Welcome to the resource topic for 2021/1034
Title:
Optimal encodings to elliptic curves of j-invariants 0, 1728
Authors: Dmitrii Koshelev
Abstract:This article provides new constant-time encodings \mathbb{F}_{\!q}^* \to E(\mathbb{F}_{\!q}) to ordinary elliptic \mathbb{F}_{\!q}-curves E of j-invariants 0, 1728 having a small prime divisor of the Frobenius trace. Therefore all curves of j = 1728 are covered. This is also true for the Barreto–Naehrig curves BN512, BN638 from the international cryptographic standards ISO/IEC 15946-5, TCG Algorithm Registry, and FIDO ECDAA Algorithm. Many j = 1728 curves as well as BN512, BN638 are not appropriate for the most efficient prior encodings. So, in fact, only universal SW (Shallue–van de Woestijne) one was previously applicable to them. However this encoding (in contrast to ours) can not be computed at the cost of one exponentiation in the field \mathbb{F}_{\!q}.
ePrint: https://eprint.iacr.org/2021/1034
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