Basic Sciences & Social Sciences Department

Designation: Associate Professor

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

Areas of Interest/Specialization: Number Theory, Algebraic Number Theory, Graph Theory, Numerical Analysis, Discrete Mathematics

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

- 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 96
^{th}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)

- 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**

- Indian Mathematical Society (IMS)
- Indian Science Congress Association (ISCA);
- Assam Mathematical Society.
- Cryptography Research Society of India(CSRI)
- Bona Mathematica
- Indian Institute of Public Administration(IIPA)

**Member of :**

- ACTA CIENCIA MATHEMATICA
- Resonance
- Editorial Board, NEHU JYOTI
- Invited Reviewer, Mathematical Reviews, American Mathematical Society
- Referee in reputed National/ International Journals

- Ms. Pinkimani Goswami, M.Sc., Tezpur Univ.
- Mr. Amplify Sawkmie, M.Sc., NEHU
- Ms Shivangi Asthana(submitted) M.Sc., NEHU

**Book/Chapter:**

**Madan Mohan Singh* and Pinkimani Goswami,**Book chapter on “Integer Factorization Problem” Emerging Security Algorithms and Techniques, edited by Khaleel Ahmad,et al CRC Press, Taylor & Francis Group*, Newyork,***2019***, pages59-78, ISBN-978-081-5361459*

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

- MR3994438 Pending Sawkmie, Amplify; Singh, Madan Mohan Digraphs associated with the kth power map on the quotient ring of polynomials over finite fields. J. Algebra Appl. 18 (2019), no. 11, 1950218, 18 pp. 05C20 (13M05)
- MR3894747 Reviewed Goswami, Pinkimani; Singh, Madan Mohan An applications of signed quadratic residues in public key cryptography. Discrete Math. Algorithms Appl. 10 (2018), no. 6, 1850081, 14 pp. (Reviewer: Robert Juricevic) 94A60 (11A07)
- MR3880217 Reviewed Sawkmie, Amplify; Singh, Madan Mohan On the uniqueness of the factorization of power digraphs modulo n. Rend. Semin. Mat. Univ. Padova 140 (2018), 185–219. 05C20 (11A07 11A15)
- MR3737060 Reviewed Goswami, Pinkimani; Singh, Madan Mohan; Bhuyan, Bubu A new public key cryptosystem over Z∗n2. Discrete Math. Algorithms Appl. 9 (2017), no. 6, 1750080, 11 pp. (Reviewer: Cunsheng Ding) 94A60 (11A07 11A15)
- MR3646271 Reviewed Goswami, Pinkimani; Singh, Madan Mohan; Bhuyan, Bubu A new public key scheme based on integer factorization and discrete logarithm. Palest. J. Math. 6 (2017), no. 2, 580–584. 94A60
- MR3569762 Reviewed Goswami, Pinkimani; Singh, Madan Mohan; Bhuyan, Bubu A new public key scheme based on DRSA and generalized GDLP. Discrete Math. Algorithms Appl. 8 (2016), no. 4, 1650057, 7 pp. 94A60 (11T71)
- MR3441326 Reviewed Sawkmie, Amplify; Singh, Madan Mohan On the tree structure of the power digraphs modulo n. Czechoslovak Math. J. 65(140) (2015), no. 4, 923–945. (Reviewer: Christian Lavault) 68R10 (05C05 05C20 11A07 11A15)
- MR1481923 Indexed Singh, Madan Mohan Solution of Ax2+B=y2 and applications. Math. Ed. (Siwan) 31 (1997), no. 3, 166–167. 11D09
- MR1623553 Indexed Singh, M. M. The Diophantine equation x2+2xy−3y2=3z2 and its consequence. Math. Student 64 (1995), no. 1-4, 138–140 (1996). 11D09
- MR1360290 Reviewed Singh, Madan Mohan Some new results on nuclear sequence spaces. Acta Cienc. Indica Math. 20 (1994), no. 4, 311–315. (Reviewer: José Bonet) 46A45 (46A11)
- MR1292377 Indexed Singh, M. M. Integer solutions of 1+2y2=x5. Math. Student 63 (1994), no. 1-4, 107–108. 11D41
- MR1292376 Indexed Singh, M. M. Integer solutions and consequences of the equation yz+zx+xy=0. Math. Student 63 (1994), no. 1-4, 102–106. 11D09
- MR0993785 Reviewed Sinha, T. N.; Singh, M. M. Some quartic equations with only trivial solutions. Math. Student 53 (1985), no. 1-4, 239–242 (1987). (Reviewer: Valeriu ?t. Udrescu) 11D25 Review PDF Clipboard Journal Article

**Selected list of Significant referred International/ National Journals: **

- Madan Mohan Singh and Amplify Sawkmie (2019). Digraphs associated with the K
^{th}power map on the quotient ring of polynomials over finite fields. Journal of Algebra and its Applications, 18 (11): 1950218 (18 pages). - Madan Mohan Singh and A. Kharbuki (2019). Hurwitz Complex Continued Fraction and complex theory of Pell’s Equation - D = 1 for some specific values of D. Indian Journal of Mathematics, 61(3): 381-394.
- Madan Mohan Singh and Shivangi Asthana (2019). On the Diophantine Equation + = . International Journal of Research in Advent Technology, 7 (5): 13-14.
- Madan Mohan Singh and Shivangi Asthana (2019). On the Diophantine Equation + = .” Annals of Pure and Applied Mathematics, 19 (2): 193-196
- Madan Mohan Singh and W. Nongbsap (2019). A Public Key Cryptography based on the m- Injectivity of over itself. Journal of Emerging Technologies and Innovative Research, 6 (3): 131-139.
- 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 - 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).
- 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.
- Madan Mohan Singh, Pinkimani Goswami and Bubu Bhuyan (2017). A new public key cryptosystem over . Discrete Mathematics, algorithms and Applications, 9 (6): 1750080(11 pages).
- Madan Mohan Singh and Shivangi Asthana (2017). On the Diophantine Equation + = . Inernational Journal of Algebra, 11 (5): 225-230.
- Madan Mohan Singh and Shivangi Asthana (2017). On the Diophantine Equation + = . Inernational Journal of Pure and Applied Mathematics, 114 (2): 301-304.
- 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.
- 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).
- 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. - 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. - 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.

- 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.
- 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
- 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.
- 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.
- Diophantine Equations and its applications’ in the
*National Seminar on Mathematics Education*organized by NERIE & NCERT, Umiam, during December 21st & 22nd , 2017. - 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. - 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. - 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
- 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.
- 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.
- 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.
- 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.
- 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.

- Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during 14th to 21st April, 2007.
- Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during November 27th to December 6th, 2008.
- Guest Faculty for B. Tech in the Department of Information Technology, Assam University, Silchar during 09th to 18th July, 2009.
- Guest Faculty for M.Sc. in the Department of Mathematics, NEHU, Shillong March, 2011 to July, 2011.
- Guest Faculty for B. Tech at NIT Arunachal in the Department of Computer Science & Engineering at Yupia during 09th to 16th September, 2012.
- Resource Person in the Refresher Course in Mathematics at the Department of Mathematics, NEHU, Shillong during March19 to April 16, 2013.
- Resource Person in the Refresher Course in Information Technology at the Department of I T, NEHU, Shillong during July, 2013.
- Guest Faculty for M.Sc. in the Department of Mathematics, NEHU, Shillong , February, 2016 to till date.
- 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
- 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.
- 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.
- 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.