# What is the opposite of embed?

We often embed items from one space into another space, e.g. embedding plaintext items from $$\{0, 1\}^m$$ into some ring $$R_q/\langle x^N + 1 \rangle$$ for RingLWE.

What is the inverse of this action called?

(Feel free to move this question to Math.SE or other related. Though I am specifically interested in the opposite of embed in the context of math and crypto, rather than the general English language.)

• There is no universally agreed dedicated term in the cryptographic community, as far as I'm aware of. One can say project, as kodlu suggests; I would personally use "decode", or perhaps something like "the party embeds the ring element back into $\{0,1\}^m$". – Geoffroy Couteau Jun 15 '19 at 22:17