International Association
for Cryptologic Research

This short note is devoted to a significant enhancement of [8] by resolving satisfactorily the problem formulated at the end of that article. More precisely, a new laconic, secure, and efficient (de)compression method is provided for points of any elliptic curve over any highly $2$-adic finite field of large characteristic. Such fields are ubiquitous in modern elliptic curve cryptography, whereas they severely slow down the conventional $x$-coordinate (de)compression technique. In comparison with the main method from the cited work, the new one requires neither complicated mathematical formulas nor conditions on the curve. Thereby, the current work is universal and much more implementation-friendly, which justifies its existence, despite the absence of interesting mathematics behind it.

8. Koshelev, D.: Point (de)compression for elliptic curves over highly $2$-adic finite fields. Advances in Mathematics of Communications 19(5), 1539–1559 (2025), https://doi.org/10.3934/amc.2025008