CRSep 13, 2017
Scalar multiplication in compressed coordinates in the trace-zero subgroup
arXiv:1709.04178v13 citations
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This is an incremental improvement for cryptography, specifically in efficient elliptic curve operations.
The paper tackled the problem of computing scalar multiplication in the degree three trace-zero subgroup of elliptic curves using compressed coordinates, resulting in the first algorithm for this task.
We consider trace-zero subgroups of elliptic curves over a degree three field extension. The elements of these groups can be represented in compressed coordinates, i.e. via the two coefficients of the line that passes through the point and its two Frobenius conjugates. In this paper we give the first algorithm to compute scalar multiplication in the degree three trace-zero subgroup using these coordinates.