Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and validate proofs. In particular, the circuits are built connecting wires that carry elements from a large prime field, whose order is determined by the number of elements of the pairing-friendly elliptic curve. In this context, it is important to generate an inner curve using this field, because it allows to create circuits that can verify public-key cryptography primitives, such as digital signatures and encryption schemes. To this purpose, in this article, we present a deterministic algorithm for generating twisted Edwards elliptic curves defined over a given prime field. We also provide an algorithm for checking the resilience of this type of curve against most common security attacks. Additionally, we use our algorithms to generate Baby Jubjub, a curve that can be used to implement elliptic-curve cryptography in circuits that can be validated in the Ethereum blockchain.
In this paper, we propose WAKU-RLN-RELAY as a spam-protected gossip-based routing protocol that can run in heterogeneous networks. It features a privacy-preserving peerto-peer (p2p) economic spam protection mechanism. WAKU-RLN-RELAY addresses the performance and privacy issues of the state-of-the-art p2p spam prevention techniques including peer scoring utilized by libp2p, and proof-of-work used by e.g., Whisper, the p2p messaging layer of Ethereum. In WAKU-RLN-RELAY, spam protection works by limiting the messaging rate of each network participant. Rate violation is disincentivized since it results in financial punishment where the punishment is cryptographically guaranteed. Peers who identify spammers are also rewarded. To enforce the rate limit, we adopt the suggested framework of Semaphore and its extended version, however, we modify that framework to properly address the unique requirements of a network of p2p resource-restricted users. The current work dives into the end-to-end integration of Semaphore into WAKU-RLN-RELAY, the modifications required to make it suitable for resource-limited users, and the open problems and future research directions. We also provide a proof-of-concept open-source implementation of WAKU-RLN-RELAY, and its specifications together with a rough performance evaluation.
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