In recent years, SNARKs have shown great promise as a tool for building trustless bridges to connect the heterogeneous ecosystem of blockchains. Unfortunately, the parameters for many of the widely used blockchains are incongruous with the conventional SNARKs, which results in unsatisfactory performance. This bottleneck necessitates new proof systems tailored for efficiency in these environments.

The primary focus of this paper is on succinct bridges from Cosmos to Ethereum, which largely boils down to efficient proofs of multiple Ed25519 signatures. But these techniques can be ported to settings that require succinct proofs of multiple secp256k1 or BLS12-381 signatures.

We explore the schemes deVirgo and zkTree, which exploit the parallelization of proof generation and the subsequent aggregation of proofs. We also describe Panther Protocol's new scheme, which uses the field-agnostic SNARK to circumvent the huge overhead of non-native field arithmetic arising from Ed25519 scalar multiplications in the arithmetic circuit.

Our benchmarks indicate that it is crucial to sidestep non-native arithmetic to the extent that it is possible. The need for EVM compatibility makes it impossible to avoid non-native arithmetic. We also found that multiple proof systems need to be securely amalgamated. The schemes customized for Ed25519 scalar multiplications are different from those well-suited for SHA-512 hashes to maximize the efficiency of a succinct bridging scheme.