Published on: 2022-08-11T15:31:48+00:00
Recently, there has been a lot of study on sublinear ring signatures. Groth/Kohlweiss 2014 introduced logarithmic scaled ring signatures, which can be achieved using taproot keys. AdamISZ wrote a blog post discussing the creation of logarithmic sized ring signatures on taproot keys [1]. However, a question remained regarding how to achieve one/N time usage of these ring signatures with key images.Noether & Goodall's Triptych [3] offers a solution to this issue. It builds on the core idea presented in the GK paper [2], which involves bit decomposition of index. In 2015, Bootle et al. published "Short Accountable Ring Signatures Based on DDH" [4], where they further generalized the concept by introducing n-ary decomposition and delta-functions to identify the index with the correct digits in n-ary.In 2020, Triptych was introduced as a combination of the above concepts along with the inclusion of a key image, similar to the basic cryptonote, LWW, LSAG design. According to Bootle et al., their construction is "2.8 times smaller" than the GK design [2]. Although adding the key image requires more space in the proof, it is still significantly compact compared to other designs. Thus, Triptych [3] offers both a key image and a compact size for high anonymity sets.The research indicates that Triptych [3] appears to be practical for genuinely big anonymity sets. Although it may be possible to achieve even more efficient constructions through bilinear pairings crypto, this method would not work on 'bare' secp256k1. However, there might be a way to transfer over to other curves via bilinear pairings crypto.AdamISZ also shared a suggested protocol for anti-Sybil measures that aims to maintain privacy without being too demanding for users. While the protocol primarily focuses on users or customers of websites or services, it could also be applicable in anti-Sybil measures for things like Lightning.The post includes various sections that can be explored through the provided link. It is worth noting that the original gist was migrated due to issues with GitHub's equation formatting feature, but comments are still available on the gist or on a linked post.The post was signed by waxwing/AdamISZ and sent using Proton Mail secure email.
Updated on: 2023-08-02T06:47:46.725260+00:00