A learning with errors (LWE) instance management method according to an embodiment may include obtaining, from one or more user devices among a plurality of user devices, one or more learning with errors (LWE) instances and one or more extended LWE instances including reuse tags associated with the LWE instances, storing the one or more extended LWE instances, receiving, from a first device among the plurality of user devices, a request for an LWE instance produced by a second device among the plurality of user devices, and identifying, based on a reuse tag included in each of the one or more extended LWE instances, a target extended LWE instance including an LWE instance produced by the second device among the one or more extended LWE instances, and providing the LWE instance included in the target extended LWE instance to the first device.