In the midst of the advancing digitization of various assets, the secure and efficient management of rapidly growing digital data poses a significant challenge. Accumulator, garnering attention as a solution to this challenge, is a cryptographic protocol designed to safely manage large-scale data within compact data spaces. It enables the compression of a data list into a short string of a specific size, with proof of the inclusion of particular input elements in the compressed list.Existing Accumulators that are secure against attacks using quantum computers face the challenge of increasing computational complexity for list updates and verifications as the number of elements in the list grows. Efficient acceleration of these processes is a critical task.

In this study, we propose Accumulator that is secure against attacks using quantum computers and, for the first time, enables list updates and verifications within a certain time frame. By incorporating this Accumulator into membership list management, zero-knowledge proofs, group signatures, and blockchain applications, our research aims to achieve more efficient data management and secure applications.