%0 Journal Article %1 iyengarnovel %A Iyengar, Vinay S. %D 2012 %E Shawon, S.M.Rahman %J International Journal on Cryptography and Information Security (IJCIS) %K Public-key cryptography %N 3 %P 57-66 %T Novel Elliptic Curve Scalar Multiplication Algorithms for Faster and Safer Public-Key Cryptosystems %U https://wireilla.com/papers/ijcis/V2N3/2312ijcis05.pdf %V 2 %X Efficient and secure public-key cryptosystems are essential in today’s age of rapidly growing Internet communications. Elliptic curve scalar multiplication in particular, which refers to the operation of multiplying a large integer by a point on an elliptic curve, is crucial for both data encryption technology as well as testing the security of cryptographic systems. The purpose of this project was to design and implement an elliptic curve scalar multiplication algorithm 10% faster than one of the best algorithms currently used: the binary double-add algorithm. The algorithm designed was based off of an operation that allowed for the tripling of a point and was derived from point doubling and addition operations. The algorithm was further optimized using an integer representation in both ternary and balanced ternary form. Finally, a novel modification was made that allowed for the pre-computation and storage of multiples of a point. The algorithms were written and tested in a C++ program that selected random points over elliptic curves in both Weierstrass and Edwards form, and multiplied them by a large range of integers using each of the various algorithms. Timings for these operations were taken in terms of processor cycles and finally averaged out. The final averaged results showed that the most optimized algorithm was 66.63% more efficient that the binary double-add algorithm. In conclusion, the algorithm designed in this research showed a large improvement in efficiency compared to one of the best algorithms in commercial use today, and has significant implications for the field of cryptography.

@article{iyengarnovel, abstract = {Efficient and secure public-key cryptosystems are essential in today’s age of rapidly growing Internet communications. Elliptic curve scalar multiplication in particular, which refers to the operation of multiplying a large integer by a point on an elliptic curve, is crucial for both data encryption technology as well as testing the security of cryptographic systems. The purpose of this project was to design and implement an elliptic curve scalar multiplication algorithm 10% faster than one of the best algorithms currently used: the binary double-add algorithm. The algorithm designed was based off of an operation that allowed for the tripling of a point and was derived from point doubling and addition operations. The algorithm was further optimized using an integer representation in both ternary and balanced ternary form. Finally, a novel modification was made that allowed for the pre-computation and storage of multiples of a point. The algorithms were written and tested in a C++ program that selected random points over elliptic curves in both Weierstrass and Edwards form, and multiplied them by a large range of integers using each of the various algorithms. Timings for these operations were taken in terms of processor cycles and finally averaged out. The final averaged results showed that the most optimized algorithm was 66.63% more efficient that the binary double-add algorithm. In conclusion, the algorithm designed in this research showed a large improvement in efficiency compared to one of the best algorithms in commercial use today, and has significant implications for the field of cryptography. }, added-at = {2019-11-21T11:01:23.000+0100}, author = {Iyengar, Vinay S.}, biburl = {https://www.bibsonomy.org/bibtex/2b30593e818e7665ff672d5bf875bb176/alinta}, editor = {Shawon, S.M.Rahman}, interhash = {c2a9ec4567481cc7854714dc9d72ad70}, intrahash = {b30593e818e7665ff672d5bf875bb176}, issn = {1839-8626}, journal = {International Journal on Cryptography and Information Security (IJCIS)}, keywords = {Public-key cryptography}, language = {English}, month = sep, number = 3, pages = {57-66}, timestamp = {2019-11-21T11:01:23.000+0100}, title = {Novel Elliptic Curve Scalar Multiplication Algorithms for Faster and Safer Public-Key Cryptosystems }, url = {https://wireilla.com/papers/ijcis/V2N3/2312ijcis05.pdf}, volume = 2, year = 2012 }