Boro, M. M. Singh, S. Dutta (2023) TOPOLOGICAL INDICES OF TOTAL GRAPH OF THE RING Zn × Zm , TWMS Journal of Applied and Engineering Mathematics,  13(4),  pp. 1434-1445
  2. L. Boro, M. M. Singh and J. Goswami(2023) The Unit Graph of a Commutative Semiring, Journal of Algebraic systems, Volume 12(1), Pages 79-89 
  3. Shivangi Asthana and M. M. Singh(2023) On the Diophantine Equations x^2 + 139^m = y^n and x^2 + 499^m = y^n, Jnanabha, Volume 53(1), Pages 207-211 DOI:10.58250/jnanabha.2023.53124 
  4. Laithun Boro and Madan Mohan Singh  (2024)  Line graphs associated to Von Neumann regular graphs of rings, Discrete Mathematics, Algorithms  and Applications, https://doi.org/10.1142/S1793830923500088
  5. Laithun Boro, Madan Mohan Singh and J. Gswami (2022)  On the line graphs associated to the unit graphs of rings,  Palestine Journal of Mathematics,  Vol. 11(4), 139–145
  6. Kamakhya Paul, Pinkimani Goswami and  Madan Mohan Singh (2022) Algebraic Braid Group Public Key Cryptography, Jnanabha, 52(02), 219-224 DOI:https://doi.org/10.58250/jnanabha.2022.52225
  7. Kharkonger D, Boro L, Singh M. M., Dutta S (2022) Some Properties of Von Neumann Regular Graphs of Rings, J. Indones. Math. Soc.Vol. 28, No. 02 (2022), pp. 185–193.
  8. Boro L, Singh M. M., Goswami J (2022) Unit Graph of the Ring  Zm X Zn Lobachevskii Journal of Mathematics, 43(02), 345-352
  9. Wannarisuk Nongbsap, Madan Mohan Singh (2021) A Cryptographic Application of the M-Injectivity of Mn(Zp) Over Itself. International Journal of Recent Technology and Engineering 10(4), 7-14.
  10. Algracia Kharbuki and Madan Mohan Singh (2021) HURWITZ COMPLEX CONTINUED FRACTION EXPANSION OF SOME COMPLEX QUADRATIC IRRATIONALS, The Mathematics Student, 90 (3-4), July-December, 61â??72
  11. Madan Mohan Singh, Laithun Boro and Jituparna Goswami (2021).  Line Graph associated to the Intersection Graph of Ideals of Rings. Journal of Mathematical and Computational Science, 11 (03), 2736-2745 .
  12. Madan Mohan Singh and Shivangi Asthana (2020). On the Diophantine Equation
    3^x + 117^y  =  z^2. GANITA, 70(2), 43-47.
  13. Madan Mohan Singh and Wannarisuk Nongbsap (2021). A public key Cryptography Based on the m- injectivity of Zpq over itself, Malaya Journal of Matematik, 9(1), 130-135.
  14. Madan Mohan Singh and Amplify Sawkmie (2019).  Digraphs associated with the Kth power map on the quotient ring of polynomials over finite fields. Journal of  Algebra and its Applications, 18 (11): 1950218 (18 pages).
  15. Madan Mohan Singh and A. Kharbuki (2019). Hurwitz Complex Continued Fraction and complex theory of Pell’s Equation x2 - Dy2 = 1 for some specific values of D. Indian Journal of Mathematics, 61(3): 381-394.
  16. Madan Mohan Singh and Shivangi Asthana (2019). On the Diophantine Equation x2 +37l =yn, JP Journal of Algebra, Number Theory and Applications, 44 (1): 15- 30.
  17. Madan Mohan Singh and Shivangi Asthana (2019).  On the Diophantine Equation 2x + 7y=z2. International Journal of Research in Advent Technology, 7 (5): 13-14.
  18. Madan Mohan Singh and Shivangi Asthana (2019). On the Diophantine Equation 53x + 143y =z2 .” Annals of Pure and Applied Mathematics, 19 (2): 193-196
  19. Madan Mohan Singh and W. Nongbsap (2019). A Public Key Cryptography based on the m- Injectivity of  Zpqr over itself. Journal of Emerging Technologies and Innovative Research,  6 (3): 131-139.
  20. Madan Mohan Singh and A. Kharbuki (2019).  Pell’s Equations in Gaussian Integers. JP Journal of Algebra, Number Theory and Applications, 42 (1): 15-32
  21. Madan Mohan Singh and P. Goswami (2018). An Application of Signed Quadratic Residues in Public Key Cryptography. Discrete Mathematics, Algorithms and Applications, 10 (5): 1850081(14 pages).
