Name
Abstract | ||
|---|---|---|
Koblitz curves are a special family of binary elliptic curves satisfying equation y(2) + xy = x(3) + ax(2) + 1, a is an element of {0, 1}. Scalar multiplication on Koblitz curves can be achieved with point addition and fast Frobenius endomorphism. We show a new point representation system mu(4) coordinates for Koblitz curves. When a = 0, mu(4) coordinates derive basic group operations-point addition and mixed-addition with complexities 7M+ 2S and 6M+ 2S, respectively. Moreover, Frobenius endomorphism on mu(4) coordinates requires 4S. Compared with the stateof-the-art lambda representation system, the timings obtained using mu(4) coordinates show speed-ups of 28.6% to 32.2% for NAF algorithms, of 13.7% to 20.1% for tau NAF and of 18.4% to 23.1% for regular tau NAF on four NIST-recommended Koblitz curves K-233, K-283, K-409 and K-571. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/978-3-030-21548-4_34 | INFORMATION SECURITY AND PRIVACY, ACISP 2019 |
Field | DocType | Volume |
Frobenius endomorphism,Combinatorics,Scalar multiplication,Computer science,Theoretical computer science,Elliptic curve,Lambda,Binary number | Conference | 11547 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Weixuan Li | 1 | 0 | 0.34 |
| Wei Yu | 2 | 9 | 5.26 |
| Bao Li | 3 | 185 | 38.33 |
| Xuejun Fan | 4 | 40 | 11.95 |