Paper 2003/088

Elliptic Curve Point Multiplication

A. G. Rostovtsev and E. B. Makhovenko

Abstract

A method for elliptic curve point multiplication is proposed with complex multiplication by Sqrt[-2] or by (1+Sqrt[-7])/2 instead of point duplication, speeding up multiplication about 1.34 times. Higher radix makes it possible to use one point duplication instead of two and to speed up computation about 1.6 times. We employ prime group order factorization in corresponding quadratic order and integer exponent reduction modulo quadratic prime in the Euclidean imaginary quadratic ring.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystemcomplex multiplicationfast algorithms
Contact author(s)
rostovtsev @ ssl stu neva ru
History
2003-05-07: received
Short URL
https://ia.cr/2003/088
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2003/088,
      author = {A. G. Rostovtsev and E. B. Makhovenko},
      title = {Elliptic Curve Point Multiplication},
      howpublished = {Cryptology ePrint Archive, Paper 2003/088},
      year = {2003},
      note = {\url{https://eprint.iacr.org/2003/088}},
      url = {https://eprint.iacr.org/2003/088}
}
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