Window Based Scalar Multiplication on Elliptic Curve Using Multi-Base Number System.

Date of Submission

December 2007

Date of Award

Winter 12-12-2008

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Bangalore)


Barua, Rana (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

Elliptic curve cryptography has a wide application in public key cryptography and has received a lot of attention because of its small key size (the equivalent key sizes for ECC are 173 and 313 bits as compared to the key sizes 1024 and 4096 bits for RSA) and increased theoretical robustness (there is no subexponential algorithm to solve elliptic curve discrete logarithm problem, ECDLP). The efficiency of an ECC mainly depends upon the scalar multiplication, i.e., the computation of the point [n]P = P + ... + P (n times), for a given point on an elliptic curve E. An extensive amount of research has been done and being done to efficiently compute and accelarate and secure the scalar multiplication. Several representations of the scalar n (binary, ternary, non-adjacent form (NAF), window methods (w-NAF)...) and various efficient methods for point addition (P +Q, [2]P, [2]P ±Q, [2w]P) have been proposed in both affine and projective coordinates. In recent years, a new representation scheme using Double-base number system (DBNS) and Multi-base number system (MBNS) has gained much popularity due to shorter length representation and sparseness. Introduction of new point additions like [3]P, [3]P ± Q, [3w]P, [5]P have given new dimensions to calculate scalar multiplication and its results are overwhelming.In this report, we propose a new window based scalar multiplication algorithm which has advantage over earlier proposed methods that it requires to search for a better window length for bases than searching for maximum bound on bases, which results a smaller size of static table and much faster search. Although it keeps a table of relatively large size of precomputed points, it has overall less storage requirement. Besides it, computation of scalar multiplication using this method has shown an almost equal complexity as earlier proposed methods


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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