  22. Madan Mohan Singh and A. Sawkmie (2018). On the uniqueness of the factorization of power digraphs modulo n. Rendiconti Del Seminario Mathematico Della Universita Di Padova, 140: 185-219.
  23. Madan Mohan Singh, Pinkimani Goswami and Bubu Bhuyan (2017). A new public key cryptosystem Z*n 2 over . Discrete Mathematics, algorithms and Applications, 9 (6): 1750080(11 pages).
  24. Madan Mohan Singh and Shivangi Asthana (2017). On the Diophantine Equation 8x +113y =z2.  Inernational Journal of Algebra, 11 (5): 225-230.
  25.  Madan Mohan Singh and Shivangi Asthana (2017). On the Diophantine Equation 3x + 13y =z2 . Inernational Journal of Pure and Applied Mathematics, 114 (2): 301-304.
  26. Madan Mohan Singh, Pinkimani Goswami and Bubu Bhuyan (2017). A new public key scheme based on integer factorization and discrete logarithm. Palestine Journal of Mathematics, 6(2): 580-584.
  27. Madan Mohan Singh, Pinkimani Goswami and Bubu Bhuyan (2016). A new public key scheme based on DRSA and generalized GDLP. Discrete Mathematics, Algorithms and Applications, 8 (4): 1650057(7 pages).
  28. Madan Mohan Singh, A. Sawkmie (2015). On the tree structure of the power digraphs modulo n. Czechoslovak Mathematical Journal, 65(140), No. 4: 923--945; MR3441326.
  29. Madan Mohan Singh, Pinkimani Goswami (2015). On the number of semi-primitive roots modulo n. Notes on Number Theory and Discrete Mathematics, 21(4): 48-55.
  30.  Madan Mohan Singh, Pinkimani Goswami and Bubu Bhuyan (2015). A new public key encryption scheme based on two cryptographic assumptions.  Malaya Journal of Matematik. 3(4): 419-422.

Conferences/Seminars (Presented/Co-author):

  1. Domination number of Von Neumann regular graphs of rings presented in the two day International Conference on Recent Trends in Modern Mathematics (RTMM-2021) organized by the PG & Research Department of Mathematics, St. Johnâ??s College, Palayamkottai, on 23rd & 24th of September, 2021.
  2. Signed Quadratic Residues and its Applications to Cryptography presented in the UGC-SAP Sponsored National Seminar on ‘Current Trends in Mathematics and Mathematical Sciences’ held during 14th -16th  March, 2017 organised by the Department of Mathematics, North-Eastern Hill University, Shillong.
  3. Some New Result on Semi- Primitive Roots Modulo n  presented in the’proceedings of the 103rd Indian Science Congress section of Mathematical Sciences (including Statistics)’ organised by University of Mysore, Mysuru during January 03 - 07, 2016
  4. A new public key scheme presented in the ‘National Conference on Emerging Trends in Mathematics and Mathematical Sciences’  during 17th -19th  December, 2015 organised by the Calcutta Mathematical Society, Kolkata.
  5. A Survey on Hurwitz Complex Continued Fraction presented at UGC-SAP Sponsored ‘National Seminar– Current Trends in Mathematics and Mathematical Sciences’ held at Department of Mathematics, NEHU, Shillong, March 14th -16th, 2017.
  6. Diophantine Equations and its applications in the ‘National Seminar on Mathematics Education ‘organized by NERIE & NCERT, Umiam, during December 21st & 22nd , 2017.
  7. Integer factorization: its historical perspective and recent development in the ‘National Seminar on Mathematics Education’ organized by NERIE & NCERT, Umiam, during December 21st & 22nd , 2017.
  8. On the length of the largest cycle consist by the quadratic residues in the UGC SAP sponsored three- day ‘National Seminar on Topology & Algebra’organized by   the Department of Mathematics, NEHU, Shillong during March 26th & 28th, 2018.
  9. An introduction to complex theory of Pell’s Equation - D  = 1 in the UGC SAP sponsored three- day ‘National Seminar on Topology & Algebra’ organized by  the Department of Mathematics, NEHU, Shillong during March 26th to 28th , 2018
  10. Complex Continued Fraction: Its applications to Binary Quadratic Forms , presented at ‘National Seminar on Pure and Applied Mathematics’ organized by Department of  Mathematics, St. Mary’s college, Shillong on 19th & 20th September, 2018.
  11. Exponential Diophantine Equations and Its Consequences, presented at ‘National Seminar on Pure and Applied Mathematics’ organized by Department of Mathematics, St. Mary’s college, Shillong on 19th & 20th September, 2018.
