Abstract
Point compression is an essential technique to save bandwidth and memory when deploying elliptic curve based security solutions in wireless communication systems. In this contribution, we provide new linear algebra (LA) based compression algorithms for multiple points on elliptic curves, that are compression algorithms which only make use of LA (with a constant number of field multiplications and at most one inversion, with no quadratic or higher degree polynomial root finding). In particular, we extend the results of Khabbazian et al. (IEEE Trans Comput 56(3):305–313, 2007) to four (resp. five) points on elliptic curves by generically storing five (resp. six) field elements and provide an asymptotic generalization to any number n of points on a curve (Formula presented.) by generically storing (Formula presented.) values.
| Original language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Designs, Codes, and Cryptography |
| DOIs | |
| Publication status | Accepted/In press - Jul 25 2016 |
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Keywords
- Cryptography
- Elliptic curves
- Point compression
ASJC Scopus subject areas
- Applied Mathematics
- Computer Science Applications
Cite this
Multiple point compression on elliptic curves. / Fan, Xinxin; Otemissov, Adilet; Sica, Francesco; Sidorenko, Andrey.
In: Designs, Codes, and Cryptography, 25.07.2016, p. 1-24.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multiple point compression on elliptic curves
AU - Fan, Xinxin
AU - Otemissov, Adilet
AU - Sica, Francesco
AU - Sidorenko, Andrey
PY - 2016/7/25
Y1 - 2016/7/25
N2 - Point compression is an essential technique to save bandwidth and memory when deploying elliptic curve based security solutions in wireless communication systems. In this contribution, we provide new linear algebra (LA) based compression algorithms for multiple points on elliptic curves, that are compression algorithms which only make use of LA (with a constant number of field multiplications and at most one inversion, with no quadratic or higher degree polynomial root finding). In particular, we extend the results of Khabbazian et al. (IEEE Trans Comput 56(3):305–313, 2007) to four (resp. five) points on elliptic curves by generically storing five (resp. six) field elements and provide an asymptotic generalization to any number n of points on a curve (Formula presented.) by generically storing (Formula presented.) values.
AB - Point compression is an essential technique to save bandwidth and memory when deploying elliptic curve based security solutions in wireless communication systems. In this contribution, we provide new linear algebra (LA) based compression algorithms for multiple points on elliptic curves, that are compression algorithms which only make use of LA (with a constant number of field multiplications and at most one inversion, with no quadratic or higher degree polynomial root finding). In particular, we extend the results of Khabbazian et al. (IEEE Trans Comput 56(3):305–313, 2007) to four (resp. five) points on elliptic curves by generically storing five (resp. six) field elements and provide an asymptotic generalization to any number n of points on a curve (Formula presented.) by generically storing (Formula presented.) values.
KW - Cryptography
KW - Elliptic curves
KW - Point compression
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UR - http://www.scopus.com/inward/citedby.url?scp=84979539143&partnerID=8YFLogxK
U2 - 10.1007/s10623-016-0251-2
DO - 10.1007/s10623-016-0251-2
M3 - Article
SP - 1
EP - 24
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
SN - 0925-1022
ER -