For research purpose, I want to know the followings.

1. What is the exact size of the set of already spent key images and how it can be checked? Do we need to download the Monero blockchain to get the size?
2. By is_key_image_spent api, we can check if a key image is a member of the set of already spent key images or not. Can this set be made a zero-knowledge set using some accumulator so that a zero-knowledge set membership or non-membership proof can be given for a particular group element (key image) bypassing this api? Does there exist any accumulator suitable for this purpose?

Thanks in advance for your insights.

For research purposes, I want to know the following:

1. What is the exact size of the set of already spent key images and how it can be checked? Do we need to download the Monero blockchain to get the size?
2. Using the is_key_image_spent api, we can check if a key image is a member of the set of already spent key images or not. Can this set be made a zero-knowledge set using some accumulator so that a zero-knowledge set membership or non-membership proof can be given for a particular group element (key image) bypassing this api? Does there exist any accumulator suitable for this purpose?

Thanks in advance for your insights.