CURRICULUM VITAE
NAME
Dr. PRABAL PAUL
GENDER
MALE
NATIONALITY
INDIAN
Date of Birth: January 1, 1978
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Qualification
Ph.D. Thesis
Ph.D. Supervisor
CURRENT DESIGNATION
Phone:
PREVIOUS DESIGNATIONS
Ph.D. from Department of Mathematics,
Indian Institute of Science, Bangalore-560012.
Defended the thesis in 2007, entitled:
On the Peak-to-Average-Power-Ratio
of Affine linear codes
Dr. C. R. Pradeep
Department of Mathematics,
Birla Institute of Technology and Sciences,
K. K. Birla Goa campus,
Bypass road, NH-17-B,
Zuarinagar,
Pin code-500019.
08322580398.
Assistant Professor
Crypto-lab
C.R.Rao AIMSCS
University of Hyderabad Campus,
Central University Post Office,
Hyderabad 500 046,
Andhra Pradesh
India.
Visiting Post Doctorate fellow
Applied Statistics unit
Indian Statistical Institute
Kolkata, India
Post Doctorate fellow
Mathematics
Harish-Chandra Research Institute
Chhatnag road
Jhunsi
Allahabad
Uttar Pradesh
Pin code-211019
(from 9th March 2007 to 8th June 2009)
Education
• M-Sc in Pure Mathematics (2001), University of Calcutta, Kolkata, India.
Marks obtained-708 out of 1000 (70.8 %).
• B.Sc in Mathematics(Major), Chemistry and Physics;
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Compulsory additional- Bengali; 1999.
Vidyasagar College, Kolkata.
University of Calcutta, Kolkata, India.
• Higher Secondary (1996),
Subjects: Bengali, English, Physics, Chemistry, Mathematics,
Additional- Biology.
Santragachi Kedarnath Institution, Howrah.
Name of the board/examination: West bengal Council of Higher Secondary Education.
• Madhyamik (Secondary) (1994),
Subjects: Work education, Physical education, Social Service, Bengali, English,
Physical Science, Life science, Mathematics, History, Geography.
Additional: Mathematics.
Bantra M. S. P. C. High School.
Name of the board/examination: West Bengal Board of Secondary Education.
Research Interest:
Number theory, Cryptography, Coding theory
1 Specific Areas of Interests: Additive Combinatorics.
2 Specific Areas of Interests: RSA crypto-system, Secret Sharing.
3 Specific Areas of Interests: PAPR of codes, Space-time-Block codes.
Research Statement:
Let me first describe my academic background in brief. Under M.Sc. program in Department of Pure Mathematics, University of Calcutta (from 1999 to 2001) I have got
opportunity to learn many courses. In my Ph-D program, I had the opportunity to
credit Differential Geometry, Operator Theory, Real Analysis-II and Algebraic Topology. During my comprehensive examination at IISc, I have learnt Commutative Algebra,
Finite Fields, Coding Theory, Number theory. I have also learnt Cryptography under
the guidance of my Ph-D superviser. In the I. M. I. programme at IISc, I have learnt
Space Time Block Codes and Algebraic Number Theory. In my post Doctoral period at
H. R. I., I have learnt Additive Number Theory and Additive Combinatorics. At Indian
Statistical Institute, Kolkata I have learnt the programming languages in the course
Programming and Methodology (offered by Prof. Subhamoy Maitra).
Current Involvement: Contribution
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I have worked in two different sets of problems during my Ph.D. tenure and two set of
problems in my Post-Doctoral tenure. The first one is on the PAPR of codes, the second
one is on Space-Time-Block Codes and the final two (during my Post-Doctoral time) are
Additive Combinatorics and Cryptography.
P. A. P. R. of linear codes: In Coding Theory, most of the work have been done on
three parameters, namely, length, size and Hamming distance. Apart from length, size
and the minimum Hamming distance of a code, another important parameter (when
a code is implemented) is the power. To transmit any particular codeword, it takes
certain amount of power. Individual codewords will consume different amount of power.
