What's the adjective for symmetrizing? Here's the word you're looking for.
Included below are past participle and present participle forms for the
verbs symmetrize and symmetrise which may be used as adjectives within certain contexts.
(set theory) Of a relation R on a set S, such that xRy if and only if yRx for all members x and y of S (that is, if the relation holds between any element and a second, it also holds between the second and the first).
(cryptography) Using the same key (or keys that are trivially related) for both encryption and decryption.