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**2023/785**

**Title:**

Generation of two ‘‘independent’’ points on an elliptic curve of j-invariant \neq 0, 1728

**Authors:**
Dmitrii Koshelev

**Abstract:**

This article is dedicated to a new generation method of two ``independent’’ \mathbb{F}_{\!q}-points P_0, P_1 on almost any ordinary elliptic curve E over a finite field \mathbb{F}_{\!q} of large characteristic. In particular, the method is relevant for all standardized and real-world elliptic curves of j-invariants different from 0, 1728. The points P_0, P_1 are characterized by the fact that nobody (even a generator) knows the discrete logarithm \log_{P_0}(P_1) in the group E(\mathbb{F}_{\!q}). Moreover, only one square root extraction in \mathbb{F}_{\!q} (instead of two ones) is required in comparison with all previous generation methods.

**ePrint:**
https://eprint.iacr.org/2023/785

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