There is also an average amount of power consumed when a code is used. For physical
and Engineering reasons, it is clear that one would like to design systems with Peak-toAverage-Power-Ratio as low as possible. Even though PAPR depends on the machine
being used, a closely related parameter PMEPR depends only on the code and PMEPR
has a mathematically tractable expression. We have developed a method (called CosetsCombining method) that helps to get bigger size affine linear codes with marginal/no
increament of PAPR. Using the Cosets Combining method, it is possible to know Mathematically wheather it is the best possible code or not. The importance of all one vector
has also been shown by us. We have two propositions that helped us in computation.
We have worked on extension of linear codes and the usefulness of a special type of
lengthening. We have given examples to strengthen our theory.
Space-Time-block codes: In the modern era of communication, i.e. in Mobile technology, more than one antennas are used. this gives a new type of codes namely SpaceTime-Block codes. We have proposed a three by three S. T. B. codes of full rank.
Additive combinatorics: We are working in weighted zero sum problems. Let me
describe the results of us in this context.
Let G be a finite abelian group, if there are k fixed weights (wieghts are units modulo
the order of the group) in a sequence of length k + r with the property that no k length
weighted zero sum is there in the sequence and 0 is the most repeated element, then the
number of distict k sums are atleast r + 1.
While proving this, the idea of Hong Bing Yu (while he gave a proof of a theorem of
Bollobas and Leader) is generalized. In a particular case, by taking all the weights to
be equals to one, the famous EGZ (Erdos, Ginzburg and Ziv) theorem can be proved.
Let G be a finite abelian group (written additively) of rank r with invariants n1 , n2 , · · · , nr
where nr is the exponent of G. In this paper, we prove an upper bound for the Davenport
constant D(G) of G as follows;
D(G) ≤ nr + nr−1 + (c(3) − 1)nr−2 + (c(4) − 1)nr−3 + · · · + (c(r) − 1)n1 + 1,
where c(i) is the Alon-Dubiner constant which depends only on the rank of the group
Zni r . Also, we have given an application of Davenport’s constant to smooth numbers
related to Quadratic sieve.
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Let n be a prime power or an odd integer greater than one. Consider a sequence
x1 , x2 , · · · , xm with m > n, in Z/nZ, and its A-weighted n-sums, where A = (Z/nZ)∗ .
We will derive a lower bound for the number of A-weighted n-sums when 0 is not an
A-weighted n-sum. This is related to a result due to Luca and Griffiths.
We have given an alternative proof for calculating fU (p, r) using basic linear Algebra,
where U is the set of units, p > 2r. We have also extended it to prove fU (p2 , 2). While
proving, subgroups of Zpr and Zp22 played an important role. We have used these results
to classify all the sequences satisfying property B 0 for the groups Zpr and Zp22 with unit
weight and p > 2r.
Cryptography: An ideal conjunctive hierarchical secret sharing scheme, constructed
based on the Maximum Distance Separable (MDS) codes, is proposed in this paper.
The scheme, what we call, is computationally perfect. By computationally perfect, we
mean, an authorized set can always reconstruct the secret in polynomial time whereas
for an unauthorized set this is computationally hard. Also, in our scheme, the size of
the ground field is independent of the parameters of the access structure. Further, it is
efficient and requires O(n3 ), where n is the number of participants.
Publications
1 Prabal Paul, C. R. Pradeep and B. Sundar Rajan; On the PAPR of cosets of
linear codes, Indian Journal of Pure and Applied Mathematics, volume 39, issue 1
(Feb-2008), (69-86).
2 S. D. Adhikari, Mohan N. Chintamani, Bhavin K. Moriya and Prabal Paul; Weighted
sums in finite abelian groups, Uniform Distribution Theory 3 (2008); no. 1; (105110).
3 M. N. Chintamani, B. K. Moriya and Prabal Paul; THE NUMBER OF WEIGHTED
n-SUMS, International Journal of Modern Mathematics, volume 5, July 2010, (215222).