  12. Generalized Pell’s Equations in Gaussian Integers, presented at UGC-SAP  ‘National Seminar on Topology and Algebra’  organized by Department of Mathematics, NEHU, Shillong on 13th & 14th March, 2019.
  13. A Note on Exponential Equations,  presented at UGC-SAP  ‘National Seminar on Topology and Algebra’  organized by Department of Mathematics, NEHU, Shillong on 13th & 14th March, 2019.
  14. The Unit graph of a Commutative Semiring, presented at UGC-SAP  ‘National Seminar on Topology and Algebra’  organized by Department of Mathematics, NEHU, Shillong on 13th & 14th March, 2019.
  15. Unit Graph of the Ring Zm x Zn, presented at ‘ National Conference on Emerging Trends in Advanced Mathematical Sciences and Its Interdisciplinary Areas (NCETAMSIIA 2020)’ organized by Department of Mathematical Sciences, Bodoland University, Kokrajhar, BTC, Assam on 21st & 22nd February, 2020.
  16. On the Diophantine Equation x2 + 139m = yn, presented at '1st International Conference On Advances in Mathematics, Science and Technology(ICAMST-2020)' organized by Department of Mathematics, Rajiv Gandhi University, Doimukh, Arunachal Pradesh on 1st – 3rd September, 2020.
  17. On the Idempotent Complete Graph of a Ring presented at 2nd Annual Convention of North East (India) Academy of Science & Technology(NEAST) & International Seminar on Recent Advances in Science & Technology organized by Mizoram University, Tanhril, Aizawl on 16th – 18th November, 2020.
  18. The Diophantine Equation x^2 + 499^m = y^n presented at 2nd Annual Convention of North East (India) Academy of Science & Technology(NEAST) & International Seminar on Recent Advances in Science & Technology organized by Mizoram University, Tanhril, Aizawl on 16th – 18th November, 2020.

Invited Speaker/ Resource Person/Guest Faculty/Chairperson

  1. Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during 14th  to 21st April, 2007.
  2. Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during November 27th to December 6th, 2008.
  3. Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during 09th to 18th  July, 2009.
  4. Guest Faculty for M.Sc. in the Department of Mathematics, NEHU, Shillong March, 2011 to July, 2011.
  5. Guest Faculty for B. Tech at NIT Arunachal in the Department of Computer Science & Engineering at Yupia during  09th  to 16th  September, 2012.
  6. Resource Person in the Refresher Course in Mathematics at the Department of Mathematics, NEHU, Shillong during March19 to  April 16, 2013.
  7. Resource Person in the Refresher Course in Information Technology at the Department  of  I T, NEHU, Shillong during July, 2013.
  8. Guest Faculty for M.Sc. in the Department of Mathematics, NEHU, Shillong , February, 2016 to July, 2022
  9. Resource Person in the UGC sponsored service level classes for Civil Services/ Banking/ SSS held at Women’s College, Shillong February 2012 to November, 2018
  10. Chairperson (one of the sessions) in the National Seminar on “ Pure and Applied Mathematics” organized by the Department of Mathematics, St. Mary’s College, Shillong on 19th & 20th September, 2018.
  11. Resource Person in the National Workshop on CRYPTOGRAPHY organized by Department of  Mathematics, University of Science & Technology, Meghalaya and Sponsored by Indian Statistical Institute, Kolkata on 25th & 26th September, 2018.
  12. Resource Person in the UGC-sponsored  Special Summer School in Basic Sciences and Technology at the UGC- HRDC, NEHU, Shillong during 08th to 21st July, 2019.
  13. Resource Person for the Webinar on “ Popularizing Mathematics “ at the Department of Mathematics, St. Mary’s College, Shillong held on 29th November,2021
  14. Delivered an invited talk on ‘ Group of Signed Quadratic Residues & its Applications to Cryptography ‘ in International Conference on Nonlinear Applied Analysis & Optimizations organized by Department of Mathematical Sciences, IIT(BHU), Varanasi, during 21st -23rd December, 2021.
  15. Delivered an invited talk on ‘Basic Science for Sustainable Development & Atmanirbharata’ in Azadi ka Amrit Mahotsav Celebration of “VIGYANUTSAV” organized by DST, SEED Division GoI and SCSTE, Meghalaya during June30, 2022
  16. Chairperson (one of the sessions) in the National Seminar on “ Recent Trends in Topology and its Applications (Virtual Mode)” organized by the Department of Mathematics, NEHU, Shillong on 4th  & 5th August, 2022. 
  17. Chairperson (one of the sessions) in the International Workshop on “ Mathematical Foundation and Applications of Gravity (Hybrid Mode)” organized by the Department of Basic Sciences & Social Sciences, NEHU, Shillong on 25th  & 26th August, 2022.