6 research outputs found
An optimal representation for the trace zero subgroup
We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field extension of any prime degree. The representation is via the coefficients of a rational function, and it is compatible with scalar multiplication of points. We provide efficient compression and decompression algorithms, and complement them with implementation results. We discuss in detail the practically relevant cases of small genus and extension degree, and compare with the other known compression methods
Scalar multiplication in compressed coordinates in the trace-zero subgroup
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.Comment: 23 page
Compression for trace zero points on twisted Edwards curves
We propose two optimal representations for the elements of trace zero subgroups of twisted Edwards curves. For both representations, we provide efficient compression and decompression algorithms. The efficiency of the algorithm is compared with the efficiency of similar algorithms on elliptic curves in Weierstrass form
Compression for trace zero points on twisted Edwards curves
We propose two optimal representations for the elements of trace zero subgroups of twisted Edwards curves. For both representations, we provide efficient compression and decompression algorithms. The efficiency of the algorithm is compared with the efficiency of similar algorithms on elliptic curves in Weierstrass form
An optimal representation for the trace zero subgroup
We give an optimal-size representation for the elements of the trace zero
subgroup of the Picard group of an elliptic or hyperelliptic curve of any
genus, with respect to a field extension of any prime degree. The
representation is via the coefficients of a rational function, and it is
compatible with scalar multiplication of points. We provide efficient
compression and decompression algorithms, and complement them with
implementation results. We discuss in detail the practically relevant cases of
small genus and extension degree, and compare with the other known compression
methods.Comment: submitte