Hashing into Generalized Huff Curves
نویسندگان
چکیده
Huff curves are well known for efficient arithmetics to their group law. In this paper, we propose two deterministic encodings from Fq to generalized Huff curves. When q ≡ 3 (mod 4), the first deterministic encoding based on Skalpa’s equality saves three field squarings and five multiplications compared with birational equivalence composed with Ulas’ encoding. It costs three multiplications less than simplified Ulas map. When q ≡ 2 (mod 3), the second deterministic encoding based on calculating cube root costs one field inversion less than Yu’s encoding at the price of three field multiplications and one field squaring. It costs one field inversion less than Alasha’s encoding at the price of one multiplication. We estimate the density of images of these encodings with Chebotarev density theorem. Moreover, based on our deterministic encodings, we construct two hash functions from messages to generalized Huff curves indifferentiable from a random oracle.
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