4 M. N. Chintamani, B. K. Moriya, W. D. Gao, P. Paul and R. Thangadurai; New
upper bounds for the Davenport and for the ErdsGinzburgZiv constants Archiv der
Mathematik, February 2012, Volume 98, Issue 2, pp 133-142
5 Appala Naidu Tentu, Prabal Paul and China Venkaiah Vadlamudi; Conjunctive Hierarchical Secret Sharing Scheme based on MDS code, accepted for publication in ‘International Workshop On Combinatorial Algorithms-2013’, France’.
http://iwoca2013.colloques.univ-rouen.fr/index.php?r=2
Courses Taught
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• Algebra-I
• Mathematics-I
• Cryptography
• Mathematics-II
• Optimization
Previous Teaching experiences
• Given lectures on Number theory to the summer students (Bachelor’s) on Number
theory and Cryptography in C. R. Rao AIMSCS (2011).
• Given a series of lectures on Algebraic Number theory and it’s applications
to Cryptography in C. R. Rao AIMSCS (2010).
• Teaching Assistant for one semester course: Linear Algebra (MA 219, AugustDecember 2005 at IISc)
Awards and Honors
• Qualified in Gate-2001 (rank-25, percentile-96.93).
• Qualified in National eligibility test (1st july 2001) and awarded C. S. I. R. fellowship.
• Awarded N. B. H. M. Post Doctoral fellowship in 2009.
Conferences, Workshops, Schools and Short Projects (in India)
1. First Indo-AMS Conference, IISc (Bang), Dec17-Dec20, 2003.
2. Workshop on Algebra and Coding theory, IISc (Bang), Nov 21-Dec8, 2005.
3. Symposium on Coding theory, IISc (Bang), Dec9, 2005.
4. Workshop on Number theory and Cryptography, IISc (Bang), Jan23-Feb11, 2006.
5. Microsoft Research Summer School (on Algorithms, Complexity and Cryptography), IISc (Bang), May22-June10, 2006.
6. International Workshop and Conference on Geometric Methods in Topology, IISc
(Bang), June12-June24, 2006.
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7. International Conference on Number Theory and Cryptography, H. R. I., Allahabad, Feb23-Feb 27, 2007.
8. Advanced Instructional School on Algebraic and Analytic Number Theory, H. R.
I., Allahabad, 3-28 December 2007.
9. Lecture series on Additive combinatorics by Prof. Harald Helfgott, IMSc, Chennai,
March 27,2008-April 2, 2008.
10. Discussion Meeting on “ Additive Combinatorics” during January 16-31, 2009.
11. HRI International Conference in Mathematics “ HRI ICM” during March 7-8 and
March 16-20, 2009.
12. International conference on “Frontiers of interface between Statistics and Sciences”
during 30th December 2009- 02nd January 2010, Hyderabad (to celebrate Prof. C.
R. Rao’s 90th birthday).
13. International Congress of Mathematicians-2010, Hyderabad during August 19-27,
2010.
14. ICM zeta 2010, IMSc Chennai during Aug 29th-Sep 3rd, 2010.
15. Indo-Crypt 2010, Hyderabad during 12th-15th December, 2010.
16. Special Number theoretic year lectures (attended from 21st Feb to 27th March
2011) at IMSc, Chennai to celebrate Prof. R. Balasubramanian’s 60th birthday.
International Conferences, Workshops, Schools and Short Projects (abroad)
1. School on Codes over rings (CIMPA school), Ankara (Turkey), August 18-29, 2008.
Conference Presentation
1. National Conference on Mathematical Foundations of Coding, Complexity, Computation and Cryptography, IISc (Bang), July20-July22, 2006
2. The symposium on Algebraic Coding Theory during Indian Mathematical Society
annual meeting held in Pune University, Pune, Dec 27-30, 2007.
3. National Seminar on Algebra, Cryptography and Number Theory, held in the
Department of Pure Mathematics, University of Calcutta, March 26-27, 2008.
Computer Knowledge
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Mathematical Software: Matlab, Mathmatica,
Operating System: Windows, Linux
Typesetting Software: Latex
Contact Address
Current:
Contact:
Department of Mathematics,
Birla Institute of Technology and Sciences,
K. K. Birla Goa campus,
Bypass road, NH-17-B,
Zuarinagar,
Pin code-500019.
08322580398.
e-mail id: [email protected]
[email protected